Try this counting problem, its really interesting!
When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.
Find all possible ways of numbering two 6-sided dice with positive integers (not necessarily distinct), so that when they are rolled, the 36 possible outcomes for the sum of the two rolls are the same as the 36 possible outcomes for the sum of two standard 6-sided dice.
+2375
Find all possible ways of numbering two 6-sided dice with positive integers (not necessarily distinct), so that when they are rolled, the 36 possible outcomes for the sum of the two rolls are the same as the 36 possible outcomes for the sum of two standard 6-sided dice.
There's an infinite amount of integers to choose from, so
you can re-number the first die any way you want to, just as
long as you re-number the second die the same way as the
first. I don't like to use infinity as a number, but you never
come to the last number, so I have to.
Rolling one die twice is the same as rolling two dice once.
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