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Contests
National and Regional Contests
Azerbaijan Contests
Azerbaijan CMO TST
2022 Azerbaijan EGMO/CMO TST
2022 Azerbaijan EGMO/CMO TST
Part of
Azerbaijan CMO TST
Subcontests
(1)
C3
1
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replace $n$ stones on a circle
Suppose
n
≥
3
n\geq 3
n
≥
3
is an integer. There are
n
n
n
grids on a circle. We put a stone in each grid. Find all positive integer
n
n
n
, such that we can perform the following operation
n
−
2
n-2
n
−
2
times, and then there exists a grid with
n
−
1
n-1
n
−
1
stones in it:
∙
\bullet
∙
Pick a grid
A
A
A
with at least one stone in it. And pick a positive integer
k
≤
n
−
1
k\leq n-1
k
≤
n
−
1
. Take all stones in the
k
k
k
-th grid after
A
A
A
in anticlockwise direction. And put then in the
k
k
k
-th grid after
A
A
A
in clockwise direction.