IBM Ponder This #120 · April 2008

Suppose you are given a collection of squares and equilateral triangles (of unit side). You are asked to form convex polygons by sticking the squares and triangles together with their sides aligned. These polygons must also have unit sides (so that for example sticking two squares together to form a domino does not count). How many distinct polygons can be formed in this way (including polygons formed by a single square or triangle)? List them, for each giving the
length of the perimeter, the number of squares and the number of triangles used to form it. We don't expect (nor will we provide) a proof that the list is exhaustive but please try to find all the examples before submitting a solution.

Solution

Best opened after a real attempt

To be added.