Maths Olympiad · topic 12 of 33 · free

Calendar puzzles — Maths Olympiad practice

Every 7 days the same day of the week comes back. So to find the day after many days, divide the number of days by 7 and look only at the remainder — that is how many days to count on.

How to solve it

Throw away the weeks — “only the days left over after whole weeks move the day of the week”

  1. Count the days between the two dates (use the month lengths: 30 or 31, February 28 in an ordinary year).
  2. Divide by 7: whole weeks do not change the day; the remainder does.
  3. Count the remainder on from the starting day.

Use it for: Day-of-the-week puzzles, birthdays, holidays and “after 100 days” questions.

Worked example: If 5 March is a Tuesday, what day of the week is 23 March? Saturday

  1. From 5 March to 23 March is 23 − 5 = 18 days.
  2. 18 ÷ 7 = 2 weeks and 4 days left.
  3. 4 days after Tuesday: Wednesday, Thursday, Friday, Saturday.

Check: Tuesdays in that March fall on 5, 12, 19 and 26, so 23 March is 4 days after the 19th — a Saturday ✓

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