Pairs of Hexominoes in Rectangles
There are 25 non-rectifiable hexominoes labelled A to Y below where the table shows the smallest known rectangle for each pairing. A yellow background indicates that the rectangle has been shown to be the smallest; a red background shows that the pairing cannot form a rectangle; and a green background indicates that research is not complete. No pairing of hexominoes H to Y is possible nor can X or Y pair with any other hexomino. These data have been supplied by Mike Reid.
Impossibility proofs for these pairings are often quite complex. An example of a proof for the G and N combination is shown here.From the table above it can be seen that there are a number of pairs which do not form rectangles. The question arises - are there any triplets of hexominoes where no pairing forms a rectangle but the triplet does? A number of examples of this are shown below most of which have been found by Mike Reid. For a list of known rectangles for various triplets click here.