Alexis Darrasse - A young Greek studying Applied Mathematics in Bordeaux, France has accumulated 1120 points.
Points on this battle were won as follows:
Points on this battle were won as follows:
1) assuming that decimal fractions of miles are allowed 9000 kg over 19 one-way trips, moving 52.63 miles 8000 kg over 17 one-way trips, moving 58.82 miles 7000 kg over 15 one-way trips, moving 66.67 miles 6000 kg over 13 one-way trips, moving 76.92 miles 5000 kg over 11 one-way trips, moving 90.91 miles 4000 kg over 9 one-way trips, moving 111.11 miles 3000 kg over 7 one-way trips, moving 142.86 miles 2000 kg over 5 one-way trips, moving 200.00 miles Take 1000 kg directly to Damascus, comsuming 200.08 kg on the way, leaving 599.84 kg and take back 200.08 kg to eat on the way back. Take the last 1000 kg directly to city B, comsuming 200.08 kg on the way, and depositing an additional 799.92 kg of grass for a total deposit of 1399.77 kg. 2) the second method assumes that the camel can only move in increments of one mile you consume 19 kg to move the remaining 9981 kg 1 mile after 53 miles/trips you reach have 8993kg left and from that point need only 17 kg per mile after 59 miles (112 total) it is 7990 -15/mile 66 more (178) will get to 7000 kg -13/mile 77 more (255) is 5999 - 11/mile 91 more (346) is 4998 - 9/mile 111 more (457) is 3999 - 7/mile 143 more (600) is 2998 - 5/mile 200 more (800) is 1998 - 3/mile final 200 (1000) needs 600 kg leaving you with 1398 kg It is possible to get a more optimised solution by using smaller and smaller increments but that would get insanely complex once you get to the inch levelFirst, the easy part. Yes, we can get some grass to Damascus. The idea is to forward all the grass to smaller distances. If we cut the distance in four and use 3000 kg of grass, we can manage to get 500 kg to Damascus. Here's how:
0 250 500 750 1000
X
10000 0 0 0 0
X
9000 750 0 0 0
X
9000 500 0 0 0
X
9000 1250 0 0 0
X
9000 1250 0 0 0
X
8000 2000 0 0 0
X
8000 1000 750 0 0
X
8000 1000 500 0 0
X
8000 0 1250 0 0
X
8000 0 250 750 0
X
8000 0 250 0 500
Now, to get as much grass as possible to destination,
we must understand why cutting the distance in pieces
works. What we are trying to do is to minimize the
distance (let's call it D) made by the camel since the
grass that will reach Danascus will be 10000 - D. The
simplest is to come and go 10 times but this will make
D=2*10000=20000 which is way too much. The fact to
notice is that if we move all the grass to 250 miles
from Cairo, we have already D=2*10*250 - 250 = 4750
but there is much less grass left, which means less
come and goes to come. We can see it this way: since
there is no way to get even half of the grass in the
second half of the distance, there is no reason to
come and go ten times that distance. So, if we take
that idea further, we can think that if we cut the
distance in more parts, we will reduce the total
distance. Now, let's calculate.
If n is the number of equal pieces in which we cut the
distance, the total amount of grass left will be:
10000*[(1-2/n)^n] + 500*[1 - (1-2/n)^n] --> 9500*e^-2
+ 500 = 1785.6852 kg which is the maximum amount you
can transport, actually you can get as close as you
want to that but never reach it.
Points on this battle were won as follows:
Points on this battle were won as follows:
CERTMGR.MSC Certificates Manager CIADV.MSC Indexing Service COMPMGMT.MSC Computer Management - users and groups DEVMGMT.MSC Device Management - system hardware configuration DFRG.MSC Disk defragmentation/disk performance optimization DISKMGMT.MSC Disk Management - disk partitions EVENTVWR.MSC Event Viewer - system event logs (display) FSMGMT.MSC Shared Folders/shared files LUSRMGR.MSC Local Users and Groups NTMSMGR.MSC Removable storage (pools, queues, requests, etc.) NTMSOPRQ.MSC Removable Storage Operator Requests PERFMON.MSC Performance Monitor SERVICES.MSC System services WMIMGMT.MSC Windows Management Infrastructure (Instrumentation service)
Through winter's cold and summer's breeze, She's the author of our milk and cheese; When she's gone and at last she rests, She leaves us numerous bequests; The briefcases that she leaves behind, protect the plans of all mankind. But belts are her halo and crown; They keep our pants from falling down.Who is she?
Points on this battle were won as follows:
127.0.0.1 x.acme.comin the file c:\windows\system32\drivers\etc\hosts
Points on this battle were won as follows:
6 = 2^(2-1)*(2^2-1) (p=2) 2^2-1=3 is prime 28 = 2^(3-1)*(2^3-1) (p=3) 2^3-1=7 is prime 496 = 2^(5-1)*(2^5-1) (p=5) 2^5-1=31 is prime 8128 = 2^(7-1)*(2^7-1) (p=7) 2^7-1=127 is prime 33550336 = 2^(13-1)*(2^13-1) (p=13) 2^13-1=8191 is prime 8589869056 = 2^(17-1)*(2^17-1) (p=17) 2^17-1=131071 is primeMore information on perfect numbers:
Points on this battle were won as follows:
cd \temp pushd \bak cd \work popd
Points on this battle were won as follows:
Aries Ram Head Mars Fire Taurus Bull Neck Venus Earth Gemini Twins Chest Mercury Air
Points on this battle were won as follows:
8 = 00001000 4 = 00000100 00001000 IMP 00000100 = 11110111 = - 00001001 = - 9 So, 8 IMP 4 = - 9 00001000 EQV 00000100 = 11110011 = - 00001101 = - 13 And 8 EQV 4 = - 13 (8 IMP 4)*(8 EQV 4) = (-9)*(-13) = 117 11110111 11110011 * 11110111 11101110 01110000 11100000 11000000 10000000 + 01110101 = 1 + 4 + 16 + 32 + 64 = 117
Cancer Crab Stomach/Breasts Moon Water
INPUT X INPUT Y PRINT X OR Y PRINT X XOR Y PRINT X AND Y PRINT NOT X PRINT NOT Y PRINT X IMP Y PRINT X EQV Y
Points on this battle were won as follows:
Points on this battle were won as follows:
Last revised March 3, 2003.
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