A number of students stand in a circle. Beginning with student #1 and going clockwise around the circle (student #2, student #3, student #4, etc.), the students count off 1,2,3,1,2,3,1,2,3,... The students who say "2" or "3" leave the circle immediately. When the count gets back to student #1, it continues to follow the same pattern (but only with the students who remain). The last student remaining wins a prize.

For example, if there are 14 students, the first round would proceed as follows

student # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |

count | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 |

and only students #1, #4, #7, #10, and #13 would be around for the second round. Since student #14 had said "2", student #1 will say "3" (and be eliminated). Round two will proceed as follows

student # | 1 | 4 | 7 | 10 | 13 |

count | 3 | 1 | 2 | 3 | 1 |

and hence students #4 and #13 will survive to the third round. Since student #13 said "1", student #4 must say "2" and be eliminated, leaving student #13 as the winner.

This month's problem is to determine the winner if there are 2004 students.

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Source: Vietnamese Olympiad in Mathematics
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