This problem has stumped me for a little while:
Given a quadrilateral with integer side lengths, what is the probability that three of its sides can be removed and reassembled to form a triangle?
Of course, this problem will use the fact that each side length of a triangle must be less than the sum of the other two side lengths, and that in a quadrilateral, each side length will be less than the sum of the other three side lengths. But how can I use combinatorics to count this?
Note: I made this problem up, so if it is a "bad problem" (cannot be done) please let me know why.
Thanks!