Being a teacher, I am constantly coming up with math problems for my students to solve that are...non-traditional...to say the least. I find that these type of problems are a motivation for our more advanced students to think outside the box and to really take the process of thinking mathematically to the extreme.
So, being the math nerdfighters, I was wondering if I could poll your brains for problems you have pondered (either of your own creation or from other sources). I personally would love to try to think my way through a few.
As an example, here's one I pondered for a while:
Oddie is tied to pole in John's backyard by a 15 foot rope. Oddie, as always, gets picked on my Garfield who prompts him to run around the pole in circles. The rope wraps around the pole at a rate of 4 inches per rotation (so the effective radius of the circle decreases by 4 inches every time Oddie completes a 360° arc). The question is: How far (as in distance, not number of times around the pole) does Oddie run before the rope is completely wrapped around the pole?
I look forward to seeing your mind twisters and any solutions you may have to mine little puzzle.