Czech and Slovak Republics 1997

For students of class 6-8 (age 12 to 14)
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Thamim Zahin
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Czech and Slovak Republics 1997

Unread post by Thamim Zahin » Mon Feb 27, 2017 9:20 pm

Each side and diagonal of a regular $2n+1$-gon ($2n+1 \ge 3$) is colored blue or green. A move consists of choosing a vertex and switching the color of each segment incident to that vertex (from blue to green or vice versa). Prove that regardless of the initial coloring, it is possible to make the number of blue segments incident to each vertex even by following a sequence of moves. Also show that the final configuration obtained is uniquely determined by the initial coloring.
I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.

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samiul_samin
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Re: Czech and Slovak Republics 1997

Unread post by samiul_samin » Sun Feb 18, 2018 3:31 pm

Hint
Denote the vertex $1,2,3,...,2n+1$
$Use mod 2$
Answer
It is always possible

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samiul_samin
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Re: Czech and Slovak Republics 1997

Unread post by samiul_samin » Sun Feb 18, 2018 3:33 pm

Solution You can get the solution in this book.
Mathematical Olympiads 1997-1998:Problems and solution from around the world

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