# Multiple Compatibility

The Compatibility Problem is to construct a figure that can be tiled with each of a set of polyforms. Multiple Compatibility involves three or more polyforms.

## Polyominoes

 Holeless Triple Pentominoes. Holeless solutions for Livio Zucca's Triple Pentominoes. Pentomino Odd Triples. Like Livio Zucca's Triple Pentominoes, with an odd number of tiles. Pento-Tetro-Tetrominoes. Given a pentomino and two tetrominoes, find a polyomino that each can tile. Pento-Pento-Trominoes. Given two pentominoes and a tromino, find a polyomino that each can tile. Pento-Pento-Tetrominoes. Given two pentominoes and a tetromino, find a polyomino that each can tile. Quadruple Pentominoes. Given four different pentominoes, find a polyomino that each can tile. Multiple Polyomino Compatibility. Figures that can be tiled by many polyominoes of the same order.

## Polyiamonds

 Triple Hexiamonds. Given three hexiamonds, construct a figure that can be tiled with each. Multiple Polyiamond Compatibility. Figures that can be tiled by many polyiamonds of the same order. Zucca's Challenge Problem for Polyiamonds. Given a set of polyiamonds of the same order, construct a figure that can be tiled with any member of the set and no other.

## Other Polyforms

 Multiple Polyhex Compatibility. Figures that can be tiled by many polyhexes of the same order. Zucca's Challenge Problem for Tetrahexes. Given a set of tetrahexes, construct a figure that can be tiled with any member of the set and no other. Zucca's Challenge Problem for Extrominoes. Given a set of extrominoes, or extended trominoes, construct a figure that can be tiled with any member of the set and no other. Multiple Compatibility for Polypents. Figures that can be tiled by many polypents of the same order. Multiple Compatibility for Pentacubes. Figures that can be tiled by many polycubes of the same order.

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Col. George Sicherman [ HOME | MAIL ]