Suppose you can replace one number cube with a nonstandard number cube, where any of the numbers 1 through 6 can appear on multiple faces. How can you arrange the numbers on the nonstandard cube so th

Suppose you can replace one number cube with a nonstandard number cube, where any of the numbers 1 through 6 can appear on multiple faces. How can you arrange the numbers on the nonstandard cube so that the mean of the rolls is the same as that of two standard number cubes, but the standard deviation is as large as possible? What is this value? Explain your thinking.