If a figure can be tiled by N 2x3 rectangles it is trivial to place the same number of U pentominoes in that figure.
Find the smallest N such that at least N+1 U pentominos can be placed in a figure tiled by N 2x3 rectangles.
A simple lower bound of Five 2x3 and Six U does not seem possible. In fact, the best I can find uses Eleven 2x3 and Twelve U plus Six unused spaces:
AA
AABBBCCC
DD AABBBCCC
DDEEEFFFGGGHH
DDEEEFFFGGGHH
IIIJJJKK HH
IIIJJJKK
KK
LL
LMMNNXXX
OO LLMNPPQQ
ORRSSMMNNPQTT
OORSUUVVPPQQT
RRSSUVWW TT
XXXUUVVW
WW
Is there a better one? This is a polyform problem variation I have not seen before.

Posted by Jer
on 20160309 09:44:32 