Divide the 12 pentominoes into two sets of 6 that form two identical shapes (shapes that overlap exactly...

geometry/pentomino.duplication New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

Divide the 12 pentominoes into two sets of 6 that form two identical
shapes (shapes that overlap exactly when placed on top of each other).
It is well known that two 5x6 rectangles can be filled.  How many
different such duplicated shapes are there?

 FF   N
FF   NN
 F   N
     N

I   L
I   L
I   L
I   LL
I

PP  TTT
PP   T
P    T

U U  V
UUU  V
     VVV

W     X
WW   XXX
 WW   X

Y   ZZ
YY   Z
Y    ZZ
Y

Show solution

Another solution is shown below:

Solution #2:

TTTX
YTXXX
YTLXVVV
YYLLLLV
YIIIIIV

ZNNN
ZZZNN
PPZWFUU
PPWWFFU
PWWFFUU

Can you find any other duplicating shapes?

This pentomino challenge and others can be seen at:

http://www.geocities.com/CapeCanaveral/Hangar/6149/ZCHAL.HTM

-- Ken Zeltner (MangoMan) <autonnic@pacbell.net>, January 1998

[ Editor: no count of the duplicated shapes was found in the collected
postings. ]