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Contests
National and Regional Contests
Greece Contests
Greece JBMO TST
2010 Greece JBMO TST
4
4
Part of
2010 Greece JBMO TST
Problems
(1)
coloring 1-8 with black or white, given rules, find each number's color
Source: Greece JBMO TST 2010 p4
4/29/2019
We color one of the numbers
1
,
.
.
.
,
8
1,...,8
1
,
...
,
8
with white or black according to the following rules: i) number
4
4
4
gets colored white and one at lest of the following numbers gets colored black ii) if two numbers
a
,
b
a,b
a
,
b
are colored in a different color and
a
+
b
≤
8
a+b\le 8
a
+
b
≤
8
, then number
a
+
b
a+b
a
+
b
gets colored black. iii) if two numbers
a
,
b
a,b
a
,
b
are colored in a different color and
a
⋅
b
≤
8
a\cdot b\le 8
a
⋅
b
≤
8
, then number
a
⋅
b
a\cdot b
a
⋅
b
gets colored white. If by those rules, all numbers get colored, find the color of each number.
combinatorics
Coloring