Puzzles

Puzzle #1


Three identical boxes, one containing two black marbles, one containing a black marble and a white marble, and a third containing two white marbles, are placed side by side on a table. Originally each box had a label on it describing its contents, but so meone has mixed up the labels so that each one is incorrect (i.e., no label is correct). The problem is to determine the contents of each box by a sampling process: choosing one box, blindly removing one marble from it, and repeating the process as m any times as it takes to positively infer the contents of each box. What sampling procedure would you use to identify the contents of each box with the fewest number of draws?


Puzzle #2


A commuter is in the habit of arriving at his suburban station each evening at exactly five o'clock. His chauffeur always meets the train and drives him home. One day he takes an earlier train, arriving at the station at four. The weather is pleasant, so instead of telephoning home he starts walking along the route always taken by his driver. They meet somewhere along the way. He gets into the car and they drive home, arriving at the house ten minutes earlier than usual. Assuming that the chauffeur always drives at a constant speed, and had left just in time to meet the five o'clock train, can you determine how long the commuter walked before he was picked up?


Puzzle #3


The following conversation took place in a home supply/hardware type store like Lowe's or National Home Center:

"How much will one cost?"
"Seventy five cents," replied the clerk.
"And how much will twelve cost?"
"A dollar fifty."
"Okay, I'll take nine hundred and twelve."
"That will be two dollars and twenty five cents."


What was the customer buying?


Puzzle #4


An explorer walks one mile due south, turns and walks one mile due east, then walks one mile due north and finds himself back where he started. He then shoots a bear. What color is the bear? The age-old answer is white because he must have started at t he North Pole. Is there anywhere else on earth where one could walk a mile south, a mile east, and a mile north and be back at the exact same spot? Explain.


Puzzle #5


A carpenter, working with a power saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes. He can easily do this by making six cuts through the cube, keeping the pieces together in the cube shape. Can he reduce the number of nec essary cuts by rearranging the pieces after each cut? Explain.


Puzzle #6


A cylindrical hole exactly 6 inches long has been drilled straight through the center of a solid sphere. What is the volume remaining in the sphere?


Puzzle #7


You have ten stacks of coins, each consisting of ten half-dollars. One entire stack is counterfeit, but you do not know which one. You know the weight of a genuine half-dollar in grams and you know that each fake one weighs one gram more than it should. You may weigh the coins on a scale that reads in grams. What is the smallest number of weighings required to identify the counterfeit stack?


Puzzle #8


A young man lives in Manhattan near a subway express station. He has two girlfriends, one in Brooklyn and one in The Bronx. To visit the girl in Brooklyn he takes a train on the downtown side of the platform; to visit the girl in The Bronx he takes a t rain on the uptown side of the same platform. Since he likes both girls equally well, he simply takes the first train that comes along. In this way he lets chance determine which girl he visits. He reaches the subway platform at a random time each Satu rday afternoon. Brooklyn and Bronx trains arrive at the station equally often - every ten minutes. Yet for some obscure reason he finds himself going to Brooklyn nine times out of ten. Can you think of a good reason why the odds so heavily favor Brookl yn?


Puzzle #9


Needing to find a successor, and having four equally intelligent and capable advisors to choose from, the leader of a mythical country devised a test to pick the best one: the four were tightly blindfolded and seated around a table. The leader then said , "I will now place either a blue mark or a red mark on each of your foreheads. You will then remove your blindfolds, and each of you who sees more blue marks than red marks on your companions will stand up. The first person who can correctly name his o wn color and the reason will be the next leader." The leader then placed the marks, the blindfolds were removed, the candidates looked around, and all four stood up. For several minutes, each stood silent, thinking. Finally, one of them spoke: "I have a blue mark." He then successfully explained how he had figured it out. How were the candidates marked, and how did one of them determine the color of his mark?


Puzzle #10


A logician vacationing in the South Seas finds herself on an island inhabited by two groups of people. Members of one group always tell the truth and members of the other group always lie. She comes to a fork in the road knowing that one of the forks le ads to town and the other into the wilderness. There is a man standing by the fork who belongs to one of the two groups on the island, but the logician can't tell by looking at him to which group he belongs. The logician thinks for a moment, then asks o ne question only. From the reply she knows which road to take. What question does she ask?


Puzzle #11


On last New Year's Day a mathematician was puzzled by the strange way in which his small daughter began to count on the fingers of her left hand. She started by calling the thumb 1, the index finger 2, the middle finger 3, the ring finger 4, the little f inger 5, then she reversed direction, calling the ring finger 6, middle finger 7, first finger 8, thumb 9, then back to the index finger for 10, middle finger for 11, and so on. She continued to count back and forth in this peculiar manner until she reac hed a count of 20 on her ring finger. "What in the world are you doing?" her father asked. The girl stamped her foot. "Now you've made me forget where I was. I'll have to start all over again. I'm counting up to 1995 to see what finger I'll end on." The mathematician closed his eyes and made a simple mental calculation. "You'll end on your _______," he said. When the girl finished her count and found that her father was right, she was so impressed by the predictive power of mathematics that she decided to work twice as hard on her arithmetic lessons. How did the father arrive at his prediction and what finge r did he predict?


Puzzle #12


A pirate ship capable of 20 knots is sitting motionless on an infinite sea in the fog. Another ship carrying tons of gold and a weak unarmed crew is sitting exactly 10 nautical miles away on one of the 360 degree radials corresponding to the degrees on a compass. It is capable of only 10 knots and immediately sets out to escape by setting a course directly away from the pirate ship at top speed. The pirate ship knows what's happening, but can't see the other ship (knowing how far away it is when it sta rts running, but not where). Is there a course the pirate ship can sail that will guarantee interception of the gold ship? They must be close enough to touch because of the fog. If so, describe the course/strategy.


Puzzle #13


Variation on #12: A pirate ship capable of 20 knots is sitting motionless on an infinite sea in the fog. Another ship carrying tons of gold and a weak unarmed crew is sitting exactly 10 nautical miles away on one of the 360 deg ree radials corresponding to the degrees on a compass. It is capable of only 10 knots and immediately sets out to escape by setting a course directly away from the pirate ship at a random speed (the gold ship may speed up or slow down or even stop, but i t cannot deviate from it's course). The pirate ship knows what's happening, but can't see the other ship (knowing how far away it is when it starts running, but not where). Is there a course the pirate ship can sail that will guarantee interception of t he gold ship? They must be close enough to touch because of the fog. If so, describe the course/strategy.


Puzzle #14


Find the digits that the various letters in the following represent to make the calculations correct:

NINE - TEN = TWO; NINE - ONE = ALL.

(Each letter represents a unique single digit)


Puzzle #15


A particular phonograph record (remember those?) measures exactly 12 inches in diameter. The center of it that contains the hole and the label is 2.5 inches in diameter. Assuming the remainder of the record is grooved uniformly and there are exactly 29 grooves per centimeter measuring radially, how many total grooves are there on the record?


Puzzle #16


If a hole is drilled through the center of a sphere such that the height of the resulting cylindrically shaped hole is exactly 6 inches, what is the remaining volume of the sphere?