the twelve pentominoes

Pentominoes are shapes formed by connecting five squares together in different ways. There are many interesting puzzles that you can create with these simple pieces.


  1. Cut out the pieces from the pattern (out of boxboard, cardboard or craft foam sheets).
  2. Try to arrange the twelve pentominoes to form an 8 × 8 square (like a chess board) with the middle four squares left blank.
  3. Try to arrange them into an 8 × 8 square with a square missing from each corner.
  4. Try to arrange them into a 6 × 10 rectangle. Try a 5 × 12, a 4 × 15, and a 3 × 20 rectangle.


  • The twelve shapes represent all the possible ways you can connect five squares along their edges if you don't count reflections.
  • Pentominoes and other "polyominoes" were invented by Solomon Golomb when he was a 22 year old graduate student at Harvard.