Question

If from a complete square pile of $n$ courses a triangular pile of the same number of courses be formed; show that the remaining shot will be just sufficient to form another triangular pile, and find the number of shot in its side.

Answer 1

No. of shots in square pile$=\frac{n(n+1)(2n+1)}{6}$

No. of shots in triangular pile$=\frac{n(n+1)(n+2)}{6}$

The difference$=\frac{n(n+1)}{6}\{n-1\}$

$\therefore$ It is sufficient to make a triangular pile of $(n-1)$ shots in a side of the base