Hexomino Pair Rectangles

Introduction

Here are the smallest known rectangles that can be formed by every pair of hexominoes, using at least one of each. These tilings originally appeared as links in the August 2010 issue of Erich Friedman's Math Magic.

Mike Reid found the last two tilings. Patrick Hamlyn independently found the solutions with 48 or fewer tiles.

See also Scaled Hexomino Pair Rectangles.

Hexomino Numbers

Table of Results

Of 595 possible pairs of hexominoes, 356 are known to be able to tile a rectangle.

 1234567891011121314151617181920212223242526272829303132333435
1 312144143143914391455145361432391439?1443910032520350426??
2 386410412491410654610122020612164144161646320142024
3 1282861261220102066612446814441464201044624416449664
4 146284446××54××68×46×××1230××16×××42812×?××
5 4464424?2672?448?41846?4104412612342026???
6 14101244423?49150?281820944862414?4102814?96??6?816496??
7 34664338410446124144624475410865453624812
8 141212×??3×400××4430×40?×××24?××?×××4?5×?××
9 39420×26498×44××206×12?×××6?××?×××286612×?××
10 149105472150440044?5614444281526??1650?8??96?6136480???
11 391420×??10××?×442×28100×××1814××?×××28?12×?××
12 14106×4284××56×2430×25?×××16?××?×××25166×?××
13 5666418444201442444463914146422401414142542034101410
14 556882063064423046320151854244281520303032610183648
15 14412×?9412××44××464?×××1050××14×××4?12×?××
16 564444844012282825434164014384042614141414477381450132
17 36104618614??152100?620?16120100?4????64168?36145414??
18 14126×4244××6××3915×40120××18?××?×××408012×?××
19 32208×6146××?××1418×14100××12?××?×××4?14×?××
20 392014×??24××?××145×3?××12?××?×××40??×?××
21 146412444246161816641084181212103010282224242161018102836
22 3912430101027??5014?4245040????10??????141121228???
23 ?1614×485××?××2242×42?×××30?×?×××87012×?××
24 1446×4144××8××408×6?×××10?×40×××30410×?××
25 41441612?10?????14151414????28??40???14?12????
26 39420×6968××?××1420×1464×××22?××?××20?15×?××
27 1001610×12?6××96××1430×14168×××24?××?××30?18×?××
28 321644×3?5××?××2530×14?×××24?××?××40?12×?××
29 546446442862825434434044021483014203040339656356
30 206242820?5?66136?16202?77680??16112704????316????
31 33412283512412636123141214?101212101215181231620?6024
32 5042016×61646××80××410×854×××1828××?×××96?20?××
33 261444??9624?????1018?1414???10???????56?????
34 ?2096×??8××?××1436×50?×××28?××?×××3?60×?×
35 ?2464×??12××?××1048×132?×××36?××?×××56?24×?×
 1234567891011121314151617181920212223242526272829303132333435

2 Tiles

3 Tiles

4 Tiles

5 Tiles

6 Tiles

7 Tiles

8 Tiles

9 Tiles

10 Tiles

12 Tiles

14 Tiles

15 Tiles

16 Tiles

18 Tiles

20 Tiles

22 Tiles

24 Tiles

25 Tiles

26 Tiles

28 Tiles

30 Tiles

32 Tiles

36 Tiles

39 Tiles

40 Tiles

42 Tiles

44 Tiles

48 Tiles

49 Tiles

50 Tiles

54 Tiles

56 Tiles

60 Tiles

64 Tiles

66 Tiles

70 Tiles

72 Tiles

77 Tiles

80 Tiles

94 Tiles

96 Tiles

100 Tiles

102 Tiles

112 Tiles

120 Tiles

132 Tiles

136 Tiles

150 Tiles

152 Tiles

164 Tiles

168 Tiles

400 Tiles

504 Tiles

Last revised 2022-11-18.
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Col. George Sicherman [ HOME | MAIL ]