Polyform Exclusion, Equalization, and Variegation

    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.
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 ]