Pentominos is a geometric puzzle in which the object is to place 12 polygons to completely fill, without overlaps, a rectangular board with 60 squares. The 12 polygons are formed by all the unique arrangements of 5 equal squares and are commonly labeled by the letters which they resemble (right).

Since the 12 polygons are 5 squares each, the board can be any size that contains 60 squares: 6x10, 5x12, 4x15, or 3x20. This app currently provides just a 5x12 board, which will likely provide you with plenty of challenge.

For a 5x12 board, there are 1010 unique solutions. Each solution has 4 variants which are considered equivalent as they are simply reflections or rotations of each other. For example, given solution 1 (right) , 2 is 1 rotated 180°, 3 is 1 reflected, and 4 is 1 rotated and reflected. It seems that it would be easy to find solutions if there are 1010 of them, but the puzzle is more difficult than it appears.

For more background information on pentominos, including some formal discussion, see Pentomino in Wikipedia.

The Pentominos app has the following features to enable you to easily play the game:

• You can rotate each piece clockwise or counterclockwise with simple taps.

• You can flip each piece vertically or horizontally with simple swipes.

• You move a piece to the board by tapping a square on the board.

• Once a piece is on the board, you can move it to another square by tapping that square.

• You remove a piece from the board by tapping its home base.

• You can remove all pieces from the board with one tap.

• You can opt for the app to indicate your progress towards a solution.

• You can opt for the app to track your unique solutions.

How to Play Pentominos >