How many three-digit numbers are divisible by 17?

The first three-digit multiple is $17\times 6=102$ (since $17\times 5=85$ has only two digits) and the last is $17\times 58=986$ (since $17\times 59=1003$ has four). The multipliers run 6, 7, …, 58, so the count is 58 − 6 + 1 = 53. Answering 52 is the classic off-by-one from forgetting to add 1, while 58 counts from a multiplier of 1.