IMSO 2008 Mathematics – Taiwan Selection – Exploration Question 3

Triominoes is played with a set of tiles, all sides of which are equal in length. Each vertex of every tile is marked with one of the digits from 0 to 5. Different vertices on the same tile may have the same digits, so the two examples below are both included.



All possible tiles, including those with duplicate or triplicate digits, are in the set. How many possible tiles are there? The following mirror-image tiles are different tiles.