# Hexomino Pairs Tiling a Rectangle with One Corner Cell Removed

• Introduction
• Enumeration
• 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 one corner cell removed.

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

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

1234567891011121314151617181920212223242526272829303132333435
1*888815815281541158888411541281528?8152812936828855928??
28*88888208152014888891528288222282082215815828151522
388*2920?84115674288152881941482282854142828645422?88286??
48829*15648??80??928?941???2031??41???8?4????
5882015*544?29??91522?8671528?46722152841428414860???
6158?6454*9????484148??415454?14??20????48?28????
7888849*8841488815920415284154415815149848281515
8152041???8*?????54??????54???????28??????
928815?29?8?*53??208?8????8???????28?41????
1015156780??4?53*??1528?54?31??15??8????4?882???
11412042???14???*?4848?28????1954??????8??????
1215148?9488????*3148??????22???????41288????
13888915418?20154831*15208215314228884131482048?415420815414
148815282248854828484815*2882841288448?1467204854142820192841?
158828???15?????2028*20????2048??8???9?8????
1688898?9?85428?82820*80?2888??20????8?8454??
174191941674120?????1528?80*???20????79?????????
18151541?15544??31??3141???*??28?????????28????
19412848?285415?????4228?28??*?41???????22??????
20282822???28?????288?8???*48??????????????
2115882041445481519228420820284148*4142448284148283142844841
222822283167?15???54?84848?????41*??????8??48???
23?2254?22?4?????41???????42?*????????????
248814?15204??8??3114?20????4??*41?????4????
251520284128?15?????48678?????48??41*?????8????
2628828?41?8?????2020??79???28????*??28??????
271292264?42?15?????4848??????41?????*???28????
28361554?8?14??????54??????48??????*??8????
2988228448928284841411498??22?288???28??*??????
302815??14?8????285428??????31????????*?????
3188848284?418?8202088?28??4??48?288??*????
325592882?60?8??82??819?4????2848?????????*???
33281586???28?????1528?54????4???????????*??
34?15????15?????4141??????48????????????*?
35?22????15?????4???????41?????????????*
1234567891011121314151617181920212223242526272829303132333435

## Solutions

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

### 559 Tiles

Last revised 2023-06-23.

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Col. George Sicherman [ HOME | MAIL ]