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Minimum distance between sets (Posted on 2023-08-21) Difficulty: 3 of 5
Let m,n be positive integers greater than 1. We define the sets Pm={1/m, 2/m, ..., (m-1)/m} and Pn={1/n, 2/n, ..., (n-1)/n}.

Find the distance between Pm and Pn, that is defined as min{|a-b|: a∈Pm, b∈Pn}

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution answer (spoiler) Comment 1 of 1
This seems like a D1. Am I missing something?

If m and n have a common factor, the distance is zero.

Otherwise the distance is 1 / (m * n).

  Posted by Charlie on 2023-08-21 08:56:10
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