# Euler Tour : Dominoes

2. A domino is a 2x1 rectangular piece of wood. On each half of the domino is a number, denoted by dots. In the figure, we show all C(5,2) = 10 dominoes we can make where the numbers on the dominoes are all pairs of values chosen from {1,2,3,4,5} (we do not include dominoes where the two numbers are the same). Notice that we have arranged the ten dominoes in a ring so 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 () dominoes formed by taking all pairs of values from {1, 2,3,. . . , n}? 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,

Does Kn have an Euler Tour?

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#### Solution Summary

The presence of an Euler Tour is determined. The solution is detailed and well presented.