A domino is a 2 x 1 tile. One face is blank; the other comprises two squares on each of which is engraved dots to the value of a number between 0 and 6 inclusive. Noting that the combinations 1 | 6 and 6 | 1 for example are regarded as the same, you might like to determine how many dominoes make up a full set.
When not used as ‘falling soldiers’(!) dominoes are placed flat on a table in line or at right angles with squares of the same number adjacent. You might like to try placing all the dominoes in a 15 x 15 square framework. Or in seven 3 x 3 square frameworks. Another idea is to set up a 7 x 8 matrix with the numbers 0 to 6, each number occurring eight times. These are the squares, which the dominos have. The squares should be the same size as the domino squares. Now see if you can cover the matrix with the set of dominoes.
A different (but easy) problem is to take an ordinary chess board and delete two opposite corner squares. Can you exactly cover this mutilated chess board with (an extended set of) dominoes?
http://www.mathematische-basteleien.de/dominos.htm
http://en.wikipedia.org/wiki/Mutilated_chessboard_problem
