Gizmodo Monday Puzzle: Do You Really Understand How Calendars Work?

‘Tis the season for New Year’s resolutions. As we all sign up for gym memberships or invest in a Peloton that will just gather dust by March, I resolve to work out your brain this year. January 1, 2024 is a Monday. So what day was January 1 last year? Because of the regularities in how we slice and organize time, you don’t need to consult a calendar or count backwards from 365 to answer that question.

Legendary mathematician John Conway, most famous for his Game of Life, exploited the structure in calendars to develop an algorithm that computes the day of the week for any date, past or future. It’s a little too complicated to lay out here, but I think with an afternoon’s worth of practice any of you could learn to do it in your head. If you want to impress your friends with your Rain Man-esque skills, read about the Doomsday rule and please report back. Whether or not you choose to become a Time Lord, this week’s challenge will test your understanding of how we organize time.

Happy new year, fellow puzzle-lovers.

Puzzle #24: Recycling Calendars

You sell calendars without years written on them. If somebody wants a 2024 calendar, you give them one whose days of the week match up correctly with 2024 (January 1 is a Monday, January 2 is a Tuesday, etc.)

1. How many distinct calendar types must you keep in stock to cover all possible years?
2. When is the next year that people will use the 2023 calendar again?
3. What is the largest possible number of years that can pass between uses of the same calendar?

The last question is particularly tricky, and you may need to remind yourself how the Gregorian calendar works!

I’ll be back next week with the solution and a new puzzle. Do you know a cool puzzle that I should feature here? Message me on Twitter @JackPMurtagh or email me at gizmodopuzzle@gmail.com