Qm
Brainteasers

Which years share the 2026 calendar?

calendarcyclesleap-yearsmodular-arithmetic

The year 2026 begins on a Thursday and has 365 days.

Which was the most recent earlier year with an identical calendar (same weekday for 1 January, same number of days), and which is the next later one? Explain the arithmetic.

Show a hint

Each ordinary year shifts 1 January forward by one weekday; each leap year by two. You need a total shift of a multiple of 7, and the target year must also be an ordinary year.

Your answer

Solving needs a free account

Answers, streaks and solutions unlock when you are signed in. Reading the question and the hint stays free.

Create a free accountSign in

Discussion

Sign in to join the discussion · reading is open to everyone

💡 Discussion rules

  1. No full solutions here. Hints and approaches only.
  2. Complexity, edge cases and intuition are the point.
  3. Interview experiences are welcome. Respect your NDAs.

Loading discussion…

Learn the concepts

The theory behind this question.

Chinese Remainder PuzzlesFermat's Little Theorem in PuzzlesInvariants and MonovariantsAdaptive Versus Pre-Committed Weighing StrategiesThe Lost Boarding Pass Problem

Related questions

How often does a whole calendar repeat exactly?What day of the week was 1 January 2000?Is your birthday on the same weekday next year?Born on 29 February, how many birthdays by age 40?One hundred days after a Monday
All questions →