Two tetrahedral (four sided) dice, one red and one blue, each with the numbers 1, 2, 3 and 4 on the faces, are rolled and the numbers showing on the two dice are added to give the total score.

a        Show that, out of the 16 different ways the dice can land there is one way to get a total of 2 or 8, two ways to get a total of 3 or 7, three ways to get a total of 4 or 6 and four ways to get 5.

Two differently numbered tetrahedral dice, one green and one yellow, are rolled. The green die has 1, 2, 2, 3 on its faces and the yellow die has 1, 3, 3, 5 on its faces. The numbers showing on the two dice are added to give the total score.

b       Show that, with these dice, the number of ways of getting each possible total is exactly the same as with the original dice.

Two ordinary cubical dice are rolled. The numbers showing on the two dice are added to give the total score.

c        What is the number of ways of getting each possible total?

Two new and unusual cubical dice are rolled. The numbers showing on these two dice are added to give the total score.

d       What numbers could be on the faces of these two dice so that the number of ways of getting each possible total are exactly the same as with the ordinary cubical dice?

How many different sets of dice like this are there?