jmc

It's easy to count the number of three-digit numbers which are multiples of 7: the smallest multiple of 7 which is a three-digit number is $15\times 7=105$, and the largest multiple of 7 which is a three-digit number is $142\times 7=994$. Therefore, there are $142-15+1=128$ three-digit numbers which are multiples of 7. There are 900 three-digit numbers in total (from 100 to 999), so there are $900-128=\boxed{772}$ three-digit numbers which are not multiples of 7.