My daughter has been looking at some old popular maths books I have on the shelf, and used the following question to check whether my brain still works:

If you want to subdivide an obtuse triangle (i.e. one angle is > 90 deg) into acute triangles (all angles < 90deg), how many  acute triangles do you need at least ?  There must be no blunt angle left over in the end!  (note that right angles are excluded by both definitions, and the length of the sides doesn't matter. there is a solution that works for all obtuse triangles, regardless of their other properties -- so don't try to prove that there is no solution!)

If that's too easy, start with a square (handy hint: you will want to draw 2 semi-circles to crack this one!)

If both are too difficult, start with an acute triangle.

enjoy !

PS I was relieved to find that my brain is still functional (just about).

PPS I'll post the solutions in a new blog entry in a week or so. (or whenever I have nothing more urgent to blog about ...)