A domino is a 21 rectangular piece of wood. On each half of the domino is a number

Chapter 51, Problem 51.3

(choose chapter or problem)

A domino is a 21 rectangular piece of wood. On each half of the domino is a number, denoted by dots. (See the cover of this book.) In the figure, we show all 5 2 D 10 dominoes we can make where the numbers on the dominoes are all pairs of values chosen from f1; 2; 3; 4; 5g (we do not include dominoes where the two numbers are the same). Notice that we have arranged the ten dominoes in a ring such that, where two dominoes meet, they show the same number. For what values of n 2 is it possible to form a domino ring using all n 2 dominoes formed by taking all pairs of values from f1; 2; 3; : : : ; ng? Prove your answer. Note: In a conventional box of dominoes, there are also dominoes both of whose squares have the same number of dots. You may either ignore these doubles or explain how they can easily be inserted into a ring made with the other dominoes.