Puzzles
Two oddly numbered dice roll exactly like a normal pair
A standard pair of dice, numbered 1-6 each, produces the classic bell-shaped spread of totals from 2 to 12. Can you find a different pair of six-sided dice, still only positive numbers, whose totals land on exactly the same numbers with exactly the same probabilities — without either die matching a standard 1-6 die?
Reveal the answer
Yes: one die reads 1, 2, 2, 3, 3, 4 and the other reads 1, 3, 4, 5, 6, 8. Named 'Sicherman dice' after George Sicherman, who found them and shared them with Martin Gardner, who popularized them in Scientific American in 1978. It's the only other whole-number solution that exists.
— Martin Gardner, Mathematical Games column — Scientific American, February 1978