Exercise 1: sample answer

Rule: a year is a leap year if it is divisible by 4, except that century years (those divisible by 100) are leap years only if they are also divisible by 400.

1600: divisible by 400, so leap.
1700: divisible by 100 but not 400, so not leap.
1900: divisible by 100 but not 400, so not leap.
2000: divisible by 400, so leap.
2024: divisible by 4 and not a century year, so leap.
2100: divisible by 100 but not 400, so not leap.

(Under the Julian rule, 1700, 1900 and 2100 would all have been leap years, which is the source of the extra days.)