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Can you place four red trominoes, four green tetrominoes and four blue pentominoes inside an 7x7 grid, such that:

  • No two polyominoes overlap
  • No two polyominoes of the same color touch each other orthogonally (horizontally or vertically)
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3 Answers 3

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I think this would work as a possibility

enter image description here

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  • $\begingroup$ oooh very nice and pretty! Amazingly that only took you 7 minutes. $\endgroup$ Jun 17, 2022 at 13:07
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    $\begingroup$ @DmitryKamenetsky I suppose that once you decide to solve it rot13(hfvat flzzrgel, naq ynl qbja ornzf sebz gur prager fdhner gb gur rqtrf, gura gur erfg orpbzrf snveyl rnfl fvapr gur erznvavat pbearef pna or svyyrq va nyzbfg serryl). You could make it harder by adding the condition that red and green cannot touch, and I think that has only one solution. $\endgroup$ Jun 17, 2022 at 13:27
  • $\begingroup$ @JaapScherphuis please post that solution $\endgroup$ Jun 17, 2022 at 14:03
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Here is a solution in which the red and green do not touch.

enter image description here

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An obvious upper bound for the maximum number of distinct shapes is $2+4+4=10$, and...

...this solution attains that upper bound: enter image description here

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  • $\begingroup$ What do you mean by 2+4+4? $\endgroup$
    – justhalf
    Jun 19, 2022 at 11:49
  • $\begingroup$ Ah, you mean the shapes, ok I got it now. $\endgroup$
    – justhalf
    Jun 19, 2022 at 12:02

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