# Square forming challenge

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

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

Bonus question: why the point deduction for cuts?

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.