Is your birthday on the same weekday next year?

Question

This year your birthday fell on a Tuesday. Your birthday is not 29 February. 1. Can it fall on a Tuesday again next year? 2. How many years can it take before it falls on a Tuesday again, and why do the possible gaps come out as 5, 6 or 11 years?

Accepted Answer

No. A birthday never lands on the same weekday in consecutive years. It comes back after 5, 6 or 11 years. Why not next year. From one birthday to the next there are either 365 days, if no 29 February lies in between, or 366 days if one does. 365 = 52 × 7 + 1, so the weekday advances by 1. 366 = 52 × 7 + 2, so it advances by 2. Either way it moves, so next year's birthday is on Wednesday or Thursday, never Tuesday. When it comes back. The weekday returns when the total advance is a multiple of 7. Ordinary years add 1 and leap years add 2. Three worked examples with the birthday 10 March: - Ga…

Is your birthday on the same weekday next year?

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