In a Ground?

Question

In a ground, N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song – one pair immediately after the other. If the total time taken for singing is 28 minutes, what is N?

Answer 1

Sorry about both answers above, the correct answer is N=7. Imagine them as vertexes of a polygon with all its diagonals - each song is represented by a diagonal /sides must be excluded, they connect adjacent persons/. The question is equivalent to the following: how many vertexes has a polygon, if its diagonals are 14 (14=28/2)? The number of diagonals of N-gon is
C[N,2] - N = N(N-1)/2 - N /C[N,2] is binomial coefficient/,
solving N(N-1)/2 - N = 14 we obtain its only positive root N=7.

Or, think it the following way: each of the 7 persons will sing a song in a duet with 4 of the others /excluding himself and 2 neighbours/, that makes 7*4=28, but every song is counted TWICE here /sung by duet AB and duet BA/, so the number of songs is 14.

Answer 2

You have 2 people singing for 2 minutes together, and then you have 2 more people singing for 2 more minutes. With that information you can see that:

number of songs sung will be (28 minutes total) / (2 minutes for each song) = 14 songs sung

but 2 people are singing each song
So N = # songs * 2 = 28.

Answer 3

28
14 pairs
Each pair is at opposite ends of a diameter