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National and Regional Contests
Russia Contests
Russian Team Selection Tests
Russian TST 2016
Russian TST 2016
Part of
Russian Team Selection Tests
Subcontests
(4)
P2
5
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P3
6
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P4
1
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Regular polygons inscribed in a circle
A regular
n
n{}
n
-gon and a regular
m
m
m
-gon with distinct vertices are inscribed in the same circle. The vertices of these polygons divide the circle into
n
+
m
n+m
n
+
m
arcs. Is it always possible to inscribe a regular
(
n
+
m
)
(n+m)
(
n
+
m
)
-gon in the same circle so that exactly one of its vertices is on each of these arcs?
P1
13
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