A 3 x 6 rectangle has 2 holes in it as shown. Can you cut it into 3 polyominoes with different areas so that they can form a square? The pieces can’t be flipped when they form the square and two solutions are the same if they are identical after rotation and/or reflection.
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$\begingroup$ If diagonal cuts are allowed, are they really polyominoes? $\endgroup$– Rand al'ThorJun 27, 2020 at 21:00
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1$\begingroup$ Oh sorry, you can’t make diagonal cuts. @Randal'Thor $\endgroup$– Display mathsJun 27, 2020 at 21:08
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1$\begingroup$ Yes you’re right @hexomino $\endgroup$– Display mathsJun 27, 2020 at 21:08
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$\begingroup$ You say "a rectangle has 2 holes". Is that the statement of the problem, and the picture is just one possible example? Or is the picture the only one you're asking about? $\endgroup$– msh210Jun 27, 2020 at 21:23
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$\begingroup$ If we can't flip pieces, how do we get reflections? $\endgroup$– msh210Jun 27, 2020 at 21:25
2 Answers
For this one, you don't even need to rotate the pieces:
Text version:
rrbggg
r br g
rrrrgg
becomes
gggb
rrgb
rggr
rrrr
And the final ones, which are closely related:
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Text version:
ggggbb ggggbb
g gg b g gg b
grgbbb rrgbbb
becomes
gggg gggg
gbgg gbgg
gbgb rbgb
rbbb rbbb
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$\begingroup$ Oh, of course, it's a small variation. I'll add it in a few minutes. $\endgroup$ Jun 28, 2020 at 13:13
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$\begingroup$ There are only two more if you allow flipping, if you want to get those as well since you are on a roll... $\endgroup$ Jun 28, 2020 at 16:05