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Found problems: 1

2018 Saint Petersburg Mathematical Olympiad, 7
Tags: catalan numbers , combinatorics
The checker moves from the lower left corner of the board $100 \times 100$ to the right top corner, moving at each step one cell to the right or one cell up. Let $a$ be the number of paths in which exactly $70$ steps the checker take under the diagonal going from the lower left corner to the upper right corner, and $b$ is the number of paths in which such steps are exactly $110$. What is more: $a$ or $b$?