Days and calendars

The days of the week go round and round in the same order: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday, and then Monday again. Because the pattern repeats every 7 days, you can find the day of the week 10 days, 100 days or even 1,000 days from now without counting them one by one. The same idea helps with dates in a month, with the lengths of the months and with leap years. You only need one division and a little care.

Seven days make a full circle

Think of the seven days written around a circle. Every 7 steps you come back to the day you started on. So 7 days from Tuesday is Tuesday, 14 days from Tuesday is Tuesday, and 70 days from Tuesday is Tuesday too. Whole weeks never change the day.

That means only the days left over after the whole weeks matter. When you divide a number by 7, the part left over is called the remainder. For example, 10 = 7 + 3, so 10 days is 1 whole week and a remainder of 3 days.

What day will it be in so many days?

1. Divide the number of days by 7 and find the remainder.
2. Start on today and count the remainder forward, one day at a time.
3. For days in the past, count the remainder backward instead.

Yesterday, tomorrow and the day after tomorrow

Some puzzles do not tell you today. They say "if tomorrow is Friday" or "the day before yesterday was Thursday". The safe method is always the same: find today first, then answer the question from today.

Dates in the same month

Dates that are 7 apart always fall on the same day of the week. If the 1st is a Monday, then the 8th, 15th, 22nd and 29th are Mondays too. To find the day of any other date, find how many days lie between the two dates by subtracting.

How long are the months?

Seven months have 31 days, four months have 30 days, and February has 28 days, or 29 in a leap year.

A classic trick question asks how many months have at least 28 days. The answer is all 12, because every month has 28 days or more. People answer 1 because they think only of February. Read the words "at least" carefully.

Because the longest month has 31 days, which is 4 weeks and 3 days, one month can have at most 5 Fridays (or 5 of any other day). In a 31-day month, three days of the week appear 5 times. A February of 28 days has exactly 4 of every day.

Leap years

The Earth takes about 365 and a quarter days to go round the Sun. To keep the calendar in step, we add one extra day, February 29, about every 4 years. A year with that extra day is called a leap year. It has 366 days.