# An other dicey challenge

Suppose we have the following two dice:

• a fair, four-sided die with numbers $$D_4 = [1,2,2,3]$$
• a fair, nine-sided die with numbers $$D_9 = [1,3,3,5,5,5,7,7,9]$$.

Rolling these two dice and adding their outcomes together results in a sum between 1 and 12. Remarkably, the probability distribution of this sum is the same as that for two regular, six-sided dice. That is, $$(D_4 + D_9) \sim (D_6 + D_6)$$.

Now, can you construct another pair of four-sided and nine-sided dice with positive integers different from the above but with the exact same property of $$(D_4 + D_9) \sim (D_6 + D_6)?$$

If $$A$$ is the highest number on the four-sided die and $$B$$ is the highest number on the nine-sided die, post the product $$A\cdot B$$.

Inspiration

×