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problemsforlunch
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Mathematical competition solutions.
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problemsforlunch
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2026-02-19 17:05:38
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problemsforlunch | Mathematical competition solutions. Skip to navigation Skip to main content Skip to primary sidebar Skip to secondary sidebar Skip to footer problemsforlunch Mathematical competition solutions. Home Problem Sets Tournaments Olympiad Number Theory+AIME Number Theory Jan 14 Posted by Justin Stevens 1993 AIME #9: Two thousand points are given on a circle. Label one of the points 1. From this point, count 2 points in the clockwise direction and label this point 2. From the point labeled 2, count 3 points in the clockwise direction and label this point 3. (See figure.) Continue this process until the labels are all used. Some of the points on the circle will have more than one label and some points will not have a label. What is the smallest integer that labels the same point as 1993? Solution From the point , the distance to each must be the same .Therefore, letting the smallest be . Therefore, Therefore, or ....
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