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Problems
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National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
2004 Swedish Mathematical Competition
5
5
Part of
2004 Swedish Mathematical Competition
Problems
(1)
n-1 lines in nxn board
Source: Swedish Mathematical Competition 2004 p5
3/21/2021
A square of side
n
≥
2
n \ge 2
n
≥
2
is divided into
n
2
n^2
n
2
unit squares (
n
∈
N
n \in N
n
∈
N
). One draws
n
−
1
n-1
n
−
1
lines so that the interior of each of the unit squares is cut by at least one of these lines. (a) Give an example of such a configuration for some
n
n
n
. (b) Show that some two of the lines must meet inside the square.
combinatorics