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Answer 2: Note that any path from \((0,0)\) to \((n,n)\) must cross the line \(x + y = n\text{.}\) That is, any path must pass through exactly one of the points: \((0,n)\text{,}\) \((1,n-1)\text{,}\) \((2,n-2)\text{,}\) …, \((n, 0)\text{.}\) For example, this is what happens in the case \(n = 4\text{:}\)

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