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Mathematics

This mathematical trick lets you work out the weekday of any date

A little help from Lewis Carroll will enable you to impress friends and family by calculating which day of the week any date is, says Peter Rowlett

By Peter Rowlett

1 January 2025

2M9CJ0J 1940s SCATTERED PAGES FROM A ONE DAY AT A TIME FLIP DESK CALENDAR NUMBERS DAYS OF WEEK PATTERN PAPER TEXTURE - s10448 HAR001 HARS REPRESENTATION

H. Armstrong Roberts/ClassicStock/Alamy

Time comes in cycles, and we deal with it using a cyclic number system. What time is 5 hours after 10pm? Hopefully you would say 3am, not 15pm. You know 10 + 5 isn’t 3, but you also know to reset to zero when you hit 12. In mathematical terms, this is called modular arithmetic: we divide 15 by 12 and keep the remainder. We write this as 10 + 5 = 3 modulo 12.

Modular arithmetic has many applications, from cryptography to magic tricks. There is a trick you can learn where you ask someone to name a date this year and…

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