I have two distinct, fair, six-sided dice that have positive integers on their sides. Neither of the dice is a "normal" die (i.e., with 1, 2, 3, 4, 5, and 6 on the sides).
Interestingly, the probability distribution of the sum of rolling these two dice is exactly the same as that of the sum of rolling 2 "normal" dice.
Let the numbers on the first die be and those on the second where and
Submit your answer as the product of these two 6-digit integers:
The dice above have 1,1,2,2,4,8 and 1,2,3,3,4,4 on their sides. Their sum can produce the same numbers (2-12) as the sum of two ordinary dice, but not with the same probability distribution.