Difference between revisions of "1993 AIME Problems/Problem 9"
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== Problem == | == Problem == | ||
| + | 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 <math>1,2,3\dots,1993\,</math> 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? | ||
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| + | [[Image:AIME_1993_Problem_9.png]] | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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== See also == | == See also == | ||
* [[1993 AIME Problems/Problem 8 | Previous problem]] | * [[1993 AIME Problems/Problem 8 | Previous problem]] | ||
* [[1993 AIME Problems/Problem 10 | Next problem]] | * [[1993 AIME Problems/Problem 10 | Next problem]] | ||
* [[1993 AIME Problems]] | * [[1993 AIME Problems]] | ||
Revision as of 23:15, 25 March 2007
Problem
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
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