2012 AIME I Problems/Problem 15
Problem 15
There are 
mathematicians seated around a circular table with seats numbered 
in clockwise order. After a break the again sit around the table. The mathematicians note that there is a positive integer 
such that
-
(
) for each 
the mathematician who was seated in seat 
before the break is seated in seat 
after the break (where seat 
is seat 
);
-
(
) for every pair of mathematicians, the number of mathematicians sitting between them after the break, counting in both the clockwise and the counterclockwise directions, is different from either of the number of mathematicians sitting between them before the break.
Find the number of possible values of with 
Solution
See also
| 2012 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Last Problem | |
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