Friday 13th

Logic Level 2

What is the maximum number of times that "Friday the 13th" can occur in a single year (from January to December)?

1 2 3 4

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1 solution

Stephen Mellor
Apr 14, 2018

We need to consider the case when there is a leap year and when there isn't a leap year. Here are two years, 2018 and 2020 (2020 being the leap year) and which day the 13th falls on:

2018:

January Saturday
February Tuesday
March Tuesday
April Friday
May Sunday
June Wednesday
July Friday
August Monday
September Thursday
October Saturday
November Tuesday
December Thursday

2020:

January Monday
February Thursday
March Friday
April Monday
May Wednesday
June Saturday
July Monday
August Thursday
September Sunday
October Tuesday
November Friday
December Sunday

We don't care what the name of the day that the 13th falls on is in these particular years, just which day of the week has the most repetition (since the days will all be shifted by the same amount in different years), and we see that it doesn't matter about a leap year, the answer will be 3 \boxed{3} . If you want an example, 2015 was a 365 day year (when the year started on a Thursday), or 2012 was a 366 day year (when the year started on a Sunday).

@Stephen Mellor , oh no!!! 13 solvers!!!

Lucia and Emma - 2 years, 10 months ago

If January starts as a Friday the thirteenth, and it is also a leap year, then you will get 4 Friday the thirteenths: January, April, July and December

Jessica Sun - 2 years, 2 months ago

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