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A man wants to reach from A to the opposite comer of the square C. The sides of the square are $$100\ m$$. A central square of $$50\ m \times 50\ m$$ is filled with sand. Outside this square, he can walk at a speed $$1\ m/s$$. In the central square, he can walk only at a speed of $$v\ m/s (v < 1)$$. What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand?

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