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Friday the 13th



 

Puzzle ID:#49250
Fun:*** (2.52)
Difficulty:** (1.37)
Category:Other
Submitted By:babyjuice*
Corrected By:dalfamnest

 

 

 



When's the next year when there won't be a Friday the 13th?


Answer

Never.

The 13th of each month will fall on different days, according to a complex pattern which takes several years to repeat, because of Leap Years. However, each day of the week comes up as the 13th within the first 9 or 10 months every year.

Assign A, B, C, D, E, F, & G randomly to Sun, Mon ... Sat.

If we assume, in a non leap year, that:
* 13 Jan is Day A, then
* 13 Feb is Day D,
* 13 Mar is Day D,
* 13 Apr is Day G,
* 13 May is Day B,
* 13 Jun is Day E,
* 13 Jly is Day G,
* 13 Aug is Day C,
* 13 Sep is Day F
Thus all seven possible days of the week have been used, within a 9-month period.

Similarly, in a leap year:
* 13 Jan is Day A, then
* 13 Feb is Day D,
* 13 Mar is Day E,
* 13 Apr is Day A,
* 13 May is Day C,
* 13 Jun is Day F,
* 13 Jly is Day A,
* 13 Aug is Day D,
* 13 Sep is Day G,
* 13 Oct is Day B,
Thus all seven possible days of the week have been used, within a 10-month period.

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