Problem #PRU-98260

Problems Methods Pigeonhole principle Pigeonhole principle (angles and lengths)

Problem

4 points $a, b, c, d$ lie on the segment $[0, 1]$ of the number line. Prove that there will be a point $x$ , lying in the segment $[0, 1]$ , that satisfies $\frac{1}{| x - a |} + \frac{1}{| x - b |} + \frac{1}{| x - c |} + \frac{1}{| x - d |} < 40.$

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