Is it possible to divide a $ 10 \times 10$ board into: $ (a)$ $ 4$ figures of type $ 1$ and $ 21$ figures of type $ 2$? $ (b)$ $ 4$ figures of type $ 1$, $ 19$ figures of type $ 2$, and $ 2$ figures of type $ 3$?
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Source: Ukraine 2005 grade 10
Tags: combinatorics proposed, combinatorics
Is it possible to divide a $ 10 \times 10$ board into: $ (a)$ $ 4$ figures of type $ 1$ and $ 21$ figures of type $ 2$? $ (b)$ $ 4$ figures of type $ 1$, $ 19$ figures of type $ 2$, and $ 2$ figures of type $ 3$?