06 April 2009

God and some humans play dice

From Tierney Lab at the New York Times:A puzzle in which God, Einstein, and Oppenheimer play dice, and its solution.


Todd Trimble said...

Surprised no one's left a comment; it's a cute puzzle.

Since the solution is already a click away, I guess it won't hurt much to give my own solution here, after some spoiler space:

The idea is for Oppenheimer to rig a rock-paper-scissors scenario, so no matter how Einstein picks, O can retain the upper hand. This can be accomplished (I believe) in a variety of ways, but one I found looks like this:
Die 1: 18, 11, 10, 9, 5, 1
Die 2: 17, 16, 8, 7, 6, 4
Die 3: 15, 14, 13, 12, 3, 2

where Die 1 has a 19/36 probability of beating die 2, die 2 has a 20/36 chance of beating die 3, and die 3 has a 22/36 chance of beating die 1.

This wasn't hard to find: basically I began by giving die 1 the highest number, die 2 the next two highest, die 3 the next 3 highest after that, and cycle around like that until done. That almost worked; I just had to tweak it a bit to make it work.

Chris Wellons said...

I was going to write a program to find all of the solutions, but generating the set of all permutations is tough business.