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National and Regional Contests
Netherlands Contests
Dutch Mathematical Olympiad
2018 Dutch Mathematical Olympiad
2
2
Part of
2018 Dutch Mathematical Olympiad
Problems
(1)
coloring red or blue the numbers 1 to 15
Source: Dutch MNO 2018 p2
9/7/2019
The numbers
1
1
1
to
15
15
15
are each coloured blue or red. Determine all possible colourings that satisfy the following rules: • The number
15
15
15
is red. • If numbers
x
x
x
and
y
y
y
have different colours and
x
+
y
≤
15
x + y \le 15
x
+
y
≤
15
, then
x
+
y
x + y
x
+
y
is blue. • If numbers
x
x
x
and
y
y
y
have different colours and
x
⋅
y
≤
15
x \cdot y \le 15
x
⋅
y
≤
15
, then
x
⋅
y
x \cdot y
x
⋅
y
is red.
combinatorics
Coloring