Three speed skaters have a friendly race on a skating oval. They all start from
the same point and skate in the same direction, but with di fferent speeds that
they maintain throughout the race. The slowest skater does 1 lap a minute, the
fastest one does 3.14 laps a minute, and the middle one does L laps a minute for
some 1 < L < 3.14. The race ends at the moment when all three skaters again
come together to the same point on the oval (which may diff er from the starting
4 point.) Find how many di fferent choices for L are there such that 117 passings
occur before the end of the race. (Note: A passing is defi ned when one skater passes
another one. The beginning and the end of the race when all three skaters are at
together are not counted as a passing.)
the same point and skate in the same direction, but with di fferent speeds that
they maintain throughout the race. The slowest skater does 1 lap a minute, the
fastest one does 3.14 laps a minute, and the middle one does L laps a minute for
some 1 < L < 3.14. The race ends at the moment when all three skaters again
come together to the same point on the oval (which may diff er from the starting
4 point.) Find how many di fferent choices for L are there such that 117 passings
occur before the end of the race. (Note: A passing is defi ned when one skater passes
another one. The beginning and the end of the race when all three skaters are at
together are not counted as a passing.)
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