Question:

In each 2-minute interval, we can select pairs of non-adjacent persons around a circular table. For $n$ persons in a circle, the maximum number of non-adjacent pairs that can sing simultaneously is $\lfloor n/2 \rfloor$. Since the process continues for 28 minutes with 2-minute songs, there are $28/2 = 14$ songs total. Each person must sing the same number of times, so if each person sings $k$ times, then $nk = 2 \times 14 = 28$ (since each song has 2 people). For $n$ persons with maximum independence, each person can sing at most $\lceil n/2 \rceil$ times. Setting $nk = 28$ and requiring the configuration to be achievable: with $n=7$, we get $k=4$, meaning each of 7 persons sings exactly 4 times in 14 songs of 2 people each, which perfectly matches the constraint that no two adjacent persons sing together.