After entertaining us with the puzzle of the three hats and the puzzle of the hundred hats (solutions here and here), John Tierney brings us the God-Oppenheimer-Einstein Dice Puzzle.
The name is actually a little misleading. God himself really plays no part in the puzzle, except as the guy who explains the game to Oppenheimer and Einstein, tells them the rules, and gives them the dice. You don’t need God to do that. God’s just there for the in-joke: he’s proving Einstein wrong by showing that he does in fact “play at dice.”
The problem is essentially this: Oppenheimer and Einstein are going to have a game where they each roll dice, and the highest number wis. Oppenheimer is given blank dice and has to write the numbers 1 to 18 on the 3 dice in any way he chooses, then Einstein chooses one and he chooses one, following which they have a “dice war.”
what’s Oppenheimer’s best strategy?
Obviously there is an element of chance, because regardless of whoever has the best dice, an unlucky throw still loses. But if they have many throws, the better dice will win out.
The answer is that Oppenheimer can always win. He can make three sets of dice, where the first dice beats the second, the second beats the third, and the third beats the first (like scissors paper rock).
The numbers on each dice would be
dice one: 1 2 9 10 17 18
dice two: 5 6 7 8 15 16
dice three: 3 4 11 12 13 14