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Soumen Nandy has accumulated 640 points.

- Standings in the War
- Archive of Battles in War XV
- Burma Shave Jingles - Another Internet Contest
- People to People - How to be an active participant on this Internet site.

- War XV - Battle 12
- War XV - Battle 11
- War XV - Battle 10
- War XV - Battle 9
- War XV - Battle 8
- War XV - Battle 7
- War XV - Battle 6
- War XV - Battle 5
- War XV - Battle 4
- War XV - Battle 3
- War XV - Battle 2
- War XV - Battle 1

**1. Forestry**- The lamp below was used for years by forest fire fighters fighting
fires at night. It does not require batteries and it is useful in
setting backfires. What kind of lamp is it and how does it work?

see Answer **2. Computers**- What are these and what does each one do?
- SANE
- gPhoto2
- CUPS
- wvdial

see Answer **3. Philosophy and Science**- Please give the primary chemical equation for the reaction that takes
place in the bottom of the lamp below.

see Answer **4. Agriculture**- In September I planned to sell 200 calves in November. I estimated that
the calves would average weighing 750 pounds each at sale time. To hedge my
sale price I paid $725 for two puts for November at 94 cents per pound. The
puts mature on November 20. I sold the calves in late October for 96 cents per
pound. On November 20 the published feeder cattle price was $1.02 per pound.
How much money did I make or lose on the two puts? If I had fully hedged all
my calves, how much would I have made or lost on the puts?

see Answer

Points on this battle were won as follows:

- Soumen Nandy - 160 points for answers to all four questions.

**1. Forestry**- There are two distinctive characteristics of this lamp: 1) its very
shallow reflector; and 2) the central and peripheral protuberances. A third
apparent characteristic, the lack of a focusing lens may be illusory, since it
may have been removed to allow a better view of the internals (though I see no
sign of this)

A shallow reflector creates a broad beam, which could be useful to a firefighter in the woods, but it doesn't create a very large protected pocket. Without a lens, any flame lamp (oil, candle, naphtha, etc.) might be blown out by wind or motion. A glass cover over a shallow confined space without the ample ventilation of, say, a classic oil-burning hurricane lamp, would soon darken to uselessness with soot. Maintaining brightness is important for a broad beam used outdoors (where distances tend to be larger) especially if natural or manmade fires are visible nearby to disrupt night vision (dark adaptation)

Direct flames tend not to be very bright. A jet (pressure nozzle flame) can be very hot and efficient, but usually has little particulate matter to glow. An free-air flame contains more glowing soot, but is less efficient with fuel, messy and still not very bright in absolute terms. Usable flames also tend to be much larger and more diffuse than the point-source of a flashlight bulb filament, which makes lenses and reflectors less effective; there's no single point to put in focus.

Many lamps use a nonburning mantle (or similar part) that will glow brightly when heated. This also creates a more defined light source that can be focused. Modern theater was made possible by the invention of the 'limelight', a bright projectable light created by a piece of lime [calcium oxide/hydroxide/carbonate] glowing from the heat of a (dimmer) gas or fuel vapor flame. Even today, we refer to fame as 'being in the limelight'. However, our lamp doesn't seem to have a mantle.

The necessity for mobility limits us. Batteries were short-lived and a week's supply was very heavy. (Besides, we were told it wasn't battery powered, and there's no bulb or socket). Wax candles aren't very bright. Compressed gas needs heavy tanks which would be dangerously explosive in a forest fire, and weren't generally used at that time. Liquid fueled chimney lamps (with a transparent glass chimney around the flame) were common, but this lamp clearly isn't one. Vaporized fuel lamps (like Coleman camp lanterns) would work, but they require that some of heat of the flame be recycled to vaporize the liquid fuel, and I don't see that here - though it's possible that the reflector contains a metal tube to vaporize the fuel.

My best guess is that this is an acetylene lamp. Today, we transport acetylene in pressurized tanks, but it was historically sold indirectly, as calcium carbide (CaC2) which reacts with water to give off acetylene gas [see Answer 3 below] Calcium carbide is neither flammable nor explosive if kept dry, a real benefit to firefighters in the field. If burned 'loosely' in free air, acetylene produces a very sooty flame because its unique structure is almost entirely (92%) carbon. Burned in a jet, and possibly combined with a glow mantle, it was bright enough for use in military searchlights

This explains the two protuberances in the reflector. In the center, a tiny 'acetylene torch' generates the light. The second protuberance could be a striker/ignitor, which would only work with a gas or vapor-fueled lamp, but would probably be very useful in the rough environment of a forest fire, where the flame might go out. Such lamps were once used by mines, bicycles, and even cars. Often the generator canister (where the water and carbide are mixed) is separate, allowing the actual lamp to be conveniently attached to a headstrap or other fixture. The acetylene jet could be cranked up as a high temperature torch.

Based on this, I did a little hunting, and found an assembly diagram for an acetylene lamp that seems identical to the one pictured. This page has more details on carbide lamps. It turns out that this model did not use a glowing mantle, as I had guessed. I don't know why it doesn't. Ironically, the Calcium oxide produced as carbide is consumed could have made an excellent mantle (see 'limelight' above)

I should also note that carbide lamps are often used by spelunkers (cave enthusiasts) even in this age of batteries. **2. Computers**- SANE (Scanner Access Now Easy) is an API (set of subroutines/drivers) that
can be used to interface raster-based devices to a Linux (or similar OS)
computer. This includes not just the usual flatbed, sheet feed and handheld
image scanners, but also TV image grabbers, digital cameras and digital video.
It can be used to develop your own programs or add functions.
gPhoto2 is a set of free ready-to-use programs for Linux (etc.) computers that
supports over 400 cameras.

WVDIAL is a dialing program that can be used for PPP (e.g. dial-up internet) on *nix operating systems

And last, but not least: CUPS (Common Unix Printing System) is meant to be a single central solution for printing with a wide variety of printers on and across UNIX platforms, including the BSD-based OS X. In a way, it harkens back to the very beginning os the GNU project, when Richard Stallman of MIT needed a certain UNIX driver for a printer, and learned that not only couldn't he get it, but he couldn't get the information he needed to write his own.

At the time, "Unix" was in murky legal waters. AT&T had once owned it, and had licensed it under various terms to various business and educational institutions. Berkeley had a license which seemed to allow it to develop and modify their branch any way they saw fit - This became BSD Unix, now a free user-developed and supported Unix. When the legal dust settled, BSD was free to do as it wanted, but the others were found to be constrained in one way or another

It was in this environment that Stallman began a project named GNU", which stands (in the classic tradition of MIT recursive acronyms) "GNU is Not Unix" GNU pooled of user-created drivers/software and the tech info essential to write new ones. Over many years, it grew until it contained not just every kind of software, but essentially a complete operating system, complete with system, programming, and end-user environment. All that was missing was the kernel - the small but essential core That gives the entire army its marching orders. Linus Torvalds, a Finnish CompSci student was playing with modifying an old 386-based Minix kernel (an instructional tool, used to teach OS design), and along with a handful of similarly inclined hackers around the world, eventually ended up creating a new working kernel that wasn't bound by all the old legal muck.

GNU had been like a Frankenstein monster, cobbled together parts that lacked a brain to be alive. Many GNU participants decided the new Linux kernel as a workable brain, and the Frankenstein monster took on a new life. The complete package attracted millions of new users around the world, and attracted interest and support from the existing Unix-like communities

Stallman is a bit peeved over this, and travels the world telling anyone who'll listen that "Linux" is just a kernel, and the epiphenomenon -the Operating system, drivers and applications- should be called GNU/Linux. He's right. The code from the GNU Project (or, for that matter, the code borrowed or derived from several other Unix-like OSs) dwarfs the Linux kernel, which is quite small. Only time will tell if anyone listens, however. In his favor is the fact that historians and intellectuals love to rewrite history as they feel it should have been - as if we poor menials who actually live here can't possibly know what happened and why as well as they do, from their detached Ivory tower perspective. **3. Philosophy and Science**- Acetylene lamps, also called carbide lamps, are fueled by calcium carbide,
which spontaneously releases acetylene when exposed to water. Acetylene
(HC=CH) is a rather interesting molecule, the closest we can come to a pure
embodiment of a carbon-carbon triple bond (C=C). Its two tiny hydrogens only
serve to fill out carbon's usual valence of four bonds. It is 92.3% carbon by
weight, which is probably as close to pure carbon as any stable compound can
be.

Covalent bonds are often said (simplistically) to be formed by 'shared electrons' co-orbiting the two atoms they connect. Since electrons repel each other, double bonds are more energetic and unstable than single bonds of the same type. They don't like being crammed together, and are eager to break apart. Triple bonds are even more unstable and energetic. [Quadruple or higher bonds are apparently too unstable to exist.]

Chemicals with single covalent bonds are common. Compounds with double bonds are fairly common, too, and provide many useful properties for the chemist's palette -e.g. its two mutually repelling bonds keep a double bond from rotating and flexing as freely as a single bond; and creates locally negative regions (which are often useful). Triple bonds, however, tend to be transient, and are used mostly when instability is desired - rocket fuels (e.g. hydrazines), explosives (e.g. azides), high energy fuels (e.g. acetylene has long been used in cutting torches) and temporary intermediates for hard-to- synthesize compounds

Having said all this, calcium carbide is fairly stable and benign if kept dry. Pure calcium carbide isn't flammable or explosive,and can even be heated to its melting point of 3600 F (!) without decomposing. It will irritate eyes and mucous membranes, because its reaction with water releases an alkali, but you can freely handle it with dry hands without harm (I wouldn't, though - trace sweat could result in irritation with prolonged exposure) Commercial calcium carbide usually contains calcium oxide, hydroxide, metallic slag, etc. -a kind of mix that makes many triple-bond compounds deadly dangerous- yet even loose crude calcium carbide is safely used by children [under, one hopes, adult supervision] in carbide cannons.

The reaction of calcium carbide with water is often incorrectly simplified as CaC_{2}+ H_{2}O => C_{2}H_{2}+ Ca(OH)_{2}.

But that's actually a combination of two separate reactions, only one involving calcium carbide:

#1: CaC_{2}+ H_{2}O => C_{2}H_{2}+ CaO + heat

#2: CaO + H_{2}O => Ca(OH)_{2}

I mention this because the first reaction is more energetically favorable (hence, the significant liberation of heat) than the second. Since a carbide lamp drips water slowly into the carbide, a partly-used or even recently exhausted lantern tank will contain almost entirely CaO (calcium oxide aka lime, quicklime, burned lime), not Ca(OH)_{2}(calcium hydroxide, aka slaked lime). Most of the Ca(OH)_{2}is only created when the carbide is used up, and excess water is added to the CaO.

Ca(OH)_{2}is a respectably corrosive alkali, and you should avoid contact with it (or CaO, due to Reaction #2) and empty and clean the tank promptly when its not in use. To make things worse. Ca(OH)_{2}and CaO both combine readily with carbon dioxide from the air (especially when wet) to form insoluble calcium carbonate, a major part of limestone, oyster shells, bones, calcite, mortar and many other annoyingly hard substances. This is useful if you're building a 'scrubber' to remove CO2 during your manned space mission, but a bit of a problem if you put your carbide lamp away without washing it.

So how do we produce this paragon of triple-bond virtue? Well, around the turn of the century, electrolysis [of the type favored by industrial chemists, not cosmetologists] was the hot new thing. In 1876, aluminum was so expensive that the Washington Monument was capped with a tiny pyramid of aluminum, so the common man could have a chance to glimpse this kingly element. (Gold wasn't nearly as precious: gold coins, gilded objects and architecture, and gold jewelry were not uncommon) But 15 years later, the electrolytic Hall process made cheap aluminum possible. Within decades, it was pennies a pound. Two inventors, inspired by this success story, tried to make metallic calcium by electrolyzing lime and coal tar, and got carbide instead. Today we use charcoal or coke (roasted coal) instead of coal tar.

You'll notice that we begin with lime, and end with lime. We begin with coal and electricity and end with carbon dioxide, water and fire. It's a tight little loop. I'm a little tired, so I didn't dig up the actual numbers for practical production, but unless the electrolytic process is horribly inefficient, calcium carbonate looks to be a surprisingly efficient way to store/convert the energy of the coal and electricity in a readily usable form. **4. Agriculture**- I'm not really up on the specifics of the feeder cattle market, but here
goes:

"Puts" and "calls" are considered options to buy or sell at a set "strike" price on a fixed date in the future, but, in reality, the underlying transaction is not actually carried out in most markets. Instead, If the option is exercised, the option-seller pays the difference between the strike price and the spot market price. (In other words, it's really an option on a futures contract, not on the commodity itself). If the option-holder actually wants the underlying commodity, they can then buy it on the spot market price. The net effect is (in principle) the same as a seller delivery of the contracted amount of commodity at the contracted price.

This is, of course a generalized description. The details of puts and calls aren't really quite that symmetric, as we'll see.

This makes buying an option seem very smart, but makes one wonder why anyone would sell an option. The answer is: options aren't free. If I sell you an option, I keep the money (minus broker fees) whether or not you exercise it. The amount I charge for the option will depend on the strike price (and my estimation of the market). A 'fair price' is like 'fair odds' from a bookie: ideally, it would balance the risks and benefits, and then swing a little towards the house to cover expenses and commissions. You shouldn't expect to come out ahead, much less bet the mortgage payment on it.

In this case, you are anticipating selling 150,000 lbs of calf, but since You didn't specify the quantity of the "put", I'm going to assume each is for "50,000 pounds of 700 to 849 pound Medium Frame #1 and Medium and Large Frame #1 feeder steers." That might sound like it came out of the blue, but that's the standard contract size for feeder cattle futures, and as I said, puts are really options on futures contracts, not any underlying commodity that you actually possess.

You "paid $725 for two puts" (I assume that means 'per put', not 'in total'. I don't know the going margin on feeder cattle puts these days, but I'm assuming you used round numbers) Therefore you are down $1450, right out of the gate.

You sold the calves in October for $0.96/lb, then had two puts come up on November 20, 50K lbs each at $0.94/lb. If exercised that would mean the option to SELL 100K lbs of the class of steer described above, for $94,000 - which is unfortunately below the spot market price of $1.02/lb 0r $102,000.

Naturally, you won't want to exercise this option, because that would effectively mean selling [theoretical] cattle for less than they go for on the spot market. Since you're not really selling your cattle [you already sold them, anyway] exercising this option would be equivalent to giving the option- seller $102K worth of cattle for $94K (=-$8K)

Fortunately, you are the option-buyer (option-holder), so you don't have to exercise the option. You can just let it drop, and only lose the money you paid to buy the option. Yeah, I'm pretty sure I got it right: you BOUGHT an OPTION TO SELL.

If you'd SOLD an OPTION TO BUY (sold a call), you'd be screwed. The other guy would have the option to execute the deal or drop it, and they'd definitely execute it, because it'd mean $8K profit for them. You'd have to cut them a check, so they could (in principle) go out and buy the 100K lbs of cattle on the spot market for more than you promised they could buy them for. Worse, the option seller always pays the broker commission, so you'd be out even more money.

If you'd BOUGHT an OPTION TO BUY, you'd be entitled to $8K from the option- seller. However, a $725 option to buy would have a different floor, and you might not meet it. Then you'd lose anyway. As I said, options are insurance. If prices are middle of the road, hedging (like any insurance policy that you don't collect on) costs you money 'for nothing'. However, (like most insurance policies) "collecting" usually barely takes the harshest edge off a calamity - - so be happy you didn't have to collect on it!

As it stands: you lost $725 per unexercised put, or $1450 compared to what you'd have if you hadn't bought the puts. If you'd 'fully hedged', you'd have bought 3 puts to cover all 150,000 lbs of your cattle, and you'd be out $725x3= $2175. (if you meant the $725 to be the total cost of your 2 puts, the dollar losses would be $725 and $1087.50, respectively)

You paid roughly 1% (or 0.5%) of your actual sale price to protect yourself from falling prices, but as it turned out, the Nov. price was higher than your safety net. When you sold in Oct, you got $2K above your floor, and if you'd waited a few weeks, you'd have gotten $12K over your floor, all other things being equal.

You're probably a little disappointed with the price you got, since hedgers set their floors low to get affordable options, but it was only a misfortune. The option was meant to protect you from calamities. If the Oct. market price had been lower (say $.60/lb) you might have actually received less for your cattle than it cost you to raise them! (and you might go bust)

Jump back to the top.

War XV - battle 11

**1. Forestry**- The trees below are divided into two groups. What is the basis for this
division?
Quercus macrocarpa Quercus virginiana Magnolia soulangiana Magnolia grandiflora Gingko biloba Pseudotsuga menziesii Larix laricina Pinus ponderosa Ilex verticillatta Ilex opaca

see Answer **2. Computers**- If I must use Samba, what do you know about my network?

see Answer **3. Philosophy and Science**- After November 1, 2003 when will be the next solar eclipse?

When will be the next lunar eclipse?

see Answer **4. Math**- Andy walks down an up-escalator and counts 150 steps. Barney walks up the
same escalator and counts 75 steps. Andy takes three times as many steps in a
given time as Barney. How many steps are visible on the escalator?

see Answer

Points on this battle were won as follows:

- Jeff Johnson - 160 points for the answers to all four questions.

**1. Forestry**- The basis for the division is made at the foliage: The group on the right are considered to be evergreens, while the group on the left are considered to be deciduous.
**2. Computers**- You must have a Windows/Linux mixed environment that you are serving.
**3. Philosophy and Science**- The next total solar eclipse will be on November 23, 2003.

http://sunearth.gsfc.nasa.gov/eclipse/solar.html

The next lunar eclipse will be on November 9, 2003.

http://sunearth.gsfc.nasa.gov/eclipse/lunar.html **4. Math**- Andy took 150 steps to reach bottom, Barney took 75 to reach the top going
1/3 of Andy's rate (or rather, Andy was 3x as fast). The net result is that
Andy traversed 1/2 of the 3x amount of steps due to the rate of the escalator
acting against him. So, the total steps he went (150) is equal to the n steps
on the escalator plus the additional steps that the escalator moved = (n-
75)/2. Setting these equal gives n + (n-75)/2 = 150, which gives the n steps
= 125.

*An alternate answer?*

Let T be time Barney takes to make 25 steps. Then Barney takes 3T to make 75, and Andy takes 2T to make 150. Suppose the escalator has N steps visible and moves n steps in time T. Then Andy covers N + 2n = 150, N - 3n = 75. Hence N = 120, n = 15.

Jump back to the top.

War XV - battle 10

**1. Forestry**- What is the most obvious missing name from this list:
- Fagus
- Nothofagus
- Lithocarpus
- Castanopsis
- Colombobalanus
- Castanea
- Chrysolepis
- Trigonobalanus

see Answer **2. Computers**- As a group, what are these?
- KDE
- GNOME
- WindowMaker
- IceWM
- CDE
- XFce
- FVWM
- AfterStep

see Answer **3. Philosophy and Science**- As a group, what are these?
- Astelia
- Blandfordia
- Burchardia
- Dianella
- Drymophila
- Milligania

see Answer **4. Culture**- Name the artist most associated with each of the songs below:
- Somewhere Over the Rainbow
- Kiss an Angel Good Morning
- Dominique
- Ring of Fire
- Candle in the Wind
- Three Coins in the Fountain
- Coal Miner's Daughter

see Answer

Points on this battle were won as follows:

- Soumen Nandy - 160 points for answers to all four questions.
- Jeff Johnson - 80 points for the answers to questions 1, 2, and 4.

**1. Forestry**- These are all genera in the family Fagacaeae (roughly the family of beeches). I'd say the most prominent member of this family not listed was Quercus (oaks)
**2. Computers**- CDE, KDE, Gnome, XFce, X window and X11 (not listed, but significant)
bill themselves as desktop environments (complete Graphical User interfaces).
WindowMaker, IceWM, FVWM and AfterStep call themselves windows managers, and
originally ran as alternatives to default components that shipped with desktop
environments like those above.

However, the distinction may be largely moot. Over time, each of the desktops managers developed, adapted or adopted applications, tools, office suites and utilities that worked especially well with its code and design philosophy [1] until the most full-featured configuration sets can almost be considered separate variants of their underlying operating system. Similarly, the features and integration of the windows managers have advanced to the point where they are comparable to the Desktop environments of a few years ago.

As far as I can recall, each of these programs are "free", "open Source", and run under free, open source variants or derivatives of Unix.

"Free" can mean one of two things: "'Free' as in 'beer'" or "'Free' as in 'freedom'"

a) "'Free' as in 'beer'" (ironically, from the old saying "There ain't no such thing as free beer") means no purchase cost. You may be able to legally download them, give copies to your friends, or install one copy across an entire department. You don't have to pay to buy it. Many companies will, however, sell you a "distro" (distribution) that contains the OS, key applications, and other tools, all configured to work well together or to accomodate a certain design philosophy or working style, and packaged with an auto-install program that will quickly set the entire system up with minimal involvement by the user. They may charge you for the convenience of this pre- packaging, the vetted compilation CDs they provide, the documentation (on disk or hardcopy) or technical support

b) "'Free' as in 'freedom'" can mean many things (as 'freedom' always does), but generally it means that the end user is free to use the program or OS in ways that traditional "proprietary" software vendors tightly restrict, like the right to inspect and critique the code, make changes, or even market your own improved or specialized version (depending on the specific license)

"'Free' as in 'freedom'" programs are usually "open source", meaning that a user has access to the 'program' written in a compilable, user-readable programming language where 'closed source' programs like MS-Windows only provide executable machine code binary files. There are a few restrictions on most open source programs, which depend on the specific license. Most licenses require you to give credit to the original author. Some licenses (e.g. BSD) let you use the code any way you wish, including making and selling proprietary commercial products on it. Other licenses (e.g. GPL) require that any derivatives you release are released under the same "free" terms that you recieved it under.

"Open Source" may allow the user community to verify the correct operation of a program, fix bugs quickly, add features or create specialty versions, and many other advantages. Many people predict that this will be the New Wave of Software, and the predominant model for general purpose software for the public, especially since India, China, and the Third World, which comprise most of the world's population, have already instituted official measures to enourage it, such as restricting the use of proprietary/closed source programs by government agencies, due to proven security concerns (e.g. non-US versions of Lotus Notes, such as the one mandated by Norway for all government communications, had an encryption backdoor -the WRF, which transmitted most of the user's crypto key to make decoding almost trivial for the NSA; and the highly regarded Swiss company Crypto AG had been selling deliberately compromised cryptography software for many decades)

[1] This process is familiar to long-term users of most operating systems. The Windows and Mac OSs of recent years are far more full-featured than they were a few years ago. Once, third party desktop GUIs, disk utilities, and memory managers were industries unto themselves, but as credible versions were incorporated ["free"] into the OS, these markets dried up. (You may recall the 'browser wars' of just a few years ago.) In some cases, after several years, the OS-included tools failed to keep up with the capabilities made available by a few small vendors who remained in the market, and those sectors have begun to revive. **3. Philosophy and Science**- These are the most popular genera in Liliaceae, the lily family
**4. Culture**- * Somewhere Over the Rainbow - probably best associated with Judy Garland,
who sang it in the 1939 movie "The Wizard of Oz"

* Kiss an Angel Good Morning - Though there have been at least three songs by that name, and many remakes by country greats like Conway Twitty and a recent remake by the contemporary singer Heather Myles, I'll always think of the Charlie Pride 1971 country-pop crossover hit (Remember when pop stations played country, rock, R&B and even oldies, all at the same time -- instead of 40 overhyped single genre songs 24/7?)

* Dominique - Jeanine Deckers, better known as Sister Luc-Gabrielle, a Dominican nun at the Fichermont Convent in Belgium, and even better known simply as "The Singing Nun" (Soeur Sourire). Her album was the best selling album in the US by the end of 1963

* Ring of Fire was the title cut of Johnny Cash's album of the same name in 1963 [the same year as "Dominique"], and "Ring of Fire: The Best of Johnny Cash" (1995) (though that can be a tenuous basis for an answer: that same year (1963) Cash also released an album called "Blood Sweat and Tears", which is of course, much more associated with another group) Today, fans of the recently deceased Cash seem to consider this his signature song, but this was not always the case. In the 70's (the closest I came to being a casual fan), songs like "I'd Walk a Mile" and "Man in Black" were considered more his trademark

* Candle in the Wind - Elton John made this a hit in the 70s and then did a remake to commemorate Princess Diana in the 90s, which was equally successful

* Three Coins in the Fountain - This was a crooner classic, expecially after the 1954 movie by the same name. THere were so many versions that I'l simply have to give this one to Frank Sinatra, who wasn't in the film, but sang the opening song.

* Coal Miner's Daughter - This was considered by many to be Loretta Lynn's theme song. It was also the title of her autobiography, which was made into a 1980 movie of the same name. She was played by Sissy spacek, who did a creditable job of singing in her style, making for very a believable mix with versions sung by Lynn herself

Jump back to the top.

War XV - battle 9

3 correct answers - 80 points

4 correct answers - 160 points

5 correct answers - 320 points

**1. Forestry**- What tree is this? Scientific name please.

see Answer **2. Forestry**- What species, utilized by golfers, is this?
**3. Computers**- If I have a file on my Windows XP computer named "Test.vbs", what
type of file is it? How is it created? If I click on this file
with my left mouse button, what program will Windows associate with
this file?

see Answer **4. Math**- Let P be a point inside a square S so that the distances from P to the
four vertices, in order, are 7, 35, 49, and x. What is x?

see Answer **5. Math**- Of 6000 apples harvested, every third apple was too small, every fourth
apple was too green, and every tenth apple was bruised. The remaining apples
were perfect.

How many perfect apples were harvested? Please explain your reasoning.

see Answer

Points on this battle were won as follows:

- Daniel Hayes - 80 points for the answers to questions 1, 3 and 5.
- Jeff Johnson - 40 points for the answers to questions 1 and 3.
- Aaron Joseph Maschinot - 40 points for the answers to questions 4 and 5.

**1. Forestry***Liquidamber styraciflua*. Common US name is the Sweetgum. Funnily enough, its common Australian name is the Liquid Amber.**3. Computers**- This file is a MS Visual Basic Script file. It could easily be produced
using MS Visual Basic or by typing the lines of script into a .txt file
and renaming it to test.vbs

The file is usually used to test small script or lines of code (tens, hundreds, maybe thousands of lines of code - but there are more effective ways to execute thousands of lines of code)

When executing, (left clicking) the file will associate itself with either the command line or a VB Script host, like wscript.exe, and then execute through the command line. **4. Math**- x = 35
short explanation: in a square with respective distances of a, b, c, and d from a point P to each sequential vertice, it can be shown that the following relation holds: (a * a) + (c * c) = (b * b) + (d * d) in this particular case, a = 7, b = 35, and c = 49. thus: d = sqrt((7 * 7) + (49 * 49) - (35 * 35)) = 35 longer explanation: let a, b, c, and d be the respective distances from a point P (located somewhere within a square of side s) to the four sequential vertices. let us further define two more lengths, x and y, according to the picture below: |--------s---------| - -------------------- | |\ __/| | | \ c __/ | | | b\ __/ | | | \ __/ | | | \/ | s | P - - - - - -| - | | /\__ | | | | / \__d | | | | a/ | \__ | y | | / \__ | | | |/ | \| | - -------------------- - |-----x------| from the pythagorean theorem, the following four equations hold: 1) (s-x)*(s-x) + y*y = a*a 2) (s-x)*(s-x) + (s-y)*(s-y) = b*b 3) x*x + (s-y)*(s-y) = c*c 4) x*x + y*y = d*d we want to solve these for d in terms of a, b, and c. to do so, simply add 1) to 3) and subtract 2): [(s-x)*(s-x) + y*y] + [x*x + (s-y)*(s-y)] - [(s-x)*(s-x) + (s-y)*(s-y)] = a*a + c*c - b*b simplifying this gives: x*x + y*y = a*a + c*c - b*b but the left side of this equation is simply equal to d*d (via 4)). thus: a*a + c*c = b*b + d*d now apply the "short explanation"...

**5. Math**- The immediate trick with this problem is not to remove (10% + 33 1/3% + 25%
or 68 1/3% of the apples) as there will be some level of overlap between
the groups.

Picture, if you will, the apples coming past you on a conveyor belt and you remove every third, tenth, etc. In some intances the 'every third' apple may also be an 'every fourth' or every tenth' apple. (eg apple no. 12 is both a 'third' apple and a 'fourth' apple. Apple no. 60 is the first apple to be a 'third', fourth and 'tenth' apple.)

Sixty is the first number that has the factors 3, 4 and 10. The three numbers will divide evenly into 60. So instead of counting 6000 apples, you could could 100 groups of sixty, removing the same numbered apples each time.

By writing down all the numbers 1 - 60 and removing the 'third', fourth, etc you are left with 28 numbers. (In case you were wondering - 1, 2, 5, 7, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 46, 47, 49, 53, 55, 57, 59)

So 28 x 100 = 2800 perfect apples.below is a listing of sixty sequential spaces where "x"'s mark the bad apples and "p"'s mark the perfect apples: apple 1 apple 10 | | | | p p x x p x p x x x p x p p x x p x p x -- apple 20 x p p x p p x x p x -- apple 30 p x x p p x p p x x p x p x x p p x p x x x p x p x x p p x -- apple 60 | | apple 51

**Soumen Nandy disagrees with the above answer. Here are his comments:**I disagree on the answer to #5. I get 2700, not 2800. IMHO, the method described needs a sample of 60 or 120, rather than 100. 100 is not divisible by 3, guaranteeing a round-off error. 60 and 120 are divisible by all the given fractions My more formal, but simpler, solution (based on the Poisson method) is given below. This kind of problem is often wrongly approached by subtracting the number "spoiled" due to each cause (2000 too small, 1500 too green, and 600 bruised). However, there is overlap in these subsets. Some of the apples that are too small are also too green or bruised. Perhaps the easiest method (one I use quite often) is the Poisson method of "inverting the probability": 2/3 are NOT too small, 3/4 are NOT too green and 9/10 are NOT bruised. The fraction that's not too small AND not too green AND not bruised is: 2/3 * 3/4 * 9/10 = 54/120 (or 2700 perfect apples out of 6000)

**Response from Duane:**I think you are wrong since the answer posted is simple in its logic and seems right and since your answer is different I would conclude that yours must be wrong. That means that you must be throwing out some perfect apples. Actually one perfect apple out of every 60. I guess the next step, if I get time, will be to go through the 60 apples as diagrammed on the web page and figure out which perfect one you are rejecting. Conversely, one could go through those 60 and figure out which one was listed as perfect in error thus proving your answer.

**Soumen Nandy replied:**I stand by my answer of 2700, based on the "complement of probability" (not "inverse", as I wrote earlier) - the method you'll find in any probability text for this kind of problem. I can't tell you "which extra apple I would discard", because the other poster didn't discard *any* apples. He discarded integers. We often use numbers an analogs for object, but it can and does get us in trouble This is a very subtle point which I find intriguing, and which I hope you will enjoy, as well. I don't mean to be quarrelsome or repetitive. "The set of integers from 1-60" (or any set of integers) is NOT a representative random sample of a batch of apples. In this case, integers have properties that relate them to one another, which apples don't share. One example: Integer multiples of four CAN'T be consecutive, while it's downright LIKELY that many consecutive real-world apples will be ripe (spoiled, bruised, etc.): every housewife knows that each apple influences the ripeness and softness of its neighbors. Conversely, apples have relations between their properties that integers don't: a green apple may be slightly smaller than it would be if it had finished growing to full ripeness; a green apple is also firmer and harder to bruise. Also, saying "one in four" apples, isn't the same thing as "X modulo 4" in integers, even though "one integer in four" will be X modulo 4. "Every fourth integer" implies a specific structure because integers have an implicit order, Apples don't have implicit order, so "one apple in four" simply means "any one-fourth of the total". In a probability problem, the hypothetical apples must be generic independent widgets, and the three criteria must be independent, or we can't answer at all without the correlation figures relating the properties/criteria [an analysis we often do in medicine]. The flaw in the solution provided is that 2 is a common factor between the NUMBERS 4 and 10, so among INTEGERS, 4 and 10 will share twice as many multiples as independent factors would. (One out of every FIVE multiples of 4 is a multiple of 10, but one in TEN of the green apples would also be bruised) The integer-mapping solution given over-reports the fraction of the fixed number of "bruised" apples that are already "green". ****Of the 15 "green" integers in the sample of 60, three (20, 40, 60) are also "bruised" (multiples of 10). Instead of predicting 150 bruised apples among the 1500 green ones, the integer-map predicts 300 green apples "would've been discarded anyway for bruising". Since there is a fixed number of unsuitable fruit, overestimating the overlap will cause you to overestimate the amount of good fruit remaining Clearly, there is another 50 apples worth of error in the mapping as well, but I haven't had time to think about it. [Besides, the problem wasn't to account for all of someone else's error, it was only to provide the right answer] Since my approach used bulk ratios (and says nothing about any individual item) and calculated the number of good fruit directly, it gives the more accurate bulk result. Again, I'm not trying to give anyone a headache. (If we can't trust integers, what can we trust?) It's just one of those times when 'counting on your fingers' doesn't work. One could construct a problem where integer mapping would give a correct answer by forcing apples to have the same rules of sequence and relation that consecutive integers have. E.g. "I have a bin conveyor with one apple per bin, and a geared device that knocks over every third bin; then later every fourth bin (whether or not that bin still has an apple in it); then knocks over every tenth bin" That's not how we usually sort apples, though, is it?

**Response from Duane:**I do find this discussion intriguing. I have a few comments. First you stated that 100 is not evenly divisible by 3 guaranteeing a round-off error. The sample was not 100 but 6000 which is evenly divisible by 3. As for the difference between apples and integers, this is basically a math problem on a web site not a pile of actual apples and in general such problems assume that the reader will make certain assumptions implicit in the problem such as the assumption that every 3rd apple may be too small although we know that in real life the apples that were too small would, most likely, be randomly distributed throughout the sample. (In the same way we can postulate a World Series between the Red Sox and the Cubs although we know that in real life, hell probably won't freeze over.) So we essentially have two questions here: Is the integer solution given correct for the mathematical question asked? To what extent can we use abstract mathematics to solve real world problems and what inconsistencies or errors do we introduce by doing so? Of course, you will probably say that math works if we just use your method of "complementing the probability". I say that since apples are distinct objects they can be represented by integers and if two mathematical methods of solving the problem give different answers then either one of the methods is incorrectly applied or a simple math mistake has been made. I suspect that your method does not properly account for overlap.

**Response from Aaron:**i’m not quite sure that i exactly follow soumen’s logic. i cannot see how the concept of a “complement of probability” (at least as i learned it in the realm of binomial or poisson probability) applies in this case. as i learned it, a “complement of probability” applies only to mutually exclusive events. but, in this case, the set of “bad” apples is made up of many groups on non- mutually exclusive “bad” apples. for example, the set of all “too small” apples (which are divisible by 3) has some overlap with the ones that are “too green” (which are disivible by 4). apple #12 (divisible by both 3 and 4), for example, proves that the sets are not mutually exclusive. but i am a practical guy; perhaps soumen is using some more advanced math than i am privy to. the best way to settle this problem is not to rely on fancy arguments but simply to count out 6000 sequential apples and see how many are “perfect”. i have written a short code (a C++ program) which will do just that. here is the code: #include<stdio.h> int main(){ int goodAppleCount=0, badAppleCount=0, isAppleBad; for(int apple=1;apple<=6000;apple++){ isAppleBad=0; //each apple is initially considered “good” if((apple% 3)==0) isAppleBad=1; if((apple% 4)==0) isAppleBad=1; if((apple%10)==0) isAppleBad=1; if(isAppleBad==1) badAppleCount++; else goodAppleCount++; if((apple%60)==0) printf("Total apples: %6d , good apples: %6d , bad apples: %6d\n", apple,goodAppleCount,badAppleCount); } } this code counts the good and bad apples and prints out the following results along the way: Total apples: 60 , good apples: 28 , bad apples: 32 Total apples: 120 , good apples: 56 , bad apples: 64 Total apples: 180 , good apples: 84 , bad apples: 96 Total apples: 240 , good apples: 112 , bad apples: 128 Total apples: 300 , good apples: 140 , bad apples: 160 Total apples: 360 , good apples: 168 , bad apples: 192 Total apples: 420 , good apples: 196 , bad apples: 224 Total apples: 480 , good apples: 224 , bad apples: 256 Total apples: 540 , good apples: 252 , bad apples: 288 . . . Total apples: 5760 , good apples: 2688 , bad apples: 3072 Total apples: 5820 , good apples: 2716 , bad apples: 3104 Total apples: 5880 , good apples: 2744 , bad apples: 3136 Total apples: 5940 , good apples: 2772 , bad apples: 3168 Total apples: 6000 , good apples: 2800 , bad apples: 3200 you can clearly see that, in every group of sixty apples, 28 are “perfect” and 32 are “bad”. this pattern continues all the way up to 6000 total apples. thus, i am forced to conclude that 2800 “perfect” apples is the correct answer.

**Response from Daniel:**To rebut some of the comments made by Soumen Nandy 1. The sample size was 60. The figure '100' mentioned referred to "100 groups of sixty". Yes, 60 or 120 are appropriate smallest group sizes. So are 180, 240, or any multiple of 60 because 60 is the smallest number that 3, 4, and 10 will divide into evenly. Thus after 60 apples have cycled through, you are back to the start of the integer map pattern. 2. Probability. Why is probability and the concept of identifying a sample incorrect for this answer? Because the way the question was written suggests that we are not taking a sample. Certainly, if 10% of the apples were bruised, and 25% of the apples were green etc then this would be a candidate for sampling and the use of statistics. However, as every third, fourth and tenth apple is involved and all the apples are checked, (assumptions, i suppose) my concept of visualising all the apples coming past you on a conveyor is also appropriate. As Soumen notes, each item must be a 'generic independant widget' Perhaps this question would have been better put as one where a mechanical device was produced with three components. If every fourth component A was faulty, every third component B was faulty and every tenth component C was faulty, then you could automatically assume that a certain number of certain devices would contain faulty components and also identify which number they were on the conveyor. The analoge nature of problems with apples (greenish or affected by the rest of the barrel) and the fact that 'real' apples won't appear on a conveyor in model order require certain assumptions to be made. Manufactured goods require less assumptions because you can build the faults in. Small only - 1400 Green only - 800 Bruised only - 200 S&G only - 400 (lower number occur more often so are more likely to co-incide) S&B only - 100 G&B only - 200 (both have 2 as a factor so co-incidence occurs more frequently) S&G&B only - 100 S(total) = 1400 + 400 + 100 + 100 = 2000 (2000/6000 = 1/3) G(total) = 800 + 400 + 200 + 100 = 1500 (1500/6000 = 1/4) B(total) = 200 + 100 + 200 + 100 = 600 (600/6000 = 1/10) where (total = all apples that are defective in this way, even if they are also defective in other ways) Summary I think that this argument comes down to models and assumptions. I made the assumption that the model was relatively simplistic and that each 'apple' was in fact an 'independant generic widget'. Thus integer mapping is appropriate and a useful tool. Soumen made the assumption we were modelling 'real' apples and used stastics and probability - better for 'real' apples, less so for widgets. I won't be as dismissive as old (lies, damned lies and statistics) Winston Churchill but I would be interested to see why or if there is a difference between a statistical result and the integer mapping (or counting :D ) techniques.

**Soumen Nandy replied:**If "taking [literally] every fourth apple" works, it must work equally well for all equivalent cases of "every fourth apple", but if I take every fourth apple, beginning with the first, second, third or fourth apple, I get four different answers.

Here are the possible sequential integer maps for this method (In case you didn't have the "New Math" in school "N mod 4" means the remainder after integer division of N by 4) I've expanded each entry to indicate each reason for discarding an apple, so that the overlaps can be plainly seen.

None of the four cases agrees, yet each must be equally valid if the logic holds. The average value [(28+26+29+25)/4 = 27] happens to agree which the value that I calculated using the standard complement probability method.`N MOD 4 = 0 [multiples of 4) 28 PERFECTS ---------------------------------------------------- 1 2 3 4 5 6 7 8 9 10 00: PPP PPP 3-- -4- PPP 3-- PPP -4- 3-- --X 10: PPP 34- PPP PPP 3-- -4- PPP 3-- PPP --X 20: 3-- PPP PPP 34- PPP PPP 3-- -4- PPP -4X 30: PPP -4- 3-- PPP PPP 34- PPP PPP 3-- 3-x 40: PPP 3-- PPP -4- 3-- PPP PPP 34- PPP -4X 50: 3-- -4- PPP 3-- PPP -4- 3-- PPP PPP 34X N MOD 4 = 1 [Case A] 26 PERFECTS ---------------------------------------------------- 1 2 3 4 5 6 7 8 9 10 00: -A- PPP 3-- PPP -A- 3-- PPP PPP 3A- --X 01: PPP 3-- -A- PPP 3-- PPP -A- 3-- PPP --X 02: 3A- PPP PPP 3-- -A- PPP 3-- PPP -A- 3-X 03: PPP PPP 3A- PPP PPP 3-- -A- PPP 3-- --X 04: -A- 3-- PPP PPP 3A- PPP PPP 3-- -A- --X 05: 3-- PPP -A- 3-- PPP PPP 3A- PPP PPP 3-X N MOD 4 = 2 [Case B] 29 PERFECTS ---------------------------------------------------- 1 2 3 4 5 6 7 8 9 10 00: PPP -B- 3-- PPP PPP 3B- PPP PPP 3-- -BX 01: PPP 3-- PPP -B- 3-- PPP PPP 3B- PPP --X 02: 3-- -B- PPP 3-- PPP -B- 3-- PPP PPP 3BX 03: PPP PPP 3-- -B- PPP 3-- PPP -B- 3-- --X 04: PPP 3B- PPP PPP 3-- -B- PPP 3-- PPP -BX 05: 3-- PPP PPP 3B- PPP PPP 3-- -B- PPP 3-X N MOD 4 = 3 [Case C] 25 PERFECTS ---------------------------------------------------- 1 2 3 4 5 6 7 8 9 10 00: --- PPP 3C- PPP PPP 3-- -C- PPP 3-- --X 01: -C- 3-- PPP PPP 3C- PPP ppp 3-- -C- --X 02: 3-- PPP -C- 3-- PPP PPP 3C- PPP PPP 3-X 03: -C- PPP 3-- PPP -C- 3-- PPP PPP 3C- --X 04: PPP 3-- -C- PPP 3-- PPP -C- 3-- PPP --X 05: 3C- PPP PPP 3-- -C- PPP 3-- PPP -C- 3-X`

The average suggests that taking many random samplings (as the laws of probability demands) of the apples would yield an overall result of 27, but strictly speaking, taking an average of cases with a common underlying flaw won't always give a correct answer - there may be a systematic bias. It just happens to work in this case, and it'd be hard for even a diehard integer mapper to agree with the average of their own method

REASONS FOR THE ERROR

---------------------

The 'common factor' of 2 between 4 and 10 creates an error of 150 apples as I noted before. One out of every FIVE green apples is also bruised, while true independence would dictate one out of TEN, as I noted earlier. If I had started counting "every fourth apple" with the first apple, NONE of the gree apples would be bruised, because all green apples would be odd-numbered, and all bruised apples would be even numbered. Even and Odd are intrinsic properties of integers, but apples can't be even or odd.

Different ratios (eliminating common factors) may produce a problem where integer mapping works, but it's an inherently flawed method. There are many integer properties that could skew the result in unexpected ways. I regret 'going all philosophical' in my original post, because it seems to have obscured what I was trying to say. "Why math works in the real world" has been a lifelong interest of mine, and it sometimes requires abstreuse wording.

Probability requires random samples, but integer mapping seems appealing/simple precisely because it substitutes order for random selection - a mistake I often see in science. Rigidly taking "every fourth apple" is no different, mathematically, than taking "the first quarter of the apples" (or any other fixed rule), and I think we can all see why a fixed sampling rule like "taking only the first 1/4th" can skew samples.

I think the logic of complement probability is simpler anyway:(probability that a random apple isn't too small) x (probability that a random apple isn't too green) x (probability that a random apple isn't bruised) --------------------------------------------------- (probability that a random apple isn't too small, green or bruised)

If there is any remaining doubt about the flaw in fixed interval integer mapping, let me suggest the simplest possible problem as a test case.

"My country has 300 million people living in it. Every second person is female. Every fourth person is a minor. [Roughly the ratios for the US] How many adult males are there?"

Try to solve this problem by the fixed interval integer mapping that so many readers have argued for. It may "sound" straightforward, but it will always give manifestly wrong answers for this problem. You can confirm the flaw by calculating the minor males, minor females, and adult females as well. Fixed interval integer mapping plainly fails.

1) Daniel and Duane: I was wrong when I said Jeff's sample size was 100. I didn't have the page on the screen in front of me, and I misremembered. Rounding errors do not figure into this case, as you correctly noted.

2) Daniel's point is very well taken. "Every fourth apple" can indeed be interpreted two different ways. However, as I showed in an earlier set of charts, taking "every fourth apple" by fixed order sorting only gives Jeff's answer 25% of the time. The average of the four possible cases, still gives my answer.

It still quite possible to read the question in the strictest possible sense (where "every fourth apple" literally means the fourth, eight, etc. apple only) but I think it turns the problem into one of grammar or usage more than "Math" (the title of the category). This is not the customary meaning of that phrase in common usage. When I was in school, the teachers split us into teams by taking "every fourth student" in line to assure some sort of fairness, and break up cliques. Had we taken the strictest possible interpretation, only one-fourth of us would've played, and the rest of us would have sat on the sidelines. Actually, we'd have sat in the principal's office. Teachers aren't known for their tolerance of 'wise guys'.

Trust me, I know. I was one of those 'wise guys'. Around this time every year, a local store advertises "All bikinis 1/2 off!" and it usually takes three or four police cars to drag me away at closing time. (*sigh*)

3) Duane stated that he suspected that my method did not correctly account for the overlap. My original post showed that under Jeff's solution, one in FIVE green apples is bruised, instead of one in TEN, so there's a proven error in counting the overlap in Jeff's answer. I feel I confirmed this with my later tables.

4) Aaron's program simply tabulates the numbers according to the logic of the original answer. It does not verify that the method gives a correct answer. Using a computer to count may *seem* more rigorous than using a pen and paper, or fingers and toes, but it isn't. Counting is counting.

Of course, Daniel's remark about differing interpretations is key. Only Duane himself can tell us if he meant this as a problem in probability where the phrases in question described independent probabilities. Probability, by its very nature, only applies to random samples. If I said "every 20th student of the 500 at the Lost Hope Grade School and Pre-Incarceration Facility is a Nandy, and 100 of the students will get an A", then the number of Nandys getting A's is NOT a probability problem (Nandys have the collective IQ of the cruft in the corner of your eye.) A Nandy with an A is a physical impossibility, not an issue of mathematical probability. Even Heisenberg can't change that.

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War XV - battle 8

**1. Forestry**- What species of forests and fields in eastern United States is this? Common and scientific name please:

see Answer **2. Computers**- You are in a maze of twisty little passages, all alike...

Magic word 'XYZZY'

A huge green fierce snake bars the way!

With what? Your bare hands?

PLUGH

Who? What? When?

see Answer **3. Philosophy and Science**- In math "XYZZY" is a mnemonic device to remember what?

see Answer **4. Art**- This "brazen snake" picture is found where? Painted by what artist?

see Answer

Points on this battle were won as follows:

- Steven Skelton - 40 points for the answers to questions 2 and 3.
- Daniel Hayes - 40 points for the answers to questions 1 and 4.
- Jeff Johnson - 40 points for the answers to questions 1 and 4.

**1. Forestry**- This is the Timber Rattlesnake,
*Crotalus horridus*or*Crotalus horridus horridus*

(I guess it depends how much you don't like them)

See: http://www.mpm.edu/collect/vertzo/herp/timber/factshe1.html **2. Computers**- This is a transcript of an Adventure computer game session. The
xyzzy is a magic word that shows up at times during the game. This game was
written by Willie Crowther in the mid 70s for the PDP-10 and Don Woods
expanded on in in 1976 at Stanford. Apparently this was a popular game in
the olden days and there are several websites devoted to trivia re.
Adventure, including various downloads of the game and similar ones. This
genre is called "Interactive Fiction". A few links:

http://www.rickadams.org/adventure/c_xyzzy.html

http://www.houghi.org/jargon/ADVENT.html **3. Philosophy and Science**- xyzzy is also used as a mneumonic in math to help doing cross
products on a matrix. here is a more detailed explanation:

"[XYZZY is] taught by math teachers the world around as a mnemonic device to remember how to do cross products. "When I first played Adventure, finding 'xyzzy' in it was like finding an old friend in an unlikely place. Or an inside joke." - Ron Hunsinger

"'Cross products?' you ask.

"Indeed. The cross product of two three-dimensional vectors is the vector whose length is the area of the parallelogram with the two given vectors as adjacent sides, and direction perpendicular to the plane of that parallelogram.

"There is a 'simple' formula for the cross product. If A = B x C, where A, B, and C are the vectors (Ax, Ay, Az), (Bx, By, Bz), and (Cx, Cy, Cz), then:

Ax = By Cz - Bz Cy

Ay = Bz Cx - Bx Cz

Az = Bx Cy - By Cx

"Notice that the second and third equations can be obtained from the first by simply rotating the subscripts, x -> y -> z -> x. The problem, of course, is how to remember the first equation.

"You do that by remembering the 'magic word,' consisting of the subscripts, taken in order: xyzzy.

(you can find all this on the first link listed above).

Apparently, the use of xyzzy in Adventure and the mathematics mneumonic are unrelated: Crowther claims to have made up the word when he needed a magic word for the adventure game. **4. Art**- Michelangelo painted "The Brazen Serpent" in 1511 as a fresco on the walls
of the Sistine Chapel.

The Biblical story (Num. 21 :4-9)

Then the Lord sent venomous snakes among them; they bit the people and many Israelites died. The people came to Moses and said, "We sinned when we spoke against the Lord and against you. Pray that the Lord will take the snakes away from us." So Moses prayed for the people. The Lord said to Moses, "Make a snake and put it up on a pole; anyone who is bitten can look at it and live." So Moses made a bronze snake and put it up on a pole. Then whenany one was bitten by a snake and looked at the bronze snake, he lived.

Representation in Art

The Israelites are depicted writhing on the ground, their limbs entwined by snakes. Moses, sometimes with Aaron, stands beside the brazen serpent. John's gospel furnishes the typological parallel: 'This Son of Man must be lifted up as the serpent was lifted up by Moses in the wilderness.' Medieval art juxtaposed the subject with the serpent in the Garden of Eden entwining the Tree of Knowledge. Both probably derive from an ancient and widespread fertility image, the 'asherah', associated with the worship of Astarte, which consisted of a snake and a tree representing respectively the male and female elements. King Hezekiah destroyed the asherah, by inference the one made by Moses, at a time when the Israelites were relapsing into idolatry (II Kings 18:4).

The presence and the identification of Moses in Michelangelo's fresco is debated.

A link to this and other sistine chapel paintings:

http://www.kfki.hu/~arthp/html/m/michelan/3sistina/5spandre/10_4pe4.html

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War XV - battle 7

**1. Forestry**- What species, utilized by golfers, is this?
**2. Computers**- What is the next character in this sequence?

xyz{|}

see Answer **3. Philosophy and Science**- Born in 1842, he wrote a two volume work on psychology in 1890 which was
called the James and later an abridgement of it called the Jimmy. He is
recognized as the father of American pragmatism. Who was he?

see Answer **4. Literature**- Where do we read the story of Dolores Haze? Who wrote the story? What
was the redundant name of Delores' step-father?
Officer, officer, there they are-- Dolores Haze and her lover! Whip out your gun and follow that car. Now tumble out and take cover.

see Answer

Points on this battle were won as follows:

- Steven Skelton - 40 points for the answers to questions 3 and 4.
- Zaheer Jhetam - 20 points for the answer to question 2.

**1. Forestry**- unanswered in War XV- Persimmon
**2. Computers**- The characters are in the order of their ASCII codes. One could use the CODE and CHAR functions in MS-Excel to check the ASCII codes for selected characters. In this case, the code for (lower case) x is 120, y is 121, z is 122, { is 123, | is 124, and } is 125. It follows that the next character should be that with ASCII code 126, which is the tilde (~).
**3. Philosophy and Science**- This is William James. Here's a biography with
references to the "James" work ("The Principles of Psychology") and the
"Jimmy" volume ("Psychology, Briefer Course"):

http://www.emory.edu/EDUCATION/mfp/jphotos.html

As a philosophy student, I always found William Jame's writing style intriguing as he seems to be able to make a complex point without being explicit: his discussion happen by inference, as it were. Some more trivia: he was the godfather of William James Sidis, said to be one of the most intelligent creatures ever born on the planet. You won't hear much about Sidis from most people but there is some discussion of him in Robert Pirsig's also somewhat circuitous book "Lila" **4. Literature**- You read this in Nabokov's "Lolita", chapter 25. the step father's name is Humbert Humbert.

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War XV - battle 6

**1. Forestry**- My GPS tells me that my home is North 36 degrees 42.461 minutes and West
85 degrees 05.430 minutes at 951 feet elevation. I am deep in the woods at
Jack's Knob. The GPS says it is North 36 degrees 44.271 minutes and West 85
degrees 05.414 minutes at 1580 feet elevation. If the batteries give out on
my GPS and I have to navigate my way home by compass, how far will I have to
go in what direction?

see Answer **2. Computers**- What is the output of the following program?
A$="Saddam Hussein" T=0 FOR Z=1 TO LEN(A$) T=T+ASC(MID$(A$,Z,1)) NEXT Z PRINT T

see Answer **3. Philosophy and Science**- How are the Lost City Vents different than magma vents?

see Answer **4. Math**- A circus performance is witnessed by 120 people who have paid a total of
$120. The men paid $5, the women $2, and the children 10 cents each. How
many of each went to the circus?

see Answer

Points on this battle were won as follows:

- Soumen Nandy - 160 points for answers to all four questions.

**1. Forestry**- You are 1.81' (arc-minutes) North of home, and a mere 0.016' East. Without
doing any math, I'd tell you that going due south 1.81 nautical miles (2.1
stature miles) would put you within 100 ft of home. 1 arc-min happens to be
about 1 nautical mile (varying slightly depending on the local curvature of
the globe) or 1.15 statute miles - so 0.016' (East) is a negligible <100
ft. I assume you can spot your house from there?

Of course, you probably want a real heading. 179.5 deg (from due North, as we pilots reckon) should put you in the same room as your original measurement. (Close enough? I'm not in a mood to muck around in arc-mins and arc-secs.) Since 1 arc-min = 1 nautical miles = 1.15 mi, you are 2.1 miles from home. Since I assume neither you nor your house can float in midair, walking on the ground will correct your elevation automatically.

BTW, 'nm' is a standard abbreviation for both nautical miles and nanometers. If you're ever in a situation where you confuse one with the other, you have worse problems than a failed GPS. **2. Computers**- Good Lord, is that Applesoft Basic? Or was MID$ used in other species of
the beast? (I've forgotten) If it's Applesoft, then the output is simply the
sum of the ASCII values of the characters in the string (Saddam Hussein).
IIRC, the APPLE II computers that ran Applesoft were natively uppercase only,
though Applesoft language could handle lowercase. I vaguely recall that the
Apple had some quirks in its use of ASCII, but I can't recall what they were.

Apple used the "lowercase = uppercase + 32" or "Flip bit5" convention (okay, so 32 is the 6th bit, but Real Programmers call the 'first bit' Bit0). The 'spacebar' used ASCII 32, and the My best calculation is 1353. **3. Philosophy and Science**- Technically a 'magma vent' spews magma (e.g. an undersea volcano), but I
doubt that's what you meant.

Common deepsea vents are "black smokers" and other hydrothermal vents, which spew mineral rich water superheated by magma that climbs up hundreds of miles into the mantle from the outer core. Their discovery spurred important biological paradigm breaking since the 1970s, by bringing certain theoretical possibilities for the biochemistry and environmental tolerance of Earth life out of the 'laughingstock' realm and into proven science - with clear implications for (e.g.) life on other planets. [It also spurred investigation of obscure thermally resistant organisms like those found in surface geysers. One of these was Thermus aquaticus, a bacteria whose heat-stable DNA polymerase made modern lab PCR (Polymerase Chain Reaction) possible. PCR cycles a chemical cocktail between high and room temperature to perform DNA replication - and, if you chose the 'primers cleverly, it can effectively perform other tasks like detecting or cutting, and then amplifying selected sequences. Arguably it is fundamental to almost all modern DNA research.

Lost City vents are also hydro-vents, but the water is heated by uncertain "chemical reactions in the mantle", rather than the intrinsic heat of magma from the core. Aside from the obvious feature of the "Lost City" spout formations -their remarkable height (up to 200 ft or more)- they are chemically almost entirely carbonates, akin to (organically produced) limestone (carbonates are salts of carbonic acid [H2CO3], which is carbon dioxide [CO2] plus water [H2O] Many organisms produce CO2). Black smokers, on the other hand deposit sulfides, silicates, and other minerals related to classical igneous sources, rathr than carbonates. Lost City vents are also located in regions where eruptions and magma chambers are uncommon.

Though Lost City vents are believed to be powered by chemical reactions, I have, since I was a child, had a far-reaching theory about the (much underappreciated) geological impact of living organisms - which did, after all, entirely craft our atmosphere. I am half-convinced that the extensive microbial communities around the Lost City Vents (much more extensive than the much more limited specialized micro-communities residing a few meters around black smokers) are related to deep organic energy sources -living heat generators rather than inorganic chemical reactions. My reasons for this have become increasingly technical over the decades (I have a degree in molecular biology) but I think they are quite compelling and have been increasingly supported with each new discovery for the past three decades. Actually, from a purely scientific basis, the bulk of the explanation would consist of data that discounts the currently preferred theories: the possibility of many of my more interesting conclusions proceed directly from existing science of the past 20 years, so only its 'plausibility' compared to existing theories is open to debate. Anyone interested in investing a million or two in a new theory of how petroleum is produced (and where it can be found in larger quantities than hitherto known) can e-mail me. Just make sure your mail doesn't even remotely resemble the hundreds of spam I get a day.

[Spam truly *is* evil - it impedes legitimate communication in every field. Spammers don't respect work or private addresses: no telemarketer would call a doctor at work to sell Viagra, breast enlargement creams and the like, but I gethundreds of those spam a day. A practicing doctor obviously doesn't need some MD of questionable ethics to write a prescription for them - and no ethical MD would prescribe potentially risky 'elective' medicines for any so- called 'patient' without an exam or medical record.]

See http://www.nature.com/nsu/010712/010712-11.html **4. Math**- 17 men @ $5, 13 women @ $2, 90 children at $0.10.

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War XV - battle 5

**1. Forestry**- What tree is this? Scientific name please.

see Answer **2. Computers**- If you had visited Alan Kay's workshop at Xerox in 1979, what might you
have found there?

see Answer **3. Philosophy and Science**- What is the significance of using telomerase to exceed the Hayflick limit?

see Answer **4. Literature**- Who wrote these words in what work?
Well, that mockingbird's gonna sail away, We're gonna forget it. That big, fat moon is gonna shine like a spoon, But we're gonna let it, You won't regret it.

see Answer

Points on this battle were won as follows:

- Steven Skelton - 80 points for the answers to questions 2, 3, and 4.

**1. Forestry***Liquidamber styraciflua*. Common US name is the Sweetgum. Funnily enough, its common Australian name is the Liquid Amber.**2. Computers**- You would have found a computer running windowing Graphical User Interface
(GUI). You might have also been introduced to the programming language
Smalltalk

See: http://ei.cs.vt.edu/~history/GASCH.KAY.HTML

Steve Jobs had co-founded Apple Computer in 1976. The first popular personal computer, the Apple 2, was a hit - and made Steve Jobs one of the biggest names of a brand-new industry. At the height of Apple's early success in December 1979, Jobs, then all of 24, had a privileged invitation to visit Xerox Parc.

This is what Steve had to say about his visit to Xerox Parc.

"And they showed me really three things. But I was so blinded by the first one I didn't even really see the other two. One of the things they showed me was object orienting programming they showed me that but I didn't even see that. The other one they showed me was a networked computer system...they had over a hundred Alto computers all networked using email etc., etc., I didn't even see that. I was so blinded by the first thing they showed me which was the graphical user interface. I thought it was the best thing I'd ever seen in my life. Now remember it was very flawed, what we saw was incomplete, they'd done a bunch of things wrong. But we didn't know that at the time but still though they had the germ of the idea was there and they'd done it very well and within you know ten minutes it was obvious to me that all computers would work like this some day."

It was a turning-point. Jobs decided that this was the way forward for Apple. **3. Philosophy and Science**- The Hayflick limit applies to the fact that certain cells (i.e. human cells)
can only divide a limited number of times in a culture. Telomeres are a
formation on the tips of chromosomes that become shorter with each division;
at a certain point the shortness of these formations prevents further cell
division. This shows the underlying cause for the observed Hayflick limit.
Telomerase is an enzyme that can correct the problem with telomeres becoming
shorter with each division. The application of telomerase to human cells in
cultures have produced cells that appear to be immortal. Actually, these
cells are modified to produce the enzyme.

In short, the significance of using telomerase to exceed the Hayflick limit demonstrates that telomeres have a central role in controlling cellular aging across cell divisions, a process also known as "cellular senescence". This in turn relates to the general question of aging.

Here's a page that discusses the issue of Cellular Senescence in depth, including the telomerase discussion as well as many other things:

http://www.senescence.info/clock.htm **4. Literature**- This is from the song "I'll Be Your Baby Tonight" by Bob Dylan (Zimmerman), c. 1968.

Jump back to the top.

War XV - battle 4

**1. Forestry**- Please list the numbers 1 through 4 on the topographic map fragment below
in order from lowest to highest in elevation.

see Answer **2. Computers**- If I find a file on my computer with the file extension .swf, what program
should I use to open the file?

see Answer **3. Philosophy and Science**- "Go, eat your bread in gladness, and drink your wine in joy; for your
action was long ago approved by God. Let your clothes always be freshly
washed, and your head never lack ointment. Enjoy happiness with a woman you
love all the fleeting days of life that have been granted to you under the sun
-- all your fleeting days. For that alone is what you can get out of life and
out of the means you acquire under the sun. Whatever it is in your power to
do, do with all your might."

Where do we find these words of existentialist philosophy?

see Answer **4. Literature**- Please divide this list into two groups and explain your reasoning.
- Atlas Shrugged
- Battlefield Earth
- The Fountainhead
- We the Living
- Mission Earth
- Fear

see Answer

Points on this battle were won as follows:

- Soumen Nandy - 160 points for answers to all four questions.
- Anne Lurie - 20 points for the answer to question 2.

**1. Forestry**- Elevations: 3 < 2 < 1 < 4
**2. Computers**- .swf is associated with files used by Macromedia Shockwave. You can open them with a standalone Macromedia Shockwave player OR with a browser that has a Shockwave plug-in. The latter may seem indirect, but almost everyone has a browser installed (and most browsers and/or Shockwave sites will auto-direct you to the appropriate plug-in, if you don't already have it.) Not everyone has the full Shockwave suite. Some people uninstall it, but leave the plug-in.
**3. Philosophy and Science**- These words are found in the Old Testament book, Ecclesiastes. Though the Bible is not where most people go looking for existentialism, the author of Ecclesiastes (who went by the pen-name Quoheleth, of which "Ecclesiastes" is a Greek corruption) is rather cynical and acerbic. Actually, I've always been surprised that so many people don't seem to recognize the diversity of voices in The Bible (Song of Solomon anyone?), but treat it as if it spoke with one stolid, overbearing voice. Job is another profoundly existential book.
**4. Literature**- Atlas Shrugged, The Fountainhead, and We the Living were written by the
novelist and founder of the Objectivist philosophy, Ayn Rand.

Battlefield Earth, Mission earth, and Fear were written by the science fiction novelist and founder of Scientology, L. Ron Hubbard.

Some will see parallels here. I, myself, was an avid follower of Objectivism in my youth, and still find strong resonance with many elements of it. However, I've always chuckled when anyone called themselves "an Objectivist": Ayn Rand was always very emphatic that Objectivism is precisely whatever she said it was -- not one dottle more, less, or other; anyone who subjugates their intellect to that of another by claiming to be an Objectivist (or worse, "a strict Objectivist") doesn't 'get it', in my humble opinion.

I always wondered if her vocal insistence was solely a reflection of her wish for control (which was well known) or also a subtle test for poseurs.

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War XV - battle 3

**1. Forestry**- This is the fruit of what tree?

see Answer **2. Computers**- During setup Windows XP may or may not install an ACPI HAL. How is this
determination made?

see Answer **3. Philosophy and Science**- If there is an Orange Catholic Bible in my sietch, where am I?

see Answer **4. Math**- Let P be a point inside a square S so that the distances from P to the
four vertices, in order, are 7, 35, 49, and x. What is x?

see Answer

Points on this battle were won as follows:

- Anne Lurie - 80 points for answers to questions 1, 2, and 3.

**1. Forestry**- This is the fruit of the Osage Orange tree.

See: http://www.mcmullans.org/canal/osage_orange.htm **2. Computers**- During the installation of Windows XP, "if your BIOS is dated 1/1/1999 or
newer, then the ACPI HAL is installed by default, regardless of whether your
devices actually understand what ACPI is." (Or whether the computer owner has
any idea what all this means!)

See: http://www.tek-tips.com/gfaqs.cfm/lev2/67/lev3/70/pid/616/fid/971 **3. Philosophy and Science**- You are on Dune.
**4. Math**- x = 35
short explanation: in a square with respective distances of a, b, c, and d from a point P to each sequential vertice, it can be shown that the following relation holds: (a * a) + (c * c) = (b * b) + (d * d) in this particular case, a = 7, b = 35, and c = 49. thus: d = sqrt((7 * 7) + (49 * 49) - (35 * 35)) = 35 longer explanation: let a, b, c, and d be the respective distances from a point P (located somewhere within a square of side s) to the four sequential vertices. let us further define two more lengths, x and y, according to the picture below: |--------s---------| - -------------------- | |\ __/| | | \ c __/ | | | b\ __/ | | | \ __/ | | | \/ | s | P - - - - - -| - | | /\__ | | | | / \__d | | | | a/ | \__ | y | | / \__ | | | |/ | \| | - -------------------- - |-----x------| from the pythagorean theorem, the following four equations hold: 1) (s-x)*(s-x) + y*y = a*a 2) (s-x)*(s-x) + (s-y)*(s-y) = b*b 3) x*x + (s-y)*(s-y) = c*c 4) x*x + y*y = d*d we want to solve these for d in terms of a, b, and c. to do so, simply add 1) to 3) and subtract 2): [(s-x)*(s-x) + y*y] + [x*x + (s-y)*(s-y)] - [(s-x)*(s-x) + (s-y)*(s-y)] = a*a + c*c - b*b simplifying this gives: x*x + y*y = a*a + c*c - b*b but the left side of this equation is simply equal to d*d (via 4)). thus: a*a + c*c = b*b + d*d now apply the "short explanation"...

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War XV - battle 2

**1. Forestry**- I am a broad leaved tree. I do not have needles or scales.

My leaves are simple not compound.

My leaves are serrated not lobed.

My leaves are doubly toothed around the margins of the leaf (doubly serrate) and asymmetrical at the base.

My leaves appear alternately on the stem, not opposite each other.

I have a dry, 1-seeded fruit with a wing.

I appear throughout Eastern North America.

What am I?

see Answer **2. Computers**- If I have a file on my Windows XP computer named "Test.vbs", what
type of file is it? How is it created? If I click on this file
with my left mouse button, what program will Windows associate with
this file?

see Answer **3. Philosophy and Science**- Which one of the following does not belong and why?
- The Moon is a Harsh Mistress
- Stranger in a Strange Land
- Starship Troopers
- The Door Into Summer
- The Puppet Masters
- Double Star
- Citizen of the Galaxy
- Farmer in the Sky
- Childhood's End

see Answer **4. Math**- Of 6000 apples harvested, every third apple was too small, every fourth
apple was too green, and every tenth apple was bruised. The remaining apples
were perfect.

How many perfect apples were harvested? Please explain your reasoning.

see Answer

Points on this battle were won as follows:

- Anne Lurie - 40 points for answers questions 1 and 3.

**1. Forestry**- This tree is the American Elm,
*Ulmus americana*.

See: http://forestry.about.com/library/treekey/bltree_key_id_start.htm **2. Computers**- This file is a MS Visual Basic Script file. It could easily be produced
using MS Visual Basic or by typing the lines of script into a .txt file
and renaming it to test.vbs

The file is usually used to test small script or lines of code (tens, hundreds, maybe thousands of lines of code - but there are more effective ways to execute thousands of lines of code)

When executing, (left clicking) the file will associate itself with either the command line or a VB Script host, like wscript.exe, and then execute through the command line. **3. Philosophy and Science**- "Childhood's End" was written by Arthur C. Clarke; all the others were
written by Robert A. Heinlein.

See:

Clarke

Heinlein **4. Math**- The immediate trick with this problem is not to remove (10% + 33 1/3% + 25%
or 68 1/3% of the apples) as there will be some level of overlap between
the groups.

Picture, if you will, the apples coming past you on a conveyor belt and you remove every third, tenth, etc. In some intances the 'every third' apple may also be an 'every fourth' or every tenth' apple. (eg apple no. 12 is both a 'third' apple and a 'fourth' apple. Apple no. 60 is the first apple to be a 'third', fourth and 'tenth' apple.)

Sixty is the first number that has the factors 3, 4 and 10. The three numbers will divide evenly into 60. So instead of counting 6000 apples, you could could 100 groups of sixty, removing the same numbered apples each time.

By writing down all the numbers 1 - 60 and removing the 'third', fourth, etc you are left with 28 numbers. (In case you were wondering - 1, 2, 5, 7, 11, 13, 14, 17, 19, 22, 23, 25, 26, 29, 31, 34, 35, 37, 38, 41, 43, 46, 47, 49, 53, 55, 57, 59)

So 28 x 100 = 2800 perfect apples.below is a listing of sixty sequential spaces where "x"'s mark the bad apples and "p"'s mark the perfect apples: apple 1 apple 10 | | | | p p x x p x p x x x p x p p x x p x p x -- apple 20 x p p x p p x x p x -- apple 30 p x x p p x p p x x p x p x x p p x p x x x p x p x x p p x -- apple 60 | | apple 51

**Soumen Nandy disagrees with the above answer. Here are his comments:**I disagree on the answer to #5. I get 2700, not 2800. IMHO, the method described needs a sample of 60 or 120, rather than 100. 100 is not divisible by 3, guaranteeing a round-off error. 60 and 120 are divisible by all the given fractions My more formal, but simpler, solution (based on the Poisson method) is given below. This kind of problem is often wrongly approached by subtracting the number "spoiled" due to each cause (2000 too small, 1500 too green, and 600 bruised). However, there is overlap in these subsets. Some of the apples that are too small are also too green or bruised. Perhaps the easiest method (one I use quite often) is the Poisson method of "inverting the probability": 2/3 are NOT too small, 3/4 are NOT too green and 9/10 are NOT bruised. The fraction that's not too small AND not too green AND not bruised is: 2/3 * 3/4 * 9/10 = 54/120 (or 2700 perfect apples out of 6000)

**Response from Duane:**I think you are wrong since the answer posted is simple in its logic and seems right and since your answer is different I would conclude that yours must be wrong. That means that you must be throwing out some perfect apples. Actually one perfect apple out of every 60. I guess the next step, if I get time, will be to go through the 60 apples as diagrammed on the web page and figure out which perfect one you are rejecting. Conversely, one could go through those 60 and figure out which one was listed as perfect in error thus proving your answer.

**Soumen Nandy replied:**I stand by my answer of 2700, based on the "complement of probability" (not "inverse", as I wrote earlier) - the method you'll find in any probability text for this kind of problem. I can't tell you "which extra apple I would discard", because the other poster didn't discard *any* apples. He discarded integers. We often use numbers an analogs for object, but it can and does get us in trouble This is a very subtle point which I find intriguing, and which I hope you will enjoy, as well. I don't mean to be quarrelsome or repetitive. "The set of integers from 1-60" (or any set of integers) is NOT a representative random sample of a batch of apples. In this case, integers have properties that relate them to one another, which apples don't share. One example: Integer multiples of four CAN'T be consecutive, while it's downright LIKELY that many consecutive real-world apples will be ripe (spoiled, bruised, etc.): every housewife knows that each apple influences the ripeness and softness of its neighbors. Conversely, apples have relations between their properties that integers don't: a green apple may be slightly smaller than it would be if it had finished growing to full ripeness; a green apple is also firmer and harder to bruise. Also, saying "one in four" apples, isn't the same thing as "X modulo 4" in integers, even though "one integer in four" will be X modulo 4. "Every fourth integer" implies a specific structure because integers have an implicit order, Apples don't have implicit order, so "one apple in four" simply means "any one-fourth of the total". In a probability problem, the hypothetical apples must be generic independent widgets, and the three criteria must be independent, or we can't answer at all without the correlation figures relating the properties/criteria [an analysis we often do in medicine]. The flaw in the solution provided is that 2 is a common factor between the NUMBERS 4 and 10, so among INTEGERS, 4 and 10 will share twice as many multiples as independent factors would. (One out of every FIVE multiples of 4 is a multiple of 10, but one in TEN of the green apples would also be bruised) The integer-mapping solution given over-reports the fraction of the fixed number of "bruised" apples that are already "green". ****Of the 15 "green" integers in the sample of 60, three (20, 40, 60) are also "bruised" (multiples of 10). Instead of predicting 150 bruised apples among the 1500 green ones, the integer-map predicts 300 green apples "would've been discarded anyway for bruising". Since there is a fixed number of unsuitable fruit, overestimating the overlap will cause you to overestimate the amount of good fruit remaining Clearly, there is another 50 apples worth of error in the mapping as well, but I haven't had time to think about it. [Besides, the problem wasn't to account for all of someone else's error, it was only to provide the right answer] Since my approach used bulk ratios (and says nothing about any individual item) and calculated the number of good fruit directly, it gives the more accurate bulk result. Again, I'm not trying to give anyone a headache. (If we can't trust integers, what can we trust?) It's just one of those times when 'counting on your fingers' doesn't work. One could construct a problem where integer mapping would give a correct answer by forcing apples to have the same rules of sequence and relation that consecutive integers have. E.g. "I have a bin conveyor with one apple per bin, and a geared device that knocks over every third bin; then later every fourth bin (whether or not that bin still has an apple in it); then knocks over every tenth bin" That's not how we usually sort apples, though, is it?

**Response from Duane:**I do find this discussion intriguing. I have a few comments. First you stated that 100 is not evenly divisible by 3 guaranteeing a round-off error. The sample was not 100 but 6000 which is evenly divisible by 3. As for the difference between apples and integers, this is basically a math problem on a web site not a pile of actual apples and in general such problems assume that the reader will make certain assumptions implicit in the problem such as the assumption that every 3rd apple may be too small although we know that in real life the apples that were too small would, most likely, be randomly distributed throughout the sample. (In the same way we can postulate a World Series between the Red Sox and the Cubs although we know that in real life, hell probably won't freeze over.) So we essentially have two questions here: Is the integer solution given correct for the mathematical question asked? To what extent can we use abstract mathematics to solve real world problems and what inconsistencies or errors do we introduce by doing so? Of course, you will probably say that math works if we just use your method of "complementing the probability". I say that since apples are distinct objects they can be represented by integers and if two mathematical methods of solving the problem give different answers then either one of the methods is incorrectly applied or a simple math mistake has been made. I suspect that your method does not properly account for overlap.

**Response from Aaron:**i’m not quite sure that i exactly follow soumen’s logic. i cannot see how the concept of a “complement of probability” (at least as i learned it in the realm of binomial or poisson probability) applies in this case. as i learned it, a “complement of probability” applies only to mutually exclusive events. but, in this case, the set of “bad” apples is made up of many groups on non- mutually exclusive “bad” apples. for example, the set of all “too small” apples (which are divisible by 3) has some overlap with the ones that are “too green” (which are disivible by 4). apple #12 (divisible by both 3 and 4), for example, proves that the sets are not mutually exclusive. but i am a practical guy; perhaps soumen is using some more advanced math than i am privy to. the best way to settle this problem is not to rely on fancy arguments but simply to count out 6000 sequential apples and see how many are “perfect”. i have written a short code (a C++ program) which will do just that. here is the code: #include<stdio.h> int main(){ int goodAppleCount=0, badAppleCount=0, isAppleBad; for(int apple=1;apple<=6000;apple++){ isAppleBad=0; //each apple is initially considered “good” if((apple% 3)==0) isAppleBad=1; if((apple% 4)==0) isAppleBad=1; if((apple%10)==0) isAppleBad=1; if(isAppleBad==1) badAppleCount++; else goodAppleCount++; if((apple%60)==0) printf("Total apples: %6d , good apples: %6d , bad apples: %6d\n", apple,goodAppleCount,badAppleCount); } } this code counts the good and bad apples and prints out the following results along the way: Total apples: 60 , good apples: 28 , bad apples: 32 Total apples: 120 , good apples: 56 , bad apples: 64 Total apples: 180 , good apples: 84 , bad apples: 96 Total apples: 240 , good apples: 112 , bad apples: 128 Total apples: 300 , good apples: 140 , bad apples: 160 Total apples: 360 , good apples: 168 , bad apples: 192 Total apples: 420 , good apples: 196 , bad apples: 224 Total apples: 480 , good apples: 224 , bad apples: 256 Total apples: 540 , good apples: 252 , bad apples: 288 . . . Total apples: 5760 , good apples: 2688 , bad apples: 3072 Total apples: 5820 , good apples: 2716 , bad apples: 3104 Total apples: 5880 , good apples: 2744 , bad apples: 3136 Total apples: 5940 , good apples: 2772 , bad apples: 3168 Total apples: 6000 , good apples: 2800 , bad apples: 3200 you can clearly see that, in every group of sixty apples, 28 are “perfect” and 32 are “bad”. this pattern continues all the way up to 6000 total apples. thus, i am forced to conclude that 2800 “perfect” apples is the correct answer.

**Response from Daniel:**To rebut some of the comments made by Soumen Nandy 1. The sample size was 60. The figure '100' mentioned referred to "100 groups of sixty". Yes, 60 or 120 are appropriate smallest group sizes. So are 180, 240, or any multiple of 60 because 60 is the smallest number that 3, 4, and 10 will divide into evenly. Thus after 60 apples have cycled through, you are back to the start of the integer map pattern. 2. Probability. Why is probability and the concept of identifying a sample incorrect for this answer? Because the way the question was written suggests that we are not taking a sample. Certainly, if 10% of the apples were bruised, and 25% of the apples were green etc then this would be a candidate for sampling and the use of statistics. However, as every third, fourth and tenth apple is involved and all the apples are checked, (assumptions, i suppose) my concept of visualising all the apples coming past you on a conveyor is also appropriate. As Soumen notes, each item must be a 'generic independant widget' Perhaps this question would have been better put as one where a mechanical device was produced with three components. If every fourth component A was faulty, every third component B was faulty and every tenth component C was faulty, then you could automatically assume that a certain number of certain devices would contain faulty components and also identify which number they were on the conveyor. The analoge nature of problems with apples (greenish or affected by the rest of the barrel) and the fact that 'real' apples won't appear on a conveyor in model order require certain assumptions to be made. Manufactured goods require less assumptions because you can build the faults in. Small only - 1400 Green only - 800 Bruised only - 200 S&G only - 400 (lower number occur more often so are more likely to co-incide) S&B only - 100 G&B only - 200 (both have 2 as a factor so co-incidence occurs more frequently) S&G&B only - 100 S(total) = 1400 + 400 + 100 + 100 = 2000 (2000/6000 = 1/3) G(total) = 800 + 400 + 200 + 100 = 1500 (1500/6000 = 1/4) B(total) = 200 + 100 + 200 + 100 = 600 (600/6000 = 1/10) where (total = all apples that are defective in this way, even if they are also defective in other ways) Summary I think that this argument comes down to models and assumptions. I made the assumption that the model was relatively simplistic and that each 'apple' was in fact an 'independant generic widget'. Thus integer mapping is appropriate and a useful tool. Soumen made the assumption we were modelling 'real' apples and used stastics and probability - better for 'real' apples, less so for widgets. I won't be as dismissive as old (lies, damned lies and statistics) Winston Churchill but I would be interested to see why or if there is a difference between a statistical result and the integer mapping (or counting :D ) techniques.

**Soumen Nandy replied:**If "taking [literally] every fourth apple" works, it must work equally well for all equivalent cases of "every fourth apple", but if I take every fourth apple, beginning with the first, second, third or fourth apple, I get four different answers.

Here are the possible sequential integer maps for this method (In case you didn't have the "New Math" in school "N mod 4" means the remainder after integer division of N by 4) I've expanded each entry to indicate each reason for discarding an apple, so that the overlaps can be plainly seen.

None of the four cases agrees, yet each must be equally valid if the logic holds. The average value [(28+26+29+25)/4 = 27] happens to agree which the value that I calculated using the standard complement probability method.

The average suggests that taking many random samplings (as the laws of probability demands) of the apples would yield an overall result of 27, but strictly speaking, taking an average of cases with a common underlying flaw won't always give a correct answer - there may be a systematic bias. It just happens to work in this case, and it'd be hard for even a diehard integer mapper to agree with the average of their own method

REASONS FOR THE ERROR

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The 'common factor' of 2 between 4 and 10 creates an error of 150 apples as I noted before. One out of every FIVE green apples is also bruised, while true independence would dictate one out of TEN, as I noted earlier. If I had started counting "every fourth apple" with the first apple, NONE of the gree apples would be bruised, because all green apples would be odd-numbered, and all bruised apples would be even numbered. Even and Odd are intrinsic properties of integers, but apples can't be even or odd.

Different ratios (eliminating common factors) may produce a problem where integer mapping works, but it's an inherently flawed method. There are many integer properties that could skew the result in unexpected ways. I regret 'going all philosophical' in my original post, because it seems to have obscured what I was trying to say. "Why math works in the real world" has been a lifelong interest of mine, and it sometimes requires abstreuse wording.

Probability requires random samples, but integer mapping seems appealing/simple precisely because it substitutes order for random selection - a mistake I often see in science. Rigidly taking "every fourth apple" is no different, mathematically, than taking "the first quarter of the apples" (or any other fixed rule), and I think we can all see why a fixed sampling rule like "taking only the first 1/4th" can skew samples.

I think the logic of complement probability is simpler anyway:(probability that a random apple isn't too small) x (probability that a random apple isn't too green) x (probability that a random apple isn't bruised) --------------------------------------------------- (probability that a random apple isn't too small, green or bruised)

If there is any remaining doubt about the flaw in fixed interval integer mapping, let me suggest the simplest possible problem as a test case.

"My country has 300 million people living in it. Every second person is female. Every fourth person is a minor. [Roughly the ratios for the US] How many adult males are there?"

Try to solve this problem by the fixed interval integer mapping that so many readers have argued for. It may "sound" straightforward, but it will always give manifestly wrong answers for this problem. You can confirm the flaw by calculating the minor males, minor females, and adult females as well. Fixed interval integer mapping plainly fails.

1) Daniel and Duane: I was wrong when I said Jeff's sample size was 100. I didn't have the page on the screen in front of me, and I misremembered. Rounding errors do not figure into this case, as you correctly noted.

2) Daniel's point is very well taken. "Every fourth apple" can indeed be interpreted two different ways. However, as I showed in an earlier set of charts, taking "every fourth apple" by fixed order sorting only gives Jeff's answer 25% of the time. The average of the four possible cases, still gives my answer.

It still quite possible to read the question in the strictest possible sense (where "every fourth apple" literally means the fourth, eight, etc. apple only) but I think it turns the problem into one of grammar or usage more than "Math" (the title of the category). This is not the customary meaning of that phrase in common usage. When I was in school, the teachers split us into teams by taking "every fourth student" in line to assure some sort of fairness, and break up cliques. Had we taken the strictest possible interpretation, only one-fourth of us would've played, and the rest of us would have sat on the sidelines. Actually, we'd have sat in the principal's office. Teachers aren't known for their tolerance of 'wise guys'.

Trust me, I know. I was one of those 'wise guys'. Around this time every year, a local store advertises "All bikinis 1/2 off!" and it usually takes three or four police cars to drag me away at closing time. (*sigh*)

3) Duane stated that he suspected that my method did not correctly account for the overlap. My original post showed that under Jeff's solution, one in FIVE green apples is bruised, instead of one in TEN, so there's a proven error in counting the overlap in Jeff's answer. I feel I confirmed this with my later tables.

4) Aaron's program simply tabulates the numbers according to the logic of the original answer. It does not verify that the method gives a correct answer. Using a computer to count may *seem* more rigorous than using a pen and paper, or fingers and toes, but it isn't. Counting is counting.

Of course, Daniel's remark about differing interpretations is key. Only Duane himself can tell us if he meant this as a problem in probability where the phrases in question described independent probabilities. Probability, by its very nature, only applies to random samples. If I said "every 20th student of the 500 at the Lost Hope Grade School and Pre-Incarceration Facility is a Nandy, and 100 of the students will get an A", then the number of Nandys getting A's is NOT a probability problem (Nandys have the collective IQ of the cruft in the corner of your eye.) A Nandy with an A is a physical impossibility, not an issue of mathematical probability. Even Heisenberg can't change that.

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War XV - battle 1

**1. Forestry**- Walking in the forest I see mahogany, ipe, angelim, jatoba and massaranduba.

Where am I?

see Answer **2. Computers**- "Android Nim", "Bee Wary", "Dueling Droids", and "Dancing Demon".

Who wrote these computer games and what is significant about them?

see Answer **3. Philosophy and Science**- As a group what are these? Please explain and comment.
- New Harmony
- Oneida
- Amana
- Biosphere 2
- Brook Farm
- Divine Colony
- Fruitlands
- Hopedale
- Jonestown
- Mormons
- Shakers
- Bishop Hill

see Answer **4. History**- America's worst harbor explosion:

New York Times headline:

Blasts and Fires Wreck City of 15,000; 300 to 1,200 Dead; Thousands Hurt, Homeless; Wide Coast Area Rocked, Damage in Millions

Much of the boom industrial city of 15,000 population was destroyed or damaged. Property loss will run into millions of dollars.

Fires followed the blasts. Poisonous gas from exploding chemicals was reported to be filtering through the area.

The explosions and resulting fires killed more than 500 people and left 200 others missing.

Where and when?

see Answer

Points on this battle were won as follows:

- Anne Lurie - 160 points for answers to all four questions.
- A Creed. Oxford, England. - 20 points for answer to question 2.

**1. Forestry**- I do believe that you are in Brazil.
**2. Computers**- Android Nim", "Bee Wary", "Dueling Droids", and "Dancing Demon" were written
by high school teacher Leo Christopherson, and they are significant because
the language he used, Interpreted Basic for the 4k TRS-80 microcomputer
Model I, had very primitive graphics and the Basic graphic commands made
most animation too slow for realistic movement of very many pixels at
once.

Christopherson used "string packing" which enabled him to move several pixels at once producing realistic movement. He loaded a string with graphics rather han text characters. Printing strings was a relatively fast operation. So by planning the pixel positions and having various strings preloaded with all the possible positions for the animated object it was possible to get enough speed to simulate movement.

See: http://www.kyphilom.com/duane/warmind2.html#II8 **3. Philosophy and Science**- These are "collective societies," wherein the entire community exists for
the primary purpose of following a central set of core beliefs.

Upon occasion, [Jonestown for example] the core beliefs were subjugated to the will of one person rather than community as a whole.

Many of the communities failed to thrive [or, in effect, were self-limiting] because they did not focus on recruiting new members and/or they advocated celibacy for community members.

See: **4. History**- That would be Texas City, TX on April 16, 1947.

"On April 16, 1947, America's worst harbor explosion occurred in Texas City, Texas, when the French ship Grandcamp, carrying ammonium nitrate fertilizer, caught fire and blew up, devastating the town. The Highflier, another ship, exploded the following day. The explosions killed more than 500 people and left 200 others missing."

See: http://www.heritagekonpa.com/april.htm

Also occurring on that date were the following events, according to http://timelines.ws/days/04_16.HTML:- 1947 Apr 16, Lew Alcinder [sic] (Kareem Abdul-Jabbar), professional basketball player, was born. He made his career with the Los Angeles Lakers (HN, 4/16/99)
- 1947 Apr 16, Financier and presidential confidant Bernard M. Baruch said in a speech at the South Carolina statehouse: "Let us not be deceived -- we are today in the midst of a cold war." (AP, 4/16/97)
- 1947 Apr 16, A lens that provided zoom effects was demonstrated in New York City. (HN, 4/16/98)

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- Soumen Nandy - 640 points.
- Jeff Johnson - Tewksbury, MA - 320 points.
- Anne Lurie - Retired in Raleigh, North Carolina; likes birdwatching, genealogy, research, and surfing the Internet! - 300 points
- Steven Skelton - Admin Tech State CRCG Office, Texas - 160 points.
- Daniel Hayes - 120 points.
- Aaron Joseph Maschinot - nuclear physicist in Boston, MA - 40 points.
- Zaheer Jhetam - Manager: Logistics and Quality - South Africa - 20 points.
- A Creed - Oxford, England. - 20 points.

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** Last revised November 19, 2003. **

URL: *http://www.kyphilom.com/duane/warmindf.html*

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