Murderous Deceit

Three men make the following statements regarding a murder that they are suspected of. Two of the men are lying, and one of them is telling the truth. Only one of the men committed the crime. Which of the three is most likely to be innocent?

A. I didn’t do it.
B. C did it.
C. A did it.

An Improbable Route

Imagine that you live on the moon. One day you see a number 14 bus. What is the most likely number of bus routes on the moon?

The Wrapped String Problem

Imagine you have a piece of string long enough to stretch around the earth (40,074 km or 4,007,400,000 cm). Then you take an extra meter of string and add it to the string around the Earth. Now you spread this extra string around the Earth, supporting it somehow, so that the string forms a circle off the ground. Imagine the newly spread string traces the trajectory of a satellite.

How high off the ground would the string be?

Repeat the experiment with a basket ball, also adding one meter of string. How high off the basketball would the string be?

Birthday Problem

Go out in Manhattan and choose 23 people at random. What is the probability that at least two of them have the same birthday?

Careful: it's over 50%.

The Monty Hall Problem

Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats [that is, booby prizes]. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?

Toothpick Tripod

Get four toothpicks. Split a toothpick at one end and put the end of a second toothpick inside the split.  The connection should be firm. Now rest a third toothpick on the intersection of the first two, such that the three form a tripod.

Using just the fourth toothpick, lift all three toothpicks from the table. Obviously, you mustn't use any tricks; the requirement is as clear as it gets.

You'll use the properties of the force of gravity to solve this, obviously.

The Cheating Arab Wives

People in a certain Arab village Arabs have a tradition to kill any married woman that cheats on her husband. (I'm surprised.) The honor rests with the husband. One Sunday at church, the priest gathered all husbands and gave to each one of them a separate paper that included the names of all the wives that went with another man, except that their wife was not included on the list.

After five days, gunfires were heard as all the cheating wives were being shot by their husbands.

How many cheating wives were there?

Intro

Howdy! We're about to start recalling some of the math and logic problems that my friends and I struggled with as students over a cup of beer, some years ago. I'm hoping you'll find these as enjoying as we have.

I don't know yet where to put the answers. I will either choose a separate post for each answer, or I'll simply throw the answer into the Comments section of the post containing the question.

I will probably put a mirror on Wordpress; keep an eye on this post for updates.