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Cut a square into 3 pieces
Rearrange them anyway you want
Cuts must be straight (but can begin/end anywhere).

  • Scoring method 1:
    For each visible square 1 point
    For each cut -1 point
  • Scoring method 2:
    For each square 1 point
    For each cut -1 point
    enter image description here

What it the highest score possible? (separate for both scoring methods)

Bonus question: why the point deduction for cuts?

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Answer for both methods

You can cut out two combs. Rotate one by $90°$. Number of squares $O(N^3)$ number of visible squares $O(N^2)$ number of cuts $O(N)$, therefore arbitrarily high score possible in either case.

enter image description here enter image description here

Bonus question:

Whatever the purpose it clearly failed.

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  • $\begingroup$ I missed that one, should have added an extra constraint that I did not think was needed... $\endgroup$
    – Retudin
    Oct 17 '20 at 17:29

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