MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
1999 National Olympiad First Round
27
27
Part of
1999 National Olympiad First Round
Problems
(1)
Coloring
Source: 0
4/21/2009
Points on a square with side length
c
c
c
are either painted blue or red. Find the smallest possible value of
c
c
c
such that how the points are painted, there exist two points with same color having a distance not less than
5
\sqrt {5}
5
.
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5
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None
<span class='latex-bold'>(A)</span>\ \frac {\sqrt {10} }{2} \qquad<span class='latex-bold'>(B)</span>\ 2 \qquad<span class='latex-bold'>(C)</span>\ \sqrt {5} \qquad<span class='latex-bold'>(D)</span>\ 2\sqrt {2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}
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None
pigeonhole principle