The Tiling the Square Puzzler (solution page)
What approaches did you use to try and solve this puzzler? Can you
prove that your solution is a minimal solution? My first attempt at
a solution was recursive. I successfully tiled the square, but I need
an infinite number of triangles to do it!
My daughter Elise came up with this solution, only requiring 24
triangles.
Jon
Orwant came up with a solution requiring only 14 triangles.
Notice the similarity to the recursive solution.
By reducing Elise's solution, I came up with a solution that requires
only 12 triangles.
By using a pentagon, Roger Kermode
came up with two solutions requiring only 10 triangles!
Vadim Gerasimov is so
clever. By using two overlapping pentagons, he has come up with a
solution requiring only 8 triangles! 
I asked Roger if he could solve the puzzle using obtuse angles.
Here's his solution (only 6):
Can you come
up with a solution that requires fewer triangles? I'll leave it
as an exercise for the reader to come up with a minimal solution for
right angles...