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Difficulty: Medium
Category: Combinatorics
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Topics: combinatorics, catalan-numbers, grid-paths, probability
Your team is backtesting a new trading algorithm. The algorithm simulates paths on a grid from (0,0) to (n,n), where n represents the number of trading days. The algorithm only executes trades on paths that never cross the diagonal line y=x. Crossing the diagonal means at some point, the path has more 'down' steps than 'right' steps. You need to determine the number of valid paths for a specific backtest period. What is the number of paths from (0,0) to (5,5) that do not cross the diagonal y=x?
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