Usually, you can make a triangle out of any three pencils, but not always. And you can NEVER make a triangle out of two matches and a telephone pole. So three sticks that form a triangle are doing something special.
Puzzle 1: Suppose you have five sticks with the property that any three of the sticks will form a triangle.
Prove that it must be possible to make an acute triangle from three of the sticks. An acute triangle is one in which every angle is less than 90 degrees.
I give up, show me the solution.
This puzzle was kindly supplied by Scott Hansen.