Question

Find the number of shot in an incomplete rectangular pile, the number of shot in the sides of its upper course being $11$ and $18$, and the number in the shorter side of its lowest course being $30$.

Answer 1

Let us add a rectangular pile having $10$ and $17$ shots in the side of its base,

$n=10,m=17$, No. of shots$=\frac{10\times 11\times 42}{6}$

$=770$

Also there are $20$ courses, so that the base of the complete pile has $30$ and $37$, shot in its sides;

$\therefore$ No. of shots in the complete pile$=\frac{30\times 31\times 82}{6}$

$=12710$

No. of shots in the incomplete pile$=12710-770$

$=11940$