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Before and After (Posted on 2004-07-23) Difficulty: 3 of 5
If all the irreducible fractions between 0 and 1, with denominators at most 99, are listed in ascending order, which two fractions would be before and after 11/21? Determine which two fractions are adjacent to 34/87 in this listing.

  Submitted by Federico Kereki    
Rating: 4.5000 (4 votes)
Solution: (Hide)
This kind of sequence is called a Farey series, and given two fractions (a/b, c/d) in sequence, they satisfy bc-ad=1.

If a/b=11/21, then 11b-21a=1, and a and b should be as large as possible but less than 99, which works out to 45/86. For the other side you find 43/82.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
same ans as Charlie - w ineff c progvectorboy2004-07-23 16:35:26
Similar ProblemGamer2004-07-23 12:30:22
Solutioncomputer solutionCharlie2004-07-23 11:19:08
Some ThoughtsStarting ideaLarry2004-07-23 10:19:03
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