# Scaled Pentomino Triples 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 three 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 Pairs 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 three 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.

 F I L 7 F I N 7 F I P 4 F I T 10 F I U 7 F I V 8 F I W 7 F I X 16 F I Y 9 F I Z 16 F L N 7 F L P 4 F L T 9 F L U 7 F L V 9 F L W 8 F L X 9 F L Y 4 F L Z 9 F N P 4 F N T 7 F N U 9 F N V 9 F N W 8 F N X 9 F N Y 4 F N Z 4 F P T 4 F P U 7 F P V 4 F P W 4 F P X 9 F P Y 4 F P Z 7 F T U 7 F T V 12 F T W 7 F T X 33 F T Y 12 F T Z 9 F U V 12 F U W 8 F U X 7 F U Y 7 F U Z 7 F V W 10 F V X 28 F V Y 9 F V Z 13 F W X 9 F W Y 7 F W Z 7 F X Y 9 F X Z ? F Y Z 9 I L N 8 I L P 6 I L T 9 I L U 6 I L V 8 I L W 8 I L X 9 I L Y 7 I L Z 9 I N P 5 I N T 8 I N U 8 I N V 8 I N W 8 I N X 4 I N Y 6 I N Z 9 I P T 7 I P U 6 I P V 5 I P W 6 I P X 4 I P Y 6 I P Z 7 I T U 8 I T V 10 I T W 8 I T X 12 I T Y 8 I T Z 13 I U V 6 I U W 10 I U X 5 I U Y 8 I U Z 9 I V W 9 I V X 12 I V Y 9 I V Z 7 I W X 16 I W Y 9 I W Z 9 I X Y 4 I X Z 31 I Y Z 9 L N P 5 L N T 9 L N U 8 L N V 9 L N W 8 L N X 10 L N Y 6 L N Z 8 L P T 7 L P U 7 L P V 8 L P W 4 L P X 7 L P Y 5 L P Z 6 L T U 10 L T V 10 L T W 9 L T X 13 L T Y 7 L T Z 10 L U V 8 L U W 8 L U X 9 L U Y 8 L U Z 8 L V W 9 L V X 10 L V Y 8 L V Z 10 L W X 9 L W Y 8 L W Z 9 L X Y 9 L X Z 17 L Y Z 7 N P T 7 N P U 7 N P V 4 N P W 5 N P X 9 N P Y 4 N P Z 4 N T U 8 N T V 10 N T W 9 N T X 9 N T Y 9 N T Z 10 N U V 10 N U W 8 N U X 9 N U Y 8 N U Z 8 N V W 9 N V X 12 N V Y 7 N V Z 8 N W X 9 N W Y 8 N W Z 9 N X Y 7 N X Z 9 N Y Z 7 P T U 8 P T V 7 P T W 7 P T X 9 P T Y 7 P T Z 8 P U V 7 P U W 4 P U X 7 P U Y 4 P U Z 8 P V W 7 P V X 9 P V Y 4 P V Z 7 P W X 8 P W Y 4 P W Z 8 P X Y 7 P X Z 9 P Y Z 7 T U V 12 T U W 10 T U X 12 T U Y 9 T U Z 14 T V W 12 T V X 69 T V Y 10 T V Z 13 T W X 16 T W Y 10 T W Z 16 T X Y 12 T X Z ? T Y Z 16 U V W 8 U V X 12 U V Y 10 U V Z 12 U W X 8 U W Y 8 U W Z 16 U X Y 7 U X Z 28 U Y Z 10 V W X 10 V W Y 8 V W Z 12 V X Y 9 V X Z 22 V Y Z 9 W X Y 12 W X Z 28 W Y Z 8 X Y Z 12

## Solutions

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

### 69 Tiles

Last revised 2023-07-09.

Back to Polyomino and Polyking Tiling < Polyform Tiling < Polyform Curiosities
Col. George Sicherman [ HOME | MAIL ]