For this problem, define a nonstandard die as a $6$-sided die that is equally likely to come up on each side, but has a different set of numbers than the usual $1,2,3,4,5,6$ on its sides. A standard die will be the usual fair die bearing the numbers $1,2,3,4,5,6$. Is it possible to design a pair of nonstandard dice, with positive integers on the faces (not necessarily all distinct), so that the probability of rolling any given total on those two dice is the same as the probability of rolling that total on two standard dice