# Scaled Pentomino Pairs Tiling a Rectangle with the Four Corner Cells Removed

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

A pentomino is a figure made of five squares joined edge to edge. There are 12 such figures, not distinguishing reflections and rotations. They were first enumerated and studied by Solomon Golomb.

Here I study the problem of arranging copies of two pentominoes at various scales to form a rectangle with the four corner cells removed.

• Pentomino Pairs Tiling a Rectangle with Four Corner Cells Removed
• Scaled Pentomino Triples Tiling a Rectangle with Four Corner Cells Removed
• ## Nomenclature

I use Solomon W. Golomb's original names for the pentominoes:

## Table of Results

This table shows the smallest total number of copies of two scaled pentominoes known to be able to tile a rectangle with four of its corner cells removed, using at least one copy of each pentomino.

FILNPTUVWXYZ
F * 12 10 4 4 34 4 10 4 × 10 ×
I 12 * 6 9 6 12 22 9 19 4 4 12
L 10 6 * 6 4 10 4 10 8 13 6 10
N 4 9 6 * 4 9 10 16 10 9 4 10
P 4 6 4 4 * 4 7 4 4 9 4 7
T 34 12 10 9 4 * 10 72 10 × 20 ×
U 4 22 4 10 7 10 * 40 8 4 8 46
V 10 9 10 16 4 72 40 * 12 × 10 13
W 4 19 8 10 4 10 8 12 * 9 8 52
X × 4 13 9 9 × 4 × 9 * 4 ×
Y 10 4 6 4 4 20 8 10 8 4 * 12
Z × 12 10 10 7 × 46 13 52 × 12 *

## Solutions

So far as I know, these solutions use as few tiles as possible. They are not necessarily uniquely minimal.

### 72 Tiles

Last revised 2023-07-09.

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Col. George Sicherman [ HOME | MAIL ]