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MathNet 2020 — Math Olympiad Vault — Part 02 Question 48

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 02

Question 48

A $20 \times 20$ grid is divided into 400 unit cells of size $1 \times 1$. Clara colors each cell black or white, then Isabelle cuts the grid into rectangles along grid lines. Every rectangle must contain at most 2 black cells. Isabelle gives Clara one chocolate for each rectangle containing 0 or 1 black cell.

Isabelle minimizes the number of chocolates, while Clara chooses her coloring to maximize it. How many chocolates will Isabelle give Clara?