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A set of tetrominoes

The Tetrominoes (shown at right) are polyominoes made of four squares. They are most familiar as the elements of the game Tetris.

Tim Bohdan of IBM in Houston, Texas suggested this problem to me,
which he got from the instructions to Blokus:

Place four sets of of differently colored tetrominoes on a board with the following constraints:
(modified Blokus rules) "Modified" blokus rules because we do not start each color in a different corner and have all pieces touching in one continuous chain. A minority of solutions have one or more such chains, but in almost all cases, there is a chain of two and a separate chain of three for each color.

To try your hand at solving this problem, use my Blokus Puzzler Applet.

For a larger set of problems based on Tetra-Tetrominoes (4 sets), see Kadon Enterprises special Twentieth Anniversary page.

For another set of solutions, using different constraints, see Page 2

With Tim's help, encouragement, and fast computers, I wrote a program to find these solutions to the 8x10 and
9x9 (minus one) boards.

Note some of the wonderful properties:

  • Left-right, top-down, or rotational symmetry.
  • Chains of length 5 of touching pieces, rather than 2 and 3.
  • Various rectangles and squares within.
  • Groupings of similar shaped pieces.
  • Solutions where various pieces or groups can be interchanged.

The 35 solutions to the 8x10 rectangle: ( Enlarge 8x10 )

The 35 solutions to the 8x10 rectangle

The 3 solutions to the 9x9 square:
The 3 solutions to the 9x9 square

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