10,11
How many different integer solutions does the inequality $|x|+|y|<100$ have?
For a natural number $n$, the equation $|x|+|y|=n$ has exactly $4n$ integer solutions, and for $n=0$ the solution is unique. Therefore, the number of solutions to the original inequality is $1+4(1+2+\ldots+99)=19801$.

## Answer

19801.