2015 IMO |
送交者: zmou 2015年07月18日19:29:32 於 [教育學術] 發送悄悄話 |
Problem 1. A finite set S of points in a plane is BALANCED if, for any two points A and B in S, there exists C in S such that AC = BC. We say S is CENTER-FREE if for any different A,B,C in S, there is no point P in S such that PA = PB = PC. Prove a). for any n > 2, there exists a balanced set of n points. b). Determine all n > 2 for which there exists a balanced and center-free set of n points. This problem is not too hard. Just use equilateral triangles and a circle. |
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