Aerith bakes some cookes. On the first day, she gives away 1 cookie and then $1 / 8$ of the remaining cookies; on the second day, she gives away 2 cookies and then $1 / 8$ of the remaining cookies, and so on. On the 7th day, she gives away 7 cookies and then there are none left. How many cookies did she bake?
The number of cookies is 49 . Working backwards, on the 6th day, $1 / 8$ of the remaining cookies must have been 1 cookie (since there were 7 left after that), so there were $6+1+7=14$ cookies at the start of the day. Similarly, since the 5 th day there were 14 cookies left, the $1 / 7$ of the remaining cookies given away was 2 cookies, so there were $5+2+14=21$ cookies to start with.

Continuing, at the start of the 4 th day, there were $4+3+21=28$, on the third day, there were $3+4+28=35$, on the second day there were $2+5+25=42$, and on the first day, there were $1+6+42=49$ cookies to start.