Puzzle 6: The necktie paradox

Two men are each given a necktie by their respective wives as a Christmas present. Over drinks they start arguing over who has the cheaper necktie. They agree to have a wager over it. They will consult their wives and find out which necktie is more expensive. The terms of the bet are that the man with the more expensive necktie has to give it to the other as the prize.

The first man reasons as follows: the probability of me winning or losing is 50:50. If I lose, then I lose the value of my necktie. If I win, then I win more than the value of my necktie. In other words, I can bet x and have a 50% chance of winning more than x. Therefore it is definitely in my interest to make the wager. The second man can consider the wager in exactly the same way; therefore, paradoxically, it seems both men have the advantage in the bet. This is obviously not possible.

What is the flaw in their reasoning?

Puzzle 5 : Perfectly Logical

Two perfect logicians, S and P, are told that integers x and y have been chosen such that x and y are both greater than 1 and x and y sum to something less than 100. S is given the value x+y and P is given the value xy. They then have the following conversation.

P: I cannot determine the two numbers.
S: I knew that.
P: Now I can determine them.
S: So can I.

Given that the above statements are true, what are the two numbers?

Puzzle 4 : Monkey and the pulley

A weightless and perfectly flexible rope is hung over a weightless, frictionless pulley attached to the roof of a building. At one end is a weight which exactly counterbalances a monkey at the other end.

What happens if the monkey begins to climb ?

Puzzle Medley

Here are some of the other interesting puzzles we have discussed:
(Shane) Two real numbers are drawn from an unknown distribution. One of them is revealed to you. You now have to guess if the second is greater or less than the number revealed to you. Is there a strategy that is better than random guessing ?
(Ravishan) You have a line of length 1m with n marbles spaced out on it. Ravi then imparts a velocity and direction to each marble. What is the time until the last marble falls off the line ? Assume no friction and perfect collisions.
(muralib) You have 12 balls and a two sided measurement scale. One of the balls (unknown to you which one) is heavier or lighter than the rest. Can you use the balance three times and figure out which is the odd ball and whether it is heavier or lighter ?

Puzzle 3 : Pick a white ball and win

You have 50 White balls, 50 Black balls and two jars. You can put the balls into the jars however you please. You will then be blindfolded and the jars will be shaken/shooked/shaked. You then have to select a ball (still blindfolded). What can you do to maximize your chances of picking a white ball ?

Puzzle 2

A man was out hiking. He set up camp, and realized he had nothing to eat. He decided to hunt for bears, since he loved bear meat. He walked 50 miles south from his camp. Then he ran 50 miles west. There he finally shot a bear. He then carried the bear 50 miles north all the way back to his camp. What color was the bear?

CAVEAT : There is more than one place his camp could be!

Puzzle 1

What is interesting about the title of this blog ?

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