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