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Programming Enigma Puzzles

14 December 2015

Posted by on **From New Scientist #2345, 1st June 2002** [link]

I recently bought a compilation of archive recordings by the Prime Players, issued as a set of three CDs. Each CD has a different playing time of not more than one hour and contains four tracks. Within each CD each track lasts a different prime whole number of minutes, and any combination of three different tracks on that CD lasts a prime whole number of minutes.

For each CD, give its playing time and the length of its longest track.

[enigma1189]

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This Python program runs in 36ms.

Solution:One CD has a total time of 48 minutes, and its longest track is 19 minutes. Another CD has a total time of 54 minutes, and its longest track is 23 minutes. The third CD has a total time of 60 minutes, and its longest track is also 23 minutes.There are only three possible CDs: