Special Parity

Level pending

Denote \(U(s)\) as a function of the maximum number of unit squares that can be formed in a grid with semiperimeter \(s\) where \(s\in \mathbb Z^+\setminus\{1\}\) [for example, \(U(6)=9\)].

If \(s_1+s_2\) and \(|s_1-s_2|\) are both odd multiples of 2, then what is the parity of \(|U(s_1)-U(s_2)|\)?

Clarification:

  • Unit square is a square with side 1.

This is one part of Quadrilatorics.
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