Monday, November 8, 2010

Acute dissections

Puzzle:
Take a 45-45-90 triangle, and cut it into acute triangle pieces.  That means each triangle piece must have angles that are strictly less than 90 degrees.  Try to do this with as few pieces as possible.

Afterwards, try the same with a square.

You may send solutions to skepticsplay at gmail dot com.

[Note: this is not an original puzzle.]

solutions posted

drransom (aka toillE) said...

As is usual with your puzzles, it's harder than it sounds. I've figured out that any solution must be asymmetric across the line of symmetry (otherwise it's recursive) but where to go from there is the tricky part.

miller said...

That just means that there can't be a cut all the way through the line of symmetry. It could still be symmetric.

Eduard said...

Triangel: 7
Square: 8

drransom said...

Damn, you're right. Shows my competence with geometry!

Reminds me of multivariable, actually. Setting up the problem often depended on applying "geometric intuition," and I always sucked at that. I tried to prove that the setup was correct instead, which was very time-consuming