Puzzle time

[BennyProfane]

http://tierneylab.blogs.nytimes.com/2009/03/30/the-god-einstein-oppenheimer-dice-puzzle/?partner=rss&emc=rss

I'm not gonna say anything at this point except....Discuss.

[tiohn]

My immediate thought is that Oppenheimer can construct a set of non-transitive dice which would favor him no matter what Einstein picks, but I'm not sure about the case with three dice and the numbers 1-18. The Wikipedia article on the subject details the construction of a set of four non-transitive dice using 1-24:

A set of four dice using all of the numbers 1 through 24 can be made to be non transitive. With adjacent pairs, one die will win approximately 2 out of 3 times.

For rolling high number, B beats A, C beats B, D beats C, A beats D.

* A: 1, 2, 16, 17, 18, 19
* B: 3, 4, 5, 20, 21, 22
* C: 6, 7, 8, 9, 23, 24
* D: 10, 11, 12, 13, 14, 15


Edit: Yes, it looks like people in the comments have already constructed the non-transitive set: (http://tierneylab.blogs.nytimes.com/2009/03/30/the-god-einstein-oppenheimer-dice-puzzle/?partner=rss&emc=rss#comment-125719)
Die number 1: 1, 2, 13, 14, 15, 16
Die number 2: 3, 4, 5, 6, 17, 18
Die number 3: 7, 8, 9, 10, 11, 12

If Einstein picks die 1, Oppenheimer picks die 2
If Einstein picks die 2, Oppenheimer picks die 3
If Einstein picks die 3, Oppenheimer picks die 1

I'm not going to bother to verify if those are non-transitive, but it seems reasonable.

[russellmz00]

“You have only revealed that you know nothing about mathematicians.”

doesn't this imply that opp and al would need to game the system? ie ties as often as possible?

[Kael]

“You have only revealed that you know nothing about mathematicians.”

doesn't this imply that opp and al would need to game the system? ie ties as often as possible?

I assume the student's answer was that Opp would balance the dice (make the total on each = 57) and therefor it would be 50/50 no matter which die Al or Opp pick. He hadn't considered a rock/paper/scissors dice configuration.

[CLWheeljack]

Yeah, the mathematician crack may have been something about them being super-competitive with each other, thus Oppenheimer would never have set up the dice to allow Einstein to tie with him.

[russellmz00]

Yeah, the mathematician crack may have been something about them being super-competitive with each other, thus Oppenheimer would never have set up the dice to allow Einstein to tie with him.

so no mathematicians worth their salt would try and beat god at his own game?

[Staff Sergeant]

I assume the student's answer was that Opp would balance the dice (make the total on each = 57) and therefor it would be 50/50 no matter which die Al or Opp pick. He hadn't considered a rock/paper/scissors dice configuration.

Is a rock/paper/scissors combination possible with numbers (as one commenter called it, "transitive")? I really doubt it but would like to see what it would be if it is possible.

[Kael]

Is a rock/paper/scissors combination possible with numbers (as one commenter called it, "transitive")? I really doubt it but would like to see what it would be if it is possible.

Combinations are possible that are statistically better than whatever is picked, such as in tihons post. But its not possible to come up with a combo that always wins (at the very least if Al picks the die with the 18 on it at least it will win if the 18 is rolled).