# Hexomino Pairs Tiling a Rectangle with the Four Corner Cells 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 the four 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 Three Corner Cells Removed
• Pentomino Pairs Tiling a Rectangle with the Four 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 its four corner cells removed, using at least one of each hexomino.

1234567891011121314151617181920212223242526272829303132333435
1*866618618181816166610636184632832?663210634616652232??
28*86121881861061046611410161461416661612211010616102122
368*410744321046321016626166261616143216616163274321610846?88
4664*142661465822166661418164?61416618?34?1618666?4?
56121014*3211?1066?14610?1818181866656326321010101418610???
61818742632*21?25??46263280?181632?1632?8????88?4????
768461121*164141610164616161016324161666418161616614462626
818183214??16*10???3632??????32??18????56??????
91861061025410*14?11106666111010661847416??3242864???
101810465866?14?14*?6616676166642??25??6????16?1610???
111663222??16???*?1610?32????1450?6????610??16??
1216101016144610?1166?*163216?10???25??10????42161650???
1364166626163610161616*426321636465616163410323056163632161843614
14666610324326610324*4410181810632666212632364444103258
15106266?806?676?16264*16???361616?46??3216?6?66??
16611161418?16?61632?32416*102?562616??14????32?321632??
17364618181816?666?101610?102*???432?10?3232????6??6
1818102616181610?1142??3618???*??32??4??????66????
194616164183216?10???4618?56??*?32??16????60??????
20321416?66?32?10???56103626???*16??????????????
2186146616432625142516616164323216*36324362632321626116163646
2232143214563216?6?50?163216?32???36*?4????3247?16???
23?16161632?16?18???3466??????32?*10???????????
246666686184661010641410416?4410*1614161614646?1432
2566161832?6?74???32216?????36??16*?????6????
26321616?10?4?16???3026??32???26??14?*??60??????
2710612323410?18?????5632??32???32??16??*???42????
28342174?10?16?????163632?????32??16???*??10????
2961032161488165632166423641632??60?1632?14?60??*??????
301610161818?16?42?1016324??????2647?6?????*?????
3166106646?8616?16164632?66??11??46?4210??*????
325221686610?14?410?50184?166???616?6???????*???
33321046???46???16?4106632????16???????????*??
34?21?4??26?????3632??????36??14?????????*?
35?2288???26?????1458??6???46??32??????????*
1234567891011121314151617181920212223242526272829303132333435

## Solutions

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

### 522 Tiles

Last revised 2023-06-26.

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Col. George Sicherman [ HOME | MAIL ]