The Embossing Company's Double Twelve Express Dominoes

This set of Double Twelve Express Dominoes was made by the Embossing Company, an Albany, N.Y., firm that produced wooden blocks and puzzles. A sheet of instructions, “HOW TO PLAY DOMINOES,” is included in the box of ninety-six rectangular tiles. Five of these are completely blank and ninety-one are made up of two squares with each square either blank or marked with up to 12 spots, usually called pips.

The traditional American domino set is called Double Six, because each rectangular tile is made up of two squares with each square blank or marked with 1, 2, 3, 4, 5, or 6 pips. In a Double Six set, one can see seven different types of tile depending on the smallest number of pips in one of its squares. If the smallest number of pips is 0, at least one square is blank and there are seven possibilities for the number of pips in the other square, i.e., 0 through 6. If the smallest number of pips is 1, neither square is blank and at least one square has a single pip. In this case there are six possibilities for the number of pips in the other square, i.e., 1 through 6. In general when the smallest number of pips that appear on a square of a tile is k, the other square must have k, k+1, …, 6 pips on it, and it is always the case that there are 7-k numbers on the list k, k+1, …, 6. If we look at all be seven possible types of tiles in a Double Six set, we find that there are 7+6+5+4+3+2+1=28 tiles.

A similar computation can be done for any Double n set of dominoes. I.e., there are n+1 tiles with one or both squares blank, n tiles with no blanks and 1 the smallest number of pips, and n+1-k tiles with no blanks and k the smallest number of pips. This leads to a total of (n+1)+ n+(n-1)+…+1 tiles, i.e., the sum of the first n+1 integers. A mathematical formula known for many centuries says that the sum of the first n integers is n(n+1)/2 so the sum of the first n+1 integers is (n+1)(n+2)/2. For a set of Double Six dominoes n+1 is 7 so we get (7)(8)/2 or 28 tiles. Other common Double n sets include Double Nine, Double Twelve, Double Fifteen, and Double Eighteen. For the Double Twelve set, n+1 is 13 so there are (13)(14)/2 or 91 tiles. In order not to leave empty space in the box, five completely blank tiles were included in this set of Double Twelve dominoes.

These dominoes belonged to Olive C. Hazlett (1890–1974), one of America's leading mathematicians during the 1920s. Hazlett taught at Bryn Mawr College, Mount Holyoke College, and the University of Illinois, after which she moved to Peterborough, N.H. Her set of dominoes was collected from the Carmelite community of Leadore, Idaho. Brothers from this community who had lived in New Hampshire had befriended Hazlett there.

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