65718 – We Solve Problems

#### Dissections with certain properties , Examples and counterexamples. Constructive proofs , Pigeonhole principle (other)

In a $10 \times 10$ square, all of the cells of the upper left $5 \times 5$ square are painted black and the rest of the cells are painted white. What is the largest number of polygons that can be cut from this square $($on the boundaries of the cells$)$ so that in every polygon there would be three times as many white cells than black cells? $($Polygons do not have to be equal in shape or size.$)$

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