Puzzles

I now run the website Puzzle Tweeter where I post one puzzle per day.

Since I am interested in puzzles, I decided to collect all puzzles I have seen in to one place.

Updated: Thursday, December 2, 2010:

I recently found the following puzzles: Math and Logic Puzzles

previous entries

Some interesting puzzles can be found here. The author is William Wu. His puzzle on 100 prisoners and a light bulb is pretty interesting.

I also found this interesting site for puzzles. The particular puzzle that it links to has a novel solution. The other puzzles are also interesting.

Here is a link to microsoft puzzles.

In this page I will post interesting puzzles as I come across them. Please leave your comments and suggestions.

Microsoft Interview Question

Why should a man-hole be round and not square? Answer

Prisoners and Hats

There are many versions of prisoners and hats puzzles. Wikipedia (here and here) gives some interesting variants. I also found this link that gives a lot of interesting hat puzzles. One may also want to see the classic puzzle on infidelity. This puzzle is from a class of Induction puzzles.

Brownian Motion

Suppose the starting point of a particle undergoing Brownian motion in 2 dimensions is chosen uniformly at random on an imaginary circle C_1. Suppose there is a solid circle C_2 completely inside C_1, not necessarily concentric. Show that the particle hits the boundary of C_2 with the uniform distribution. Answer

Pick the best of two envelopes

This puzzle or rather paradox is a PhD Quals question of Thomas Cover. There are two sealed envelopes A and B. One of them has $x and the other has $2x. You are given an envelope at random. You open the envelope and look at the amount of money available. Now you have the option of either keeping the money or switching to the other envelope. Is there a strategy in which you get to keep the envelope containing $2x with a probability greater than 1/2? Answer

Patches on a Coat

Problem statement due to Austin Kim. I have a coat with area 5. The coat has 5 patches on it. Each patch has area at least 2.5. Prove that 2 patches exist with common area of at least 1. Answer

More on Coupon collector's problem

Problem due to Lei Zhao. For those who are not familiar with the Coupon Collector's problem and its solution I refer you to Wikipedia. Suppose there are n coupons to be collected. After all coupons are collected, what is the probability that coupon 1 is collected exactly once? Answer