## prisoners and boxes - converse

Posted on: April 8th, 2013 by
Let's refer to the classic prisoners and boxes puzzle I proposed previously on puzzletweeter. I am restating the problem here for convenience: This is the classic prisoners and boxes puzzle: There are 100 prisoners numbered 1,2,... 100 and 100 boxes. Each box is numbered and the number is stored inside the box as a label. The boxes are identical, there's no way to tell Continue reading the story "prisoners and boxes - converse"

## Integer points

Posted on: April 7th, 2013 by
1

An integer point in a plane is a point whose coordinates are integers. Suppose we arbitrarily choose 5 integer points in a plane. Show that we can always find 2 among these 5 integer points such that the line segment joining the 2 points contains at least 1 more integer point. via MAA

## Average

Posted on: April 6th, 2013 by
We all feel like politicians are 4-legged animals. Well, can you argue that more than 99% of the politicians have more legs than average? via Prof. Berlekamp in the 2013 Kailath lecture Hint: ... ... ... ... ... ... ... ... ... ... ... ... One of the politicians broke one of his legs in the Vietnam war.

## What song?

Posted on: April 5th, 2013 by
1

A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, "I have an amazing talent; I know almost every song that has ever existed." The rich man laughs. The poor man says, "I am willing to bet you all Continue reading the story "What song?"

## Life or death

Posted on: April 4th, 2013 by
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You are a prisoner sentenced to death. The Emperor offers you a chance to live by playing a simple game. He gives you 50 black marbles, 50 white marbles and 2 empty bowls. He then says, "Divide these 100 marbles into these 2 bowls. You can divide them any way you like as long as you use all the marbles. Then I will blindfold you Continue reading the story "Life or death"

## Good rational approximation of reals

Posted on: April 3rd, 2013 by
Let a be irrational. Show that there exist infinitely many rational numbers r = p/q such that $|a-r|\leq 1/q^2$. via cut the knot

## Weighing

Posted on: April 2nd, 2013 by