So, in my computer science class, we are given this problem here:
Is it possible to modify the faces on a pair of conventional six-sided dice so as to exactly replicate the probabilities of a normal pair (i.e., there will be only one way of throwing a two, two ways of throwing a three, etc.)- and, if so, how? Only positive integers are permitted on the faces. Write a program that solves this puzzle.
I don't want code, I'll figure that out, but before I do that, I need to see if it is possible, but the question is slightly confusing. Any help?
With a normal pair of dice, the probabilities of $2,3,4,\dots 12$ are $\frac 1{36},\frac 2{36},\frac 3{36}\dots \frac 1{36}$ You are to assign numbers to the faces of two cubes so when you roll those cubes you have the same chance of each sum. As positive integers are only permitted, to make $2$ you need a $1$ on each die. To make $3$ have $\frac 2{36}$ you could have a single $2$ on each die, or you could have two $2$'s on one die. You are to write a program (probably backtracking) to determine the numbers on the faces.