Difference between revisions of "2005 OIM Problems/Problem 6"
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== Problem == | == Problem == | ||
| − | Given a positive integer <math>n</math>, <math>2n</math> points are aligned in a plane as <math>A_1, A_2,\cdots, A_{2n}. Each point is colored blue or red using the following procedure: In the plane, < | + | Given a positive integer <math>n</math>, <math>2n</math> points are aligned in a plane as <math>A_1, A_2,\cdots, A_{2n}</math>. Each point is colored blue or red using the following procedure: In the plane, <math>n</math> circles with end diameters <math>A_i</math> and <math>A_j</math> are drawn, disjoint two by two. Each <math>A_k</math>, <math>1 \le k \le 2n</math>, belongs to exactly one circle. The dots are colored so that the two points of the same circle have the same color. Find how many different colorations of the <math>2n</math> points can be obtained by varying the <math>n</math> |
circumferences and the distribution of colors. | circumferences and the distribution of colors. | ||
Revision as of 17:22, 14 December 2023
Problem
Given a positive integer 
, 
points are aligned in a plane as 
. Each point is colored blue or red using the following procedure: In the plane, circles with end diameters 
and 
are drawn, disjoint two by two. Each 
, 
, belongs to exactly one circle. The dots are colored so that the two points of the same circle have the same color. Find how many different colorations of the points can be obtained by varying the
circumferences and the distribution of colors.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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