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Tough Negotiations (Posted on 2007-02-27) Difficulty: 2 of 5
In a surprise move, N. Crocosia agreed to halt its nuclear program in return for 20 million iPods. According to the terms of the agreement, all iPods should come read-only, prerecorded with the same 10 tracks, 1 hour long each. The first half of each track is a speech by the country's leader followed by music in the second half without any pauses.

The Ministry of Songs provided 24 songs for the musical part, all with different durations in whole minutes. In addition, they requested that two of the leader's favorite songs, 10 and 12 min long, be together, as well as two others, respectively 4 and 13 min long.

Can these conditions be met?

No Solution Yet Submitted by Art M    
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Solution Human search | Comment 2 of 3 |
Can't work.

The 10 and 12 minute songs can be treated as a 22 minute song.   This is enough to make it impossible.

Each of the following must be on a separate track, because any two of them exceed 30 minutes:
24, 23, 22, 10+12, 21, 20, 19, 18, 17, 16, 15

But this says that at least 11 tracks are required, and we only have 10 available.

It is even more impossible (if that makes sense) if we also require that 4 + 13 are together, because that requires a 12th track.

I think those N. Crocasians are just stalling.

  Posted by Steve Herman on 2007-02-27 13:28:22
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