perplexus.info :: Tricks : Four singers

Four singers (Posted on 2018-03-26)

Four singers take part in a musical round of 4 equal lines, each finishing after singing the round through three times.
The second singer begins when the first singer begins the second line,the third singer begins when the first singer begins the third line,the fourth singer begins when the first singer begins the fourth line.

Find the fraction of the total singing time that all four are singing at the same time.

No Solution Yet Submitted by Ady TZIDON

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Is it a "Trick" or not? (spoiler)

| Comment 1 of 3

The D1 solution, without "Tricks" would be to say that there are 7 intervals of time and that in the respective intervals, 1, 2, 3, 4, 3, 2 and 1 singers are singing at once. In only one of the seven intervals are all four singing at the same time: that's 1/7 of the time.

But does Ady really have a trick up his sleeve? Is he counting "singing time" measured in singer-seconds rather than seconds? There were 4*4 = 16 singer-minutes expended (if each round took 1 minute--other lengths being proportional), of which 4 were spent while all four singers were singing. That would make the answer 4/16 = 1/4.

Posted by Charlie on 2018-03-26 10:41:59

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