August 31st, 2006
How many spots are there in a complete set of dominoes?
It’s a lovely problem that offers the opportunity to discuss methods of calculation, and methods for avoiding mistakes. It links to combinations and permutations, as well as triangle numbers, and is a really simple question to pose. An intermediate question is to ask how many dominoes there are in a set, and establish that solution before continuing to the original question.
What a domino is
Dominoes are tiles divided into two. On either side of the tile there is a number of spots from zero to six. You could write a domino as 1|6, which is a domino with one spot on one side, six dots on the other side. Every possible combination of domino is in a set including ‘doubles’ such as 0|0 and 6|6. Note that 1|6 and 6|1 are considered as the same; since tiles can be turned around freely, order is not important.
What if the maximum number of spots in a domino set changed? How does the number of dominoes change? How does the total number of spots change?