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Puzzles, Games, and Mind Teasers

For the Very Intelligent

The statement below is false.
The statement above is true.

There is three errers in this sentence.
Can you find them?

Puzzlr - Word Puzzles


If you enjoy the puzzles, etc. on this page, please check back about once a week. I intend to be adding to the page for years. Check the last date the page was modified at the bottom of the page.

To make God laugh, tell him your plans.
John Chancellor


A physicist, a biologist, and a mathematician watched two people go into an empty house. After a while three people came out. They thought about that for a while.
"We must have miscounted.", said the physicist.
"They must have reproduced.", said the biologist.
"If exactly one more person enters, the house will again be empty.", said the mathematician.
From Reader's Digest

Web Links


Puzzle Books

Many of these problems are from the book:
Games for the Superintelligent by James F. Fixx / Hardcover / Published 1998
Value Priced at: $7.99
Click on the title above to order the book.

Here are some more books you may find interesting:

Brain Twisters from the World Puzzle Championships Vol 2
Stanley Newman(Editor) / Paperback / Published 1995
Check Your IQ : The Mensa Uk Puzzle Editors
Ken Russell, et al / Paperback / Published 1998
The Essential IQ Workout
Norman Sullivan / Paperback / Published 1998
Games Magazine Presents Brain Twisters from the World Puzzle Championships Vol 3
Will Shortz(Editor), Ron Osher (Editor) / Paperback / Published 1997
Hard-To-Solve Brainteasers
Jaime Poniachik, Lea Poniachik / Paperback / Published 1998
Mensa Assess Yourself
Paperback / Published 1998
Mensa IQ Workout
Paperback / Published 1998
Mensa Lateral Thinking
Paperback / Published 1998
Mensa World Shapes
Paperback / Published 1998
The Puzzle King : Sam Loyd's Chess Problems and Selected Mathematical Puzzles
Sid Pickard(Editor) / Paperback / Published 1996
Solitaire Battleships : 108 Challenging Logic Puzzles
Peter Gordon, Mike Shenk / Paperback / Published 1998
Aha! Gotcha : Paradoxes to Puzzle and Delight
Martin Gardner / Paperback / Published 1982
Calculus Made Easy : Being a Very-Simplest Introduction to Those Beautiful Methods of Reckoning Which Are Generally Called by the Terrifying Names of
Martin Gardner, Silvanus Phillips Thompson / Hardcover / Published 1998
Classic Brainteasers
Martin Gardner, Jeff Sinclair (Illustrator) / Hardcover / Published 1994
Codes, Ciphers and Secret Writing
Martin Gardner / Paperback / Published 1984
Entertaining Mathematical Puzzles
Martin Gardner, Anthony Ravielli / Paperback / Published 1986
Hexaflexagons and Other Mathematical Diversions : The First Scientific American Book of Puzzles and Games
Martin Gardner / Paperback / Published 1988
Knotted Doughnuts and Other Mathematical Entertainments
Martin Gardner / Paperback / Published 1986
The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications
Martin Gardner / Hardcover / Published 1997
Making the Alphabet Dance : Recreational Wordplay
Ross Eckler, Martin Gardner (Introduction) / Paperback / Published 1997
Relativity Simply Explained
Martin Gardner / Paperback / Published 1997
My Best Mathematical and Logic Puzzles
Martin Gardner / Paperback / Published 1994
Perplexing Puzzles and Tantalizing Teasers/2 Volumes in 1
Martin Gardner, Laszlo Kubinyi (Illustrator) / Paperback / Published 1988

Java Games

  1. Nim
  2. Connect 4
  3. Master Mind
  4. Conway's Game of Life
  5. Colors
  6. Mine Field
  7. Othello or Reversi

War of the Minds - An Internet Contest.

The War of the Minds consists of a number of battles. Each battle is made up of four questions, each on a different subject. The war is won by the first player to get 640 points or the first player to get 320 points ahead of his nearest competitor.

Points are accumulated by winning questions. The winner of a question is the first player to send the correct answer. Players are limited to one set of answers per battle. A set of answers can answer any number of questions in the battle from one to four. Points are accumulated faster by winning more questions in a single battle.

Click on the War of the Minds link to view the current battle and, perhaps, participate or to simply view the questions and answers of the archive of battles.


Nim

Nim starts with matches placed in the following pattern.
                ! ! ! ! ! ! !         (7)
                  ! ! ! ! !           (5)
                    ! ! !             (3)
                      !               (1)
This game is for two players.
The object of the game is to make your opponent remove the last match.
Rules are:
  1. Players alternate moves.
  2. Any number of matches may be removed by either player on his move, provided that he takes from only one horizonal row at a time.
  3. The player who removes the last match loses.

Diamond Mining

This is a card game for two players. (It is possible for three to play.)
Start the game by removing all hearts and jokers from a standard playing card deck leaving 13 cards in each of three suits; Diamonds, Clubs, and Spades. The dealer shuffles the diamonds, allows the player to his right to cut the stack, and places the 13 diamonds face down in the center of the table. The clubs are given to one player and the spades to the other.

The stack of Diamonds is called the "Diamond Mine". The black cards in each player's hand become his bankroll. The object of the game is to capture Diamonds as they become available by each player bidding on them from his bankroll and placing cards won face up in his "stash" on the table. The winner at the end of the game is the player with the highest Diamond point total in his stash.

Diamonds count points as follows:

Bankroll cards rank 2 through 10, Jack, Queen, King, Ace from lowest to highest.

To begin play each player fans his cards face down and allows his opponent to draw one card which is discarded unseen.

At this point there remain 13 cards in the Diamond Mine and 12 cards for bids in each player's hand or bankroll.

The top card in the Diamond Mine is turned face up and becomes available for bidding. Each player examines his bankroll, chooses one card and places it face down in front of him. After both cards are placed they are turned face up and become the player's bid for the Diamond. The player who has bid the highest card wins the Diamond and adds it to his stash fanned face up on the table. In case of a tie bid the Diamond is discarded. Cards bid are left visible face up on the table throughout the game.

Play continues for 12 rounds by turning up the next Diamond in turn and placing bids. The last Diamond is never turned or available for bid.

At the end of play the player with the highest total card points in his stash is the winner.

For added interest the loser may be required to pay the winner one penny or one dollar for each point difference between the two stash totals.

This is a game of psychology because the winner will be the player who can best anticipate the bid of his opponent.

I have written and made available a computer program in which you can play "Diamond Mine" against the computer. The program is about 27K bytes. It is an MSDOS exe file.
Click here to download the program.

Variation: Count diamonds equally as 1 point each and dispense with drawing and discarding the two black cards at the beginning so that all 13 diamonds are available.


Oh, Drat!

A party card game best for four to seven players
May be played by as few as two players.

This game is played with a standard 52 card deck of playing cards. The dealer is either the player to draw the highest card or the winner of the last game if a series of games is being played.

The dealer shuffles the deck of cards, lets the player to his right cut the cards and deals seven cards to each player beginning at his left. The rest of the deck is discarded for that round. In each subsequent round one less card is dealt to each player so that on the second round each player gets six cards, etc. A game may, therefore, consist of up to seven rounds. The dealer for each round is the player who captured the most tricks in the previous round. If two or more players tie for most tricks captured, the dealer is determined by those players drawing for high card.

The winner of the game is the last player remaining. To continue play in the game a player must capture at least one trick in each round. If a player fails to capture at least one trick in a round he is out of the game and must set out the rest of play for the remaining rounds of that game.

After examining his hand the dealer declares one suit as trumps for that round and plays a card face up on the table to lead off the first trick. Each player in turn beginning to the dealer's left then plays a card face up on the trick. Each player must play a card of the same suit as the lead card if he can. If not, he can play any card. The trick is won by the player who played the highest card of the lead suit unless a card of trump suit has been played. In that case the trick is won by the player who played the highest trump card.

The winner of a trick then leads off play for the next trick.

Options for more interesting play:


Complete the Sequence

O T T F F S S
What is the next letter?

Click here for answer.

Using a Barometer

A high school student got into trouble with the school's administrative hierarchy because of his imaginative answers to a physics question. The student was asked on an examination to describe a method for finding the height of a building by using a barometer. The student, bright enough to be bored by the obvious answer, decided to describe not one but two alternate methods. Take the barometer, he wrote, and drop it from the top of the building, timing the interval until you see it smash on the ground. Then using the standard formula for acceleration of a falling object, calculate the height of the building. Or, he went on, find the owner of the building and say to him, "If you'll tell me how tall your building is I'll give you a good barometer."

Cooking a Roast

A class of engineering students were given the following question on an exam: How long should a three pound beef roast stay in a 325 degree oven for the center to reach a temperature of 150 degrees?

One student, described as a "Big Project man," didn't come up with an answer but did offer a plan for a series of precise experiments that would yield an accurate answer in six to nine months. Another student, an advocate of the practical approach, went out and bought a roast, an oven thermometer, and a watch. He wrote his report while munching medium-rare roast beef sandwiches. A third student used logic. Reasoning that animal tissue is mostly water and therefore should have about the same specific heat and conductivity, he applied heat transfer theory to produce his answer (it proved, incidentally, to be quite close to that of the second student). The quickest answer, however, came from a student who called his mother on the phone and got the answer from her. Which of these men promises to be the most effective engineer?


Time and Tide

A ship is at anchor. Over its side hangs a rope ladder with rungs a foot apart. The tide rises at the rate of 8 inches per hour. At the end of six hours how much of the rope ladder will remain above water, assuming that 8 feet were above water when the tide began to rise?

Click here for answer.


Dog's Mead

This puzzle concerns a farm that has been in the Dunk family for some years. A part of the farm is a rectangular piece of ground known as Dog's Mead.
Additional background information:
The year is 1939; 4840 square yards=one acre; 4 roods=one acre; 20 shillings=one pound
        1         2    3         XXXX 4
        ---- ---- ---- ---- ---- XXXX ---- 
             XXXX 5         XXXX 6     
        ---- XXXX ---- ---- XXXX ---- ---- 
             XXXX      XXXX 7          
        ---- XXXX ---- XXXX ---- ---- ---- 
        XXXX 8         9         XXXX XXXX
        XXXX ---- ---- ---- ---- XXXX XXXX 
        10        XXXX 11        12   13
        ---- ---- XXXX ---- ---- ---- ---- 
             XXXX XXXX XXXX 14         
        ---- XXXX XXXX XXXX ---- ---- ---- 
        15        XXXX 16        XXXX  
        ---- ---- XXXX ---- ---- XXXX ---- 
   
                        Across
1.  Area in square yards of Dog's Mead
5.  Age of Martha, Father Dunk's aunt
6.  Difference in yards between length and breadth of Dog's Mead
7.  Number of roods in Dog's Mead times 8 down
8.  The year the Dunks acquired Dog's Mead
10. Father Dunk's age
11. Year of Mary's birth
14. Perimeter in yards of Dog's Mead
15. Cube of Father Dunk's walking speed in mph
16. 15 across minus 9 down
  
                        Down
1.  Value in shillings per rood of Dog's Mead
2.  Square of the age of Father Dunk's mother-in-law
3.  Age of Mary, Father Dunk's other daughter
4.  Value in pounds of Dog's Mead
6.  Age of Ted, Father Dunk's son, who is twice the age of his sister, Mary, in 1945
7.  Square of the breadth of Dog's Mead
8.  Time in minutes it takes Father Dunk to walk 1 1/3 times around Dog's Mead
9.  The number which, when multiplied by 10 across, gives 10 down
10. See 9 down
12. Addition of the digits of 10 down plus 1
13. Number of years Dog's Mead has been in the Dunk family
   

Click here for answer.


Bang

Two automobiles are approaching each other each traveling at a constant velocity of 60 mph. When the autos are two miles apart, a very fast fly leaves the front bumper of one of the autos and travels toward the other at a speed of 120 mph. Upon reaching that auto, the fly immediately reverses direction. This continues until the autos collide. How far did the fly travel?

Click here for answer.


Batter Up

Andy dislikes the catcher. Ed's sister is engaged to the second baseman. The center fielder is taller than the right fielder. Harry and the third baseman live in the same building. Paul and Allen each won $20 from the pitcher at pinochle. Ed and the outfielders play poker during their free time. The pitcher's wife is the third baseman's sister. The pitcher, catcher, and infielders except Allen, Harry, and Andy, are shorter than Sam. Paul, Andy, and the shortstop lost $50 each at the racetrack. Paul, Harry, Bill, and the catcher took a trouncing from the second baseman at pool. Sam is involved in a divorce suit. The catcher and the third baseman each have two children. Ed, Paul, Jerry, the right fielder, and the center fielder are bachelors. The others are married. The shortstop, the third baseman, and Bill each cleaned up $100 betting on the fight. One of the outfielders is either Mike or Andy. Jerry is taller than Bill. Mike is shorter than Bill. Each of them is heavier than the third baseman.

Using these facts, determine the names of the men playing the various positions on the baseball team.

Click here for answer.


Taking Sides

Given: Four pieces of cardboard. You are told that each one is either red or green on one side and that each one has either a circle or a square on the other side. They appear on the table as follows:
1. Red 2. Green 3. Circle 4. Square
Which ones must you pick up and turn over in order to have sufficient information to answer the question: Does every red one have a square on its other side?

Click here for answer.


Bear Hunting

A hunter arose early, ate breakfast, and headed south. Half a mile from camp he tripped and skinned his nose. He picked himself up, cursing, and continued south. Half a mile farther along he spotted a bear. Drawing a bead, he pulled the trigger, but the safety was on. The bear saw him and headed east at top speed. Half a mile later the hunter caught up, fired, but only wounded the beast, which limped on toward the east. The hunter followed and, half a mile later, caught and killed the bear. Pleased, the hunter walked the mile north back to his camp to find that it had been ransacked by a second bear.

What color was the bear that tore up his camp?

The clues are all there.

Click here for answer.


Moving Matches

Suppose you have the following problem laid out on the table with matches. Obviously, the equation is false. How can you make it true by moving only one match? (Only the roman numerals are made of matches. You cannot move either the division sign or the equality sign.)
        xxiii
        ----- = ii
         vii

Click here for answer.


Fork in the Road

A traveler comes to a fork in the road and does not know which way to go to reach his destination. There are two men at the fork, one of whom always lies while the other always tells the truth. The traveler doesn't know which is which. He may ask one of the men only one question to find his way. What is his question and which man does he ask?

Click here for answer.


Multiplying by 4

Supply a digit for each letter so that the equation is correct. There is only one set of digits that will work. A given letter always represents the same digit and each letter represents a different digit:
 
        A B C D E
              x 4
        ---------
        E D C B A
 

Click here for answer.


Biblical Arithmetic

If you multiply the number of Jacob's sons by the number of times which the Israelites encompassed Jericho on the seventh day, and add to the product the number of measures of barley which Boaz gave Ruth, divide this by the number of Haman's sons, subtract the number of each kind of clean beasts that went into the Ark, multiply by the number of men that went to seek Elijah after he was taken to Heaven, subtract from this Joseph's age at the time he stood before Pharaoh, add the number of stones in David's bag when he killed Goliath, subtract the number of furlongs that Bethany was distant from Jerusalem, divide by the number of anchors cast out when Paul was shipwrecked, subtract the number of persons saved in the Ark, and the answer will be the number of pupils in a certain Sunday school class.

How many pupils were in the class?

Click here for answer.


Spooked

What non plural word has five consonants in a row?

Click here for answer.


Shopping in Luncyville

During the summer in Luncyville the shoe store is closed every Monday, the hardware store is closed every Tuesday, the grocery store is closed every Thursday, and the bank is open only on Monday, Wednesday, and Friday. Everything, of course, is closed on Sunday. One afternoon Mrs. Abbott, Mrs. Briggs, Mrs. Culver, and Mrs. Denny went shopping together, each with a different place to go. On their way they made the following remarks:
 
        Mrs. Abbott:  Mrs. Denny and I wanted to go earlier in
                      the week but there wasn't a day when we
                      could both take care of our errands.
        Mrs. Briggs:  I didn't want to come today but tomorrow
                      I couldn't do what I have to do.
        Mrs. Culver:  I could have gone yesterday or the day 
                      before just as well as today.
        Mrs. Denny:   Either yesterday or tomorrow would have 
                      suited me.
 
Which place did each woman need to visit in town?

Click here for answer.


Homeward Bound

Each day a man's wife meets him at the railroad station and drives him home. One day he arrives at the station an hour early and begins to walk home along the road his wife always takes. She meets him en route and takes him the rest of the way home. Had he waited at the station, she would have picked him up exactly on time. As it turned out, he reached his home twenty minutes early. How long did the man walk?

Click here for answer.


Hotel Problem

Three men went to a hotel and were told that there was only one room left and that it would cost $30 for the night. They paid $10 apiece and went to the room. The desk clerk, discovering that by mistake he had overcharged them by $5.00, asked the bellboy to return the $5.00. The bellboy, not being as honest as the desk clerk, reasoned that since $5.00 is not easy to divide three ways, he would keep $2.00 and return $1.00 to each of the three men. Each man then actually paid only $9.00 apiece or a total of $27.00 for the room. Add to this the $2.00 the bellboy kept and the total is $29.00. Where did the missing dollar go?

Click here for answer.


Loose Cash

What is the largest sum of money--all in current coins and no silver dollars, American money--that I could have in my pocket without being able to give change for a dollar, half dollar, quarter, dime, or nickel?

Click here for answer.


Sudden Death

Several of us were gathered for one of Mrs. Bucket's candlelight suppers and, after the meal, retired to the sitting room for coffee, pie and conversation. For some reason unknown the conversation turned to the topic of sudden deaths. Col. McBain then told the following story:

"An English officer, after a gruesome experience during the Boxer rebellion in China some years ago, fell asleep in church during the sermon. He was dreaming that the executioner was approaching him to cut off his head, and just as the sword was descending on the officer's unhappy neck his wife lightly touched her husband on the back of his neck with her fan to awaken him. The shock was too great, and the officer fell forward dead."

"An interesting story", I said, "but, of course, it could never have happened in that way."

What is the problem with the story that convinced me that it never happened?

Click here for answer.


An Epitaph (A.D. 1538)

Two grandmothers, with their two granddaughters;
Two husbands, with their two wives;
Two fathers, with their two daughters;
Two mothers, with their two sons;
Two maidens, with their two mothers;
Two sisters, with their two brothers;
Yet only six in all lie buried here;
All born legitimate, from incest clear.
How might this happen?

Click here for answer.


Water Lilies

Water lilies double in area every twenty four hours. At the beginning of summer there is one water lily on a lake. It takes sixty days for the lake to become completely covered with water lilies. On what day is it half covered?

Click here for answer.


The Fishing Boat - A Story of Life

An American businessman was visiting a seaside Mexican village. As he strolled along the dock he saw a Mexican fisherman bring his small fishing boat into the dock returning from a fishing trip. The businessman was impressed by the quality of the fisherman's catch. He said to the man, "You have some fine fish there. How long did it take you to catch those?"

"Not long, Seņor."

"But its only ten o'clock in the morning. Why did you return from fishing so early?"

"Because, Seņor, I have caught as many fish as are necessary to support my family for today."

"Then how will you spend the rest of the day?"

"I will go home, play with my kids for a while, take a siesta with my wife, and then have a good dinner. Afterward I will go down to the cantina where I will pick my guitar and then play cards with my friends."

The businessman said, "Well you are in luck, because I have a business degree from Harvard and I can tell you how to make a success of your life. You should fish until four or five in the afternoon."

"Why would I do that, Seņor?"

"Because, by doing so you can catch enough fish to sell to make extra money which you can save until you get enough to buy a larger fishing boat and hire a helper. With the larger boat and the helper you can catch even more fish enabling you, one day, to own a fleet of fishing boats. With the fleet you will be able to make enough money in a few years to buy the fishing cannery, cutting out the middle man and increasing your profits. With the extra profits your enterprise will grow large enough in several years that you can set up a company headquarters in New York and soon you will be able to offer stock in your company on the stock exchange. Once you are listed on the stock exchange you can find a buyer and sell out for a very large fortune."

"But, Seņor, how long would this take?"

"Oh, about fifteen or twenty years."

"What would I do then, Seņor?"

"Why, then you would have enough money to retire to a little seaside village, perhaps here in Mexico. You could get up each morning without a care in the world. You could do a little fishing and have time to play with your kids, take a siesta with your wife, eat a good dinner and then go down to the cantina, play your guitar, and spend time with your friends. Life would be wonderful."


Cutting the Cake - A Space problem.

Cut a cake into eight equal pieces with only three cuts.

Click here for answer.

   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Sequence
The next letter is "E". The sequence is One, Two, Three, Four, Five, Six, Seven.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Time and Tide
8 feet will remain above water because as the ship rises so will the rope ladder.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Dog's Mead
  
        3 8 7 2 0 X 5
        4 X 9 1 X 4 4
        0 X 2 X 3 8 4
        X 1 1 1 0 X X
        7 2 X 1 9 1 8
        9 X X X 7 9 2
        2 7 X 1 6 X 9
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Bang
The two autos took one minute to collide, so the fly traveled two miles. One minute at 120 mph.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Batter Up
Harry is the pitcher, Allen the catcher, Paul the first baseman, Jerry the second baseman, Andy the third baseman, Ed the shortstop, Sam the left fielder, Mike the right fielder, and Bill the center fielder.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Taking Sides
Most people erroneously include No. 4 in their answer. But consider: No. 2 does not matter, since the question is concerned only with red cards. If No. 1 has a circle, the answer to the question is no. Similiarly, if No. 3 is red the answer is no. If No. 1 is a square, No. 3 is green, and No. 4 is either red or green the answer is yes. Therefore the answer is No. 1 and No. 3.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Bear Hunting
White. It is a polar bear, for the North Pole is one of the few places on earth where you can go one mile south, one mile east, and one mile north and still end up at your starting point. (The others are near the South Pole.)
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Moving Matches
        xxii    __
        ----- = ii  ( or pi)
         vii
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Fork in the Road
He asks either man, "If I were to ask you if this is the way I should go, would you say yes?" If the man he asks is the one who tells the truth, he will, of course, get the right answer. If the man he asks is the man who always lies, that man lies about the answer he would give, thus giving the correct answer. By forcing the liar to lie twice, one lie negating the other, the traveler forces him to tell the truth.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Multiplying by 4
The peculiar beauty of this one is that it can be done in an elegantly logical way. It is worth going through step by step, as an illustration of how an apparently difficult problem yields to a certain sort of mind:

a. The puzzler realizes that, since A multiplied by 4 yields only a one- digit answer, it must be either 1 or 2.

b. Since E x 4 must yield an even number, A must be 2.

c. Since the only numbers that, when multiplied by 4, yield a figure ending with 2, are 3 and 8, E must be either 3 or 8.

d. Since A x 4 cannot be 13 -- i.e., cannot be a two-digit number -- it must be 8. Therefore E is 8.

e. Since a 3 is carried over to D in the top line, it must also be added to D in the answer. We can see that B x 4 must yield a one-digit number. That means that B must be either a 1 or a 2. If it is a 2, then with the 3 added to it, D would be 11 -- impossible. So B must be 1.

f. Now consider D. The question here is simple: What number, when multiplied by 4 and enlarged by the carried 3, will yield a number ending in 1? Two numbers fill the bill: 2 and 7. Since we already know that B is 1, the missing number must be 7.

g. The B in the top line must have a carried 3 add to it in order to yield 7 in the answer, so C, when its carried 3 is added to it, must be at least 30. The only numbers that will work, therefore, are 7, 8 or 9. A little experimentation shows that 9 is the missing number.

        21978
           x4
        -----
        87912
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Biblical Arithmetic
There were seven in the Sunday school class. The successive numbers required by the questions in their order are as follows; 12, 7, 6, 10, 7, 50, 30, 5, 15, 4, 8.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Spooked

Witchcraft!

   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Shopping in Luncyville
Mrs. Abbott had to go to the hardware store. Mrs. Briggs had to go to the bank. Mrs. Culver had to go to the grocery store, and Mrs. Denny had to go to the shoe store.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Homeward Bound
50 minutes.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Hotel Problem
The cost of the room was $27 minus $2.00 or $25. The error comes from mistakenly adding $27 and $2.00 and getting the misleading figure of $29. Many readers will recognize this as one of the oldest puzzles around.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Loose Cash Problem
The largest sum is $1.19, composed of a half dollar, quarter, four dimes, and four pennies.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Sudden Death
If the officer immediately fell dead, how did anyone know what he had been dreaming?
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Epitaph
If two widows had each a son, and each widow married the son of the other and had a daughter by the marriage, all the relationships will be found to result.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Water Lilies
On the fifty-ninth day.
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
Answer to Cutting the Cake
Make two vertical cuts at right angles to each other along the diameters and a horizonal cut through the middle of the cake.

Also from Andrew Patton for 'cutting the cake', you could also cut it once, stack it on itself, cut it again, and then stack and cut it again...8 pieces. I was thinking, the cake doesn't necessarily have frosting on it, it could be a pound cake, so it's not definitely a bad idea....Whereas your solution, well, nobody would eat a slice of cake that looked like that. hehe, just kiddin'.

   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 
   
  
 

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