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Contests
National and Regional Contests
Canada Contests
Canadian Mathematical Olympiad Qualification Repechage
2015 Canadian Mathematical Olympiad Qualification
7
7
Part of
2015 Canadian Mathematical Olympiad Qualification
Problems
(1)
Ternary string
Source: Canada Repêchage 2015/7
6/18/2016
A
(
0
x
,
1
y
,
2
z
)
(0_x, 1_y, 2_z)
(
0
x
,
1
y
,
2
z
)
-string is an infinite ternary string such that:[*] If there is a
0
0
0
in position
i
i
i
then there is a
1
1
1
in position
i
+
x
i + x
i
+
x
,[*] if there is a
1
1
1
in position
j
j
j
then there is a
2
2
2
in position
j
+
y
j + y
j
+
y
,[*] if there is a
2
2
2
in position
k
k
k
then there is a
0
0
0
in position
k
+
z
k + z
k
+
z
.For how many ordered triples of positive integers
(
x
,
y
,
z
)
(x, y, z)
(
x
,
y
,
z
)
with
x
,
y
,
z
≤
100
x, y, z \leq 100
x
,
y
,
z
≤
100
does there exist
(
0
x
,
1
y
,
2
z
)
(0_x, 1_y, 2_z)
(
0
x
,
1
y
,
2
z
)
-string?
combinatorics