You walk into a room in which there are three primates: a chimpanzee, an orangutan, and a gorilla. The chimpanzee is holding a banana in each hand, the orangutan is holding a big stick, and the gorilla is holding nothing. Which primate in the room is the smartest?
Hint: View the comments for hints.
via Wu Riddles

## Monthly Archives for January, 2013

## De Bruin Card Trick

A dealer(magician) starts with 16 cards on a deck arranged in some particular order. 4 people are seated in a table around the magician. The magician asks each person in turn to cut the deck at any particular point. Then he distributes the top 4 cards one at a time to each person in the table. Then he concentrates for a while. Since the mental …

**Continue reading the story**"De Bruin Card Trick"## Benford's law

Benford's law is an interesting anomaly regarding the distribution of the first digit in a collection of data.
"Now, we have noted elsewhere that by definition the first digit of a decimal number cannot be a zero. That leaves nine ciphers, though, and one might expect each of them to appear about one out of nine times in that first position. For each, about 11% would make sense. …

**Continue reading the story**"Benford's law"## Fermat Theorem Puzzle

A computer scientist claims that he proved somehow that the Fermat theorem is correct for the following 3 numbers:

and that the guy from Princeton was wrong). As the press conference starts, a 10-years old boy raises …

**Continue reading the story**"Fermat Theorem Puzzle"## Simple proofs of the Isoperimetric Inequality

The isoperimetric inequality states that "Among all planar shapes with the same perimeter the circle has the largest area."
Here is the simplest geometric proof that I know of:
http://www.cut-the-knot.org/do_you_know/isoperimetric.shtml
There are other proofs too:
http://cornellmath.wordpress.com/2008/05/16/two-cute-proofs-of-the-isoperimetric-inequality/
and
http://forumgeom.fau.edu/FG2002volume2/FG200215.pdf
Acknowledgement: Thanks to the late prof. Thomas Cover for pointing out a simple proof.
Let me know if any of these proofs can be extended to dimension 3 or higher dimensions.

## Is Axiom of choice correct?

**Puzzle #0:**There are people in a line, and each has a number on his hat. Each player can look to the numbers of the players in front of him. So, if is the number of player , then player knows . Now, from …

**Continue reading the story**"Is Axiom of choice correct?"

## Beat your friend at a casino

Suppose your friend invests $1 in a casino and earns $X, where X is a Random variable with mean 1, i.e. E[X]=1. Suppose you know the cdf F(x) of the random variable X. Find the cdf of a random variable Y with mean 1 (E[Y]=1) so as to maximize .
For hint: View comments on this article.
Acknowledgement: Thanks to the late prof. Thomas Cover for sharing …

**Continue reading the story**"Beat your friend at a casino"## Yue's "swap" problem

Given a regular 13-gon, a red-blue coloring of the vertices is said to be "symmetric" if there exists an axis of symmetry which passes through the center of the 13-gon. A "swap" is an operation in which we exchange the colors of any two vertices. I claim that any red-blue coloring of the vertices is at most one swap away from being symmetric. Prove/disprove my claim.