Coin through a hole
Take a piece of paper and cut out a perfect circle with diameter .
What is the diameter of the largest unaltered coin which may be passed through the hole without tearing it?
Pick the largest diameter that does not exceed the answer.
(Consider the coin to be very thin, and the paper to be very flexible and tear resistant, but not at all stretchy. You could also use a piece of film such as a plastic grocery bag.)
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1 solution
The theoretical limit is π c m
If the paper is folded across the center of the hole, the hole becomes a half-circle that can be flattened out by pulling back the opposite sides of the crease. The hole then becoms a slit whose width is nearly half the circumference of the circle. The answer is then half the diameter of the hole minus the width of the coin.
3 c m gives enough room for a thin coin.