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 2016-03-09 09:44:32