11. Stephanie enjoys swimming. She goes for a swim on a particular date if, and only if, the day, month (where January is replaced by '01' through to December by '12') and year are all of the same parity (that is they are all odd, or all are even). On how many days will she go for a swim in the two-year period between January 1st of one year and December 31st of the following year inclusive?
11. 183 We first observe that exactly one odd year and exactly one even year are under consideration.
In an odd year we need only consider odd months. January, March, May and July each has 16 odd days while September and November has 15. Therefore the number of days Stephanie will swim in the odd year is $4 \times 16+2 \times 15=94$.
In an even year we need only consider even months. April, June, August, October and December has 15 even days and February has 14 (regardless of whether or not it is a leap year). Therefore the number of days Stephanie will swim in the even year is $5 \times 15+14=89$. Hence she will swim for $94+89=183$ days over the two years.