1

Part of 1973 Bundeswettbewerb Mathematik

Problems(2)

All but one digit is 5 => no perfect square

Source:

A positive integer has 1000 digits (decimal system), all but at most one of them being the digit

5

. Show that this number isn't a perfect square.

Square with 51 points => 3 covered by disk

Source: Bundeswettbewerb Mathematik 1973, round 2, problem 1

In a square of sidelength

7

51

points are given. Show that there's a disk of radius

1

covering at least

3

of these points.

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