Suppose 23 August 2020 falls on a Sunday. What day of the week is 23 August 2029?

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Thursday. Take 23 August 2020 as the known reference day, a Sunday. The span to 23 August 2029 covers 9 one-year gaps. Each gap runs from 23 August of one year to 23 August of the next. Check which gaps pass through a 29 February. The gap starting in 2023 passes through February 2024, a leap year. The gap starting in 2027 passes through February 2028, also a leap year. No other gap in this span passes through a leap February. So 2 of the 9 gaps carry an extra day, and 7 gaps are ordinary. Each ordinary gap contributes 1 odd day, and each leap-affected gap contributes 2. The total is 7 times 1, plus 2 times 2, which equals 7 plus 4, or 11 odd days. Divide 11 by 7. That gives 1 full week, with a remainder of 4 days. Move 4 days forward from Sunday. Sunday plus 4 lands on Thursday, after passing Monday, Tuesday, and Wednesday. So 23 August 2029 falls on a Thursday.

Suppose 23 August 2020 falls on a Sunday. What day of the week is 23 August 2029?

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