2017 JBMO Problems/Problem 4
Problem
Consider a regular 2n-gon ,
in the plane ,where
is a positive integer . We say that a point
on one of the sides of
can be seen from a point
that is external to
, if the line segment
contains no other points that lie on the sides of
except
.We color the sides of
in 3 different colors (ignore the vertices of
,we consider them colorless), such that every side is colored in exactly one color, and each color is used at least once . Moreover ,from every point in the plane external to
, points of most 2 different colors on
can be seen .Find the number of distinct such colorings of
(two colorings are considered distinct if at least one of sides is colored differently).
Solution
See also
2017 JBMO (Problems • Resources) | ||
Preceded by Problem 3 |
Followed by Last Problem | |
1 • 2 • 3 • 4 | ||
All JBMO Problems and Solutions |