Difference between revisions of "1989 IMO Problems/Problem 5"
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==Problem== | ==Problem== | ||
| − | Let <math>n\geq3</math> and consider a set <math>E</math> of <math>2n − 1</math> distinct points on a circle. Suppose | + | Let <math>n\geq3</math> and consider a set <math>E</math> of <math>2n − 1</math> distinct points on a circle. Suppose that exactly <math>k</math> of these points are to be colored black. Such a coloring is “good” if there is at least one pair of black points such that the interior of one of the arcs between them contains exactly <math>n</math> points from set <math>E</math>. Find the smallest value of <math>k</math> such that every such coloring of <math>k</math> points of <math>E</math> is good. |
| − | that exactly <math>k</math> of these points are to be colored black. Such a coloring is “good” | ||
| − | if there is at least one pair of black points such that the interior of one of the | ||
| − | arcs between them contains exactly <math>n</math> points from set <math>E</math>. Find the smallest value | ||
| − | of <math>k</math> such that every such coloring of <math>k</math> points of <math>E</math> is good. | ||
Revision as of 10:51, 17 June 2020
Problem
Let 
and consider a set 
of $2n − 1$ (Error compiling LaTeX. Unknown error_msg) distinct points on a circle. Suppose that exactly 
of these points are to be colored black. Such a coloring is “good” if there is at least one pair of black points such that the interior of one of the arcs between them contains exactly 
points from set . Find the smallest value of such that every such coloring of points of is good.
