No room! No room!they cried out when they saw Alice coming.

—Lewis Carroll,
*Alice's Adventures in Wonderland*

The *exclusion problem* is to remove as few cells as possible
from a given region of the plane so as to exclude a given polyform.
*Equalization problems* involve equalizing the distribution
of cells within a region.
The *variegation problem* is to color the cells of the plane with
as few colors as possible so that a given polyform, no matter where it lies
in the plane, has cells of all different colors.

Hexomino Exclusion. Exclude a hexomino from a checkerboard. | |

Polyking Exclusion. Exclude a polyking from a checkerboard. | |

Polyiamond Exclusion. Exclude a polyiamond from the plane. | |

Polyhex Exclusion. Exclude a polyhex from the plane. | |

Polycairo Exclusion. Exclude a polycairo from the plane. | |

Two-Pentomino Magic Squares. Arrange copies of two pentominoes in a square grid to place the same number of cells in each row and column. | |

Polyabolo Magic Squares. Arrange copies of a polyabolo in a square grid to place the same number of cells in each row and column. | |

Polyiamond Variegation. Color the cells of the polyiamond plane so no copy of a polyiamond has duplicate colors. | |

Polyhex Variegation. Color the cells of the polyhex plane so no copy of a polyhex has duplicate colors. |

Back to Polyform Curiosities.

Col. George Sicherman [ HOME | MAIL ]