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.
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 singerseconds rather than seconds? There were 4*4 = 16 singerminutes expended (if each round took 1 minuteother 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 20180326 10:41:59 