# Square made up with polyominoes

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.

• If diagonal cuts are allowed, are they really polyominoes? – Rand al'Thor Jun 27 '20 at 21:00
• Oh sorry, you can’t make diagonal cuts. @Randal'Thor – Display maths Jun 27 '20 at 21:08
• Yes you’re right @hexomino – Display maths Jun 27 '20 at 21:08
• 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? – msh210 Jun 27 '20 at 21:23
• If we can't flip pieces, how do we get reflections? – msh210 Jun 27 '20 at 21:25

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:

Text version:
ggggbb ggggbb
g gg b g gg b
grgbbb rrgbbb
becomes
gggg gggg
gbgg gbgg
gbgb rbgb
rbbb rbbb

• Nice! There is one left. – Display maths Jun 28 '20 at 12:53
• @Displaymaths found it! Nice puzzle! – Glorfindel Jun 28 '20 at 13:05
• Oh sorry, there is a last one. – Display maths Jun 28 '20 at 13:11
• Oh, of course, it's a small variation. I'll add it in a few minutes. – Glorfindel Jun 28 '20 at 13:13
• There are only two more if you allow flipping, if you want to get those as well since you are on a roll... – theonetruepath Jun 28 '20 at 16:05

Here's one solution:

Other solutions may be possible.

• True, there are more. – Display maths Jun 27 '20 at 22:09