How can you use division to determine what day of the week Halloween was on in 2004 if Halloween of 2003 was on a Friday?

Answer 1

In general, if Halloween were on Friday last year then it would be on a Saturday this year. However since there is a February 29th in between, it jumps two days ahead, so it would be on a Sunday.

The way you would use division to determine this is by recognizing that 365=(52x7)+1. Since every week is 7 days, you know that if Halloween was on a Friday, then seven days later it will be Friday again, and seven days after that it will be Friday, etc. So, after 364=7x52 days, it will be Friday and the 365th day will be Saturday. This is why, in general, Halloween would be one day later. Since, however, 2004 is a leap year, the year is 366=(7x52)+2 days long, so in this case it would actually be on Sunday. Check out modular arithmetic to see a more general presentation of this issue.