# Hexomino Pairs Tiling a Rectangle with Three Corner Cells Removed

• Introduction
• Nomenclature
• Table
• Solutions
• ## Introduction

A hexomino is a plane figure made of six squares joined edge to edge. There are 35 such figures, not distinguishing reflections and rotations.

The problem of arranging copies of a polyomino to form a rectangle has been studied for a long time. Here I study the problem of arranging copies of two hexominoes to form a rectangle with three corner cells removed.

If you find a smaller solution or solve an unsolved case, please write.

• Hexomino Pairs Tiling a Rectangle with One Corner Cell Removed
• Hexomino Pairs Tiling a Rectangle with Two Opposite Corner Cells Removed
• Hexomino Pairs Tiling a Rectangle with Two Neighboring Corner Cells Removed
• Hexomino Pairs Tiling a Rectangle with the Four Corner Cells Removed
• Pentomino Pairs Tiling a Rectangle with Three Corner Cells Removed

## Table of Results

This table shows the smallest total number of copies of two hexominoes known to be able to tile a rectangle with three of its corner cells removed, using at least one of each pentomino. Since the parity of the target shapes is unbalanced, at least one of the hexominoes must have unbalanced cell parity. Those hexominoes that do not are shown in green.

1234567891011121314151617181920212223242526272829303132333435
1*×7×××××××?×16×?16××?××25××?×?××××4×?×
2×*3×××××××4×10×1010××19××17××10×10××××13×?×
373*3110?104517?27321719271719452737164742164525??27?164757??
4××31*××××××?×16×219××?××19××37×?××××?×?×
5××10×*×××××?×13×?16××42××62××?×37××××37×?×
6××?××*××××?×42×??××47××?××?×?××××?×?×
7××10×××*×××16×22×213××16××27××16×19××××19×?×
8××45××××*××?×?×??××?××?××?×?××××?×?×
9××17×××××*×?×17×224××?××?××?×?××××?×?×
10××?××××××*?×32×??××?××?××?×?××××71×?×
11?427???16???*??32??????2747?2????38?2????
12××32×××××××?*32×??××?××?××?×?××××?×?×
1316101716134222?1732?32*1617?245457622277145?3745??4549317??
14××19×××××××32×16*3213××32××45××58×52××××17×?×
15?10272??2?2???1732*47????2257?7????37??????
161610171916?13?24????1347*???2724??13???????27???
17××19×××××××?×2×??*×?××?××?×?××××42×?×
18××45×××××××?×45×??×*?××?××?×?××××?×?×
19?1927?424716?????4532????*?37???????72??????
20××37×××××××?×76×?27××?*×?××?×?××××?×?×
21××16×××××××27×22×2224××37×*37××37×37××××2×?×
222517471962?27???47?274557?????37*??????62??3???
23××42×××××××?×71×??××?××?*×?×?××××?×?×
24××16×××××××2×45×713××?××?×*37×?××××2×?×
25?104537??16??????58??????37??37*??????????
26××25×××××××?×37×??××?××?××?*?××××?×?×
27?10??37?19?????4552??????37?????*???32????
28××?×××××××?×?×??××?××?××?×?*×××?×?×
29××27×××××××38×?×37?××72××62××?×?×*××?×?×
30××?×××××××?×45×??××?××?××?×?××*×?×?×
31××16×××××××2×49×??××?××?××?×32×××*?×?×
3241347?37?19??71??317?2742???23?2???????*2??
33××57×××××××?×17×??××?××?××?×?××××2*?×
34?????????????????????????????????*?
35××?×××××××?×?×??××?××?××?×?××××?×?*
1234567891011121314151617181920212223242526272829303132333435

## Solutions

So far as I know, these solutions have minimal area. They are not necessarily uniquely minimal.

### 76 Tiles

Last revised 2023-06-19.

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Col. George Sicherman [ HOME | MAIL ]