Scaled TwoPentomino L Shapes
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.
Only five scaled pentominoes can tile Lshaped polyominoes:
Here I show which pairs of pentominoes can tile an Lshaped polyomino,
using the pentominoes at various sizes.
If you find a solution with fewer tiles than one of mine,
please write!
Bryce Herdt contributed improvements.
Carl Schwenke and Johann Schwenke also contributed improvements.
See also Scaled
TwoPentomino Rectangles.
I use Solomon W. Golomb's original names for the pentominoes:
This table shows the fewest scaled pentominoes known to be
able to tile some Lshaped polyomino, using at least one of each pentomino.
The Lshaped polyominoes are not necessarily the smallest that can be tiled,
only the smallest that can be tiled with the fewest tiles.
 F  I  L  N  P  T  U  V  W  X  Y  Z 
F
 *
 6
 5
 ×
 3
 ×
 2
 4
 ×
 ×
 5
 ×

I
 6
 *
 2
 4
 2
 5
 5
 2
 6
 8
 4
 5

L
 5
 2
 *
 2
 2
 5
 3
 2
 3
 6
 5
 5

N
 ×
 4
 2
 *
 2
 11
 6
 5
 ×
 ×
 8
 ×

P
 3
 2
 2
 2
 *
 2
 2
 2
 4
 6
 2
 2

T
 ×
 5
 5
 11
 2
 *
 42
 6
 15
 ×
 8
 ×

U
 2
 5
 3
 6
 2
 42
 *
 4
 ×
 6
 2
 12

V
 4
 2
 2
 5
 2
 6
 4
 *
 30
 ×
 5
 2

W
 ×
 6
 3
 ×
 4
 15
 ×
 30
 *
 ×
 8
 ×

X
 ×
 8
 6
 ×
 6
 ×
 6
 ×
 ×
 *
 6
 ×

Y
 5
 4
 5
 8
 2
 8
 2
 5
 8
 6
 *
 5

Z
 ×
 5
 5
 ×
 2
 ×
 12
 2
 ×
 ×
 5
 *

So far as I know, these solutions
have the fewest possible tiles. They are not necessarily uniquely minimal.
2 Tiles
3 Tiles
4 Tiles
5 Tiles
6 Tiles
8 Tiles
11 Tiles
12 Tiles
15 Tiles
30 Tiles
42 Tiles
Last revised 20240228.
Back to Polyomino and Polyking Tiling
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Col. George Sicherman
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