Make the hole

  1. Trace a dime. Put a dime in the middle of the paper and trace around it with a pen.
  2. Cut it out. Fold the paper across the middle of the circle and cut along the half-circle line, so you get a clean round hole when you unfold it. Lay the dime on the hole to show it fits and the quarter on the hole to show it obviously does not.
  3. The challenge. Hand over the paper and the quarter. Let them try. They may stretch it, tear it, or ask for a smaller quarter.

The solution

  1. Fold across the hole. Fold the paper in half, with the crease running straight through the center of the hole. The hole becomes a half circle on the fold.
  2. Drop the quarter in. Put the quarter inside the fold so it rests in the half circle, with its edge poking down into the opening.
  3. Bend the paper up. Hold the folded paper by its two ends, either side of the hole. Bring your hands up and toward each other, so the paper curves upward like a smile and the folded edge straightens out.
  4. Watch it go. As the paper bends, the curved edge of the hole stretches into a long, nearly straight slot. Keep bending gently and the quarter slips through and drops onto the table. The paper is not torn.

Why it works: the size of a hole is not only its width but the length of its edge. Bent open, the hole's edge becomes a slot half as long as its circumference: about 28 mm for a dime-sized hole, more than a quarter's 24.3 mm width.

Do not upgrade the coin

A half dollar (30.6 mm) is wider than the slot and will not pass a dime-sized hole, however politely you bend. If you are outside the US, test your own coins: the coin that passes must be narrower than about one and a half times the diameter of the traced coin.

Presentation

This is a challenge, not an illusion, so let people try first. The longer they struggle, the better the solution plays. Milo prefers to say nothing at all, fold, bend, and slide the paper back across the bar.

Credit where due: A classic recreational-math puzzle. The numbers: a US dime is 17.91 mm across, so its traced circle has a circumference of about 56.3 mm and folds into a slot about 28.1 mm long. A quarter is 24.26 mm across and fits. A half dollar, at 30.61 mm, does not.

Next: Which hand holds the penny?