Answer to Question #173529 in Discrete Mathematics for ANJU JAYACHANDRAN

Question

3c) 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.

Answer 1

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.