You have 8 wooden right-angle isosceles triangles (the lengths of the two lines that make up the right angle are equal). These are numbered from 1 to 8. Every single triangle is equal in size. Using these triangles how many DIFFERENT squares can you make. (Not neccesarily all at once)

Note: A square must be entirely wooden in order for it count. A square cannot have the exact same combination of triangles that have already been used.e.g if you used triangles 1 and 2 in one combination you can never have a square made from only triangles 1 and 2. (However triangles 1 and 3 would make a distinct square)

I think there are 3 possible sizes of squares that can be made:

1. using 2 blocks (longest sides together, such that the shortest edges form the sides of the square)
2. using 4 blocks (shortest sides together such that the longest sides form the edges of the square)
3. using 8 blocks (four squares of type 1, such that the sides of the square are twice the length of the shortest side of the triangle)

By my reckoning there are 28 possible combinations of type 1 (8C2); 70 possible combinations of type 2 (8C4); and 1 possible combination of type 3. Which makes 99 combinations altogether.

Posted by fwaff on 2003-01-20 06:13:11