Friday, April 06, 2007

Fridays the 13th

There is always one in every year.

Proof as follows.

Assume that 13th Jan is on day 1 (of 7) - it doesn't matter which. Jan has 31 days, so 4 weeks & 3 days, so 13th Feb will be on day 4 and so on - table below.

MonthNormal YearLeap Year
Jan11
Feb44
Mar45
Apr71
May23
Jun56
Jul71
Aug34
Sep67
Oct12
Nov45
Dec67


As you can see from this, in both cases, all 7 numbers / weekdays are used. Therefore regardless of which day of the week the year starts (or 13th of Jan is on - these conditions are equivalent for this argument), there will always be at least one Friday 13th. Also, you can see that the most there can be is 3 in a year - if Feb 13th is a Friday (for normal years) or if Jan 13th is (for leap years).

So this year July 13th will be a Friday (although you could have got this trivially from any calendar) as 2007 is a 7 = "Friday" year (and is not a leap year).

Inspired by posting the TerryWatch poll for this week. Now back to being rude about things :)

S-E

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