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Rectangles and U Pentominos (Posted on 2016-03-08) Difficulty: 3 of 5
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.

See The Solution Submitted by Brian Smith    
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Possible solution. | Comment 1 of 4
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
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