Suppose that each side of every piece in the domino game (see Example 2.16)

is marked with a number of spots, where this number is chosen from the set

{0, 1, 2,…, n − 1}. For which value of n, 66 different tiles can be produced (at least)? In that case, i.e. in a domino with 66 different tiles, what is the probability if we select a tile at random that the numbers of spots on the two sides of the tiles

(i) are equal (e.g. a double 4)?

(ii) differ by one (e.g. 4–5)?

(iii) differ by two (e.g. 3–5)?