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If 5 points are chosen in a square of side 2cm, show that there will always be two points at a distance of at most √ 2cm.

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We bisect the square in 4 equal parts.

So by pigeonhole principle 1 portion contains atleast two points.

Now the length of the sides of each square becomes 1 cm.

So the maximum distance between two points in a square (newly formed) is the length of the

diagonal=\sqrt{2} .

Hence in the square portion which contains 2 points are at a distance atmost \sqrt{2} cm.

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Question ID: mtid-5-stid-8-sqid-3266-qpid-1965