The following grid has been constructed using the shapes of unfolded cubes.

enter image description here

Determine the minimum number of shapes (red and green) needed to cover the blue grid. The shapes may overlap, but must remain in their original scale.

Rotations of the shapes are accepted, but not mirrorings. The shapes should cover all blue squares and no white squares. If you are not giving a fancy graphics solution, the solution should at least contain a reasonable justification for your number.

  • 2
    $\begingroup$ Mirrorings aren't accepted? But the cross is a mirror of itself! Oh no! $\endgroup$ Commented Dec 10, 2015 at 19:52
  • $\begingroup$ Do you want the full diagram, or just the number of shapes? If it's the full diagram, I would suggest clarifying that. $\endgroup$
    – user20
    Commented Dec 10, 2015 at 20:06

1 Answer 1


The minimum number of shapes is 28:

enter image description here

  • 2
    $\begingroup$ Since this has no overlaps and both pieces have the same number of squares, it must indeed be a minimal answer. Nice job. $\endgroup$ Commented Dec 10, 2015 at 21:14
  • $\begingroup$ Unless I made a mistake or assumption somewhere, this is also the only non-overlapping solution. $\endgroup$
    – JTL
    Commented Dec 10, 2015 at 21:20
  • 1
    $\begingroup$ @JTL I think it's the only one. There are about 8 shapes at the borders which can't be placed differently. Starting from there the rest can be filled. If I knew from the start, that there is a perfect solution, it would have been much simpler. $\endgroup$
    – Sleafar
    Commented Dec 10, 2015 at 21:28
  • $\begingroup$ @Sleafar Yes, that's what I found. I just assumed or hoped there was, or that if there wasn't, finding the optimum would be trivial from a mostly perfect solution. $\endgroup$
    – JTL
    Commented Dec 10, 2015 at 21:33

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