Paper-Cutting Trick

Image: a hand cutting an index card and a boy holding a paper ring around his head

You can bet a friend that you can put your head through a hole in a 3x5 inch (7.6x12.7 centimeter) file card—and win!


  • One 3x5 inch (7.6x12.7 centimeter) file card
  • Scissors


1. Fold the file card in half lengthwise and make 13 partial cuts widthwise. First cut through the folded side, then turn the card around and cut toward the fold. Keep repeating the process. (Cut to within a quarter inch (half centimeter) of the edges of the card.)

2. Very carefully open the card and cut lengthwise along the fold. Do not cut the two end sections.

3. Gently stretch the card as far as it will go and put it over your head.


The secret to this trick comes from a branch of mathematics called topology. It teaches that figures can be stretched without changing their area.

Text by National Geographic Kids staff
Illustration by Tony Anthony