Child Photograph Rows

Let $n$ be the number of rows and $x$ be the number of children in the front row. Total children $S_n = \frac{n}{2}[2x - (n-1)3] = 630$. Test options for $n$:

• $n = 3 \implies 3x - 9 = 630 \implies 3x = 639 \implies x = 213$ (Integer, possible).
• $n = 4 \implies 4x - 18 = 630 \implies 4x = 648 \implies x = 162$ (Integer, possible).
• $n = 5 \implies 5x - 30 = 630 \implies 5x = 660 \implies x = 132$ (Integer, possible).
• $n = 6 \implies 6x - 45 = 630 \implies 6x = 675 \implies x = 112.5$ (Not an integer, IMPOSSIBLE).

Thus, 6 rows is not possible.