3 × 4

complete

smallest rectangle: 3 × 4

**Proposition.** Any rectangle tiled by the A hexomino has one side
divisible by 4.

**Proof.** It suffices to show that it doesn't tile any
(4m + 2) × (4n + 2) rectangle. Consider the numbering

(x, y) |---> { 1 if x and y are both even { 0 otherwise.

No matter how it is placed, each A hexomino covers an odd total. Also, a (4m + 2) × (4n + 2) rectangle covers an odd total. However, it would be tiled by an even number of A hexominoes, which cover an even total, a contradiction. QED.

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Updated May 25, 2005.