6. Winnie wrote all the integers from 1 to 2017 inclusive on a board. She then erased all the integers that are a multiple of 3 . Next she reinstated all those integers that are a multiple of 6 . Finally she erased all integers then on the board which are a multiple of 27. Of the 2017 integers that began in the list, how many are now missing?
6. 373 Winnie begins with 2017 integers. There are $2016 \div 3=672$ multiples of three which are erased. This leaves $2017-672=1345$ integers. There are $2016 \div 6=336$ multiples of six which are reinstated. This leaves $1345+336=1681$ integers. The only multiples of twenty-seven that then remain in the list are those that are multiples of six. Winnie therefore erases all the multiples of fifty-four. There are $1998 \div 54=37$ multiples of fifty-four which are erased. This leaves $1681-37=1644$ integers. Of the 2017 integers she began with $2017-1644=373$ are now missing.