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Omni-MATH / The sides of a 99 -gon are initially colored so that consecutive sides are red, blue, red, blue,..., red, blue, yellow. We make a sequence of modifications in the coloring, changin…

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problem

The sides of a 9999 -gon are initially colored so that consecutive sides are red, blue, red, blue,..., red, blue, yellow. We make a sequence of modifications in the coloring, changing the color of one side at a time to one of the three given colors (red, blue, yellow), under the constraint that no two adjacent sides may be the same color. By making a sequence of such modifications, is it possible to arrive at the coloring in which consecutive sides are red, blue, red, blue, red, blue,..., red, yellow, blue?
Plain-text mathematical notation (without MathML)
The sides of a 99 -gon are initially colored so that consecutive sides are red, blue, red, blue,..., red, blue, yellow. We make a sequence of modifications in the coloring, changing the color of one side at a time to one of the three given colors (red, blue, yellow), under the constraint that no two adjacent sides may be the same color. By making a sequence of such modifications, is it possible to arrive at the coloring in which consecutive sides 
are red, blue, red, blue, red, blue,..., red, yellow, blue?
Original LaTeX notation
The sides of a $99$ -gon are initially colored so that consecutive sides are red, blue, red, blue,..., red, blue, yellow. We make a sequence of modifications in the coloring, changing the color of one side at a time to one of the three given colors (red, blue, yellow), under the constraint that no two adjacent sides may be the same color. By making a sequence of such modifications, is it possible to arrive at the coloring in which consecutive sides 
are red, blue, red, blue, red, blue,..., red, yellow, blue?

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Source and history

task_id
d9331935-2c5b-5e4b-a0f3-d498191200a2
task_key
test--d9331935-2c5b-5e4b-a0f3-d498191200a2
task_revision_id
1
config / split
/ test

Official source

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