total length of the irrigation ditches > 70, in square 12x12
Source: 1984 German Federal - Bundeswettbewerb Mathematik - BWM - Round 1 p4
November 21, 2022
combinatoricscombinatorial geometrygeometric inequalitygeometry
Problem Statement
In a square field of side length there is a source that contains a system of straight irrigation ditches. This is laid out in such a way that for every point of the field the distance to the next ditch is at most . Here, the source is as a point and are the ditches to be regarded as stretches. It must be verified that the total length of the irrigation ditches is greater than m. The sketch shows an example of a trench system of the type indicated.
https://cdn.artofproblemsolving.com/attachments/6/5/5b51511da468cf14b5823c6acda3c4d2fe8280.png