14.24. How many different integer solutions does the inequality $|x|+|y|<100$ have?
14.24. Answer: 338350. The equations $|x|+|y|=0,|x|+|y|=1$, $|x|+|y|=2, \ldots,|x|+|y|=99$ have, respectively, $1,2^{2}, 3^{2}, \ldots$ $\ldots, 100^{2}$ integer solutions. Therefore, the desired number is $1^{2}+2^{2}+3^{2}+\ldots+100^{2}=\frac{100 \cdot 101 \cdot 201}{6}$ (see problem 9.12).