Today is 1st April. The day of the week is Wednesday. This is a leap year. The…

Concept

The weekday of a date advances by (elapsed days mod 7) positions, because the week repeats every 7 days. Over one calendar year, an ordinary (365-day) year contributes a 1-day shift (365 mod 7 = 1), while a leap year (366-day, containing 29 February) contributes a 2-day shift (366 mod 7 = 2). Which shift a given year contributes depends only on whether that year's own 29 February falls inside the span being counted — not on whether the very first year of the span was itself a leap year.

Application

1. The starting date, 1 April, falls in a leap year, but that year's 29 February has already passed by 1 April, so it does not affect the shift counted from this date onward.

2. Under the standard 4-year leap cycle, the next leap year is 4 years after the starting year, so all three of the years that follow the starting year are ordinary years — none of their 29 Februaries falls between 1 April of the starting year and 1 April three years later.

3. Each of the three year-transitions therefore contributes only the ordinary-year shift of 1 day: the first transition adds 1 day, the second adds 1 day, and the third adds 1 day, for a total shift of 1 + 1 + 1 = 3 days.

4. Advancing Wednesday by 3 days steps through Thursday, Friday and lands on Saturday, so the day of the week 3 years after this date is Saturday.

Cross-check

Equivalently, the total elapsed time is 365 + 365 + 365 = 1095 days, since no 29 February falls in the span. Dividing by 7 gives 1095 = 7 x 156 + 3, an odd-day count of 3, which matches the 3-day advance found above and confirms Saturday.