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Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
2011 Dutch Mathematical Olympiad
5
5
Part of
2011 Dutch Mathematical Olympiad
Problems
(1)
all numbers coloured bw, if a,b white then a-b and a+b have diff. colours
Source: Dutch NMO 2011 p5
9/6/2019
The number devil has coloured the integer numbers: every integer is coloured either black or white. The number
1
1
1
is coloured white. For every two white numbers
a
a
a
and
b
b
b
(
a
a
a
and
b
b
b
are allowed to be equal) the numbers
a
ā
b
a-b
a
ā
b
and
a
+
a +
a
+
b have di fferent colours. Prove that
2011
2011
2011
is coloured white.
Coloring
combinatorics