In 2008, September and December both began on a Monday. But every year, there are two months that do not begin on the same day of the week as any other month. What are those two months?
This brainteaser was written by Derrick Niederman.
Solution: May and June.
To see how this works, all you need to know is that months with 30 days push the first of the month ahead two days of the week, whereas months with 31 days push ahead three days. For example, March has 31 days, so if March 1 is a Tuesday, then April 1 is a Friday (move ahead three days of the week). Similarly, April has 30 days, so May 1 will be a Sunday (move ahead just two days of the week).
The table below summarizes what will happen in leap and non‑leap years. August does not share the same day with any other month in a non‑leap year, and October does not share the same day with any other month in a leap year — but only May and June never share the same day of the week with any other months, whether it’s a leap year or not.
Month
Months with Same First Day in a Non‑Leap Year
Months with Same First Day in a Leap Year
January
October
April, July
February
March, November
August
March
February, November
November
April
July
January, July
May
None
June
January, April
September
December
February, March
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