Take a piece of paper and cut out a perfect circle with diameter 1 inch.

What is the diameter of the largest unaltered coin which may be passed through the hole without tearing it?

(Consider the coin to be very thin, and the paper to be very flexible and tear resistant, but not at all stretchy.)

   In spite of Charlie's foldings, I really cannot see how the circle can be legally distorted so that 2 points on it will be at a (3-dimensional) distance greater than 1. It looks to me like any distortion will only make points closer, or at best, the same distance apart.

   Furthermore, genuinely proving a maximum distance would seem extremely  difficult -- even formulating the allowable transformations of the paper would seem hugely challenging.

   So I'm going to say that those who claim otherwise are somehow mistaken -- the answer is 1 inch.

Posted by Richard on 2006-05-29 15:21:32