Self-sorting Cards

cards with holes and slots

No matter how you mix this stack of cards, it only takes four quick operations to sort them back into numerical order. These cards use binary numbers to do their magic. Binary numbers are numbers in the base two numeral system that are composed of ones and zeros. The pattern of slots and holes along the top edge of each card corresponds with the ones and zeros of the card number.


  • Sixteen business cards or index cards
  • A hole-punch. Preferably the type that punches a single hole at a time.


  1. Punch four evenly-spaced holes along the top edge of one card.
  2. Punch four holes in the rest of the cards using the first card as a template so that the all the holes line up.
  3. binary numbers 0 to 15Number the cards from zero to fifteen and pencil in the binary representation of the number on the card.
  4. card number sevenCut a slot that extends from the hole to the edge of the card wherever there is a one is the binary number. For example the number 7 is 0111 in binary. So for the card number seven, leave the first hole on the left as it is, but cut a slot to the next three holes.
  5. Mix the cards up.
  6. Sort the cards by placing an opened paper clip into the first hole on the right and lifting up. All the cards that have a slot at that position should remain in your hand. Place the cards that were lifted by the paper clip in front of the others. Repeat this for each of the remaining holes moving from right to left. Each time place the cards from the paper clip on the front of the stack. After four operations, the stack is in order.