Qm
Brainteasers

Which month always starts on the same weekday as December?

calendarmodular-arithmetic

Two months in the same year "match" if their first days fall on the same weekday, so their calendar pages line up.

Which month matches December in every year, whether or not it is a leap year? Find all the matching groups for ordinary years and for leap years, and explain why one pair survives both.

Show a hint

Two months start on the same weekday when the number of days between their first days is a multiple of 7. Add up month lengths and reduce modulo 7.

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

What day of the week was 1 January 2000?One hundred days after a MondayWhy 4/4, 6/6, 8/8, 10/10 and 12/12 share a weekdayEvery year has a Friday the 13thWhy January 1 and December 31 share a weekday
All questions →