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July 27th, 2013, 05:49 PM   #1
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Logic

Prove that for all years, there is at least 13th Friday.
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July 31st, 2013, 01:51 AM   #2
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Re: Logic

For a normal year, the 13th of each month will be offset from the 13th Jan as follows:

0336 1462 5035

And for a leap year:

0340 2503 6146

So, in a normal year, if the 13th of January is a Monday, then the 13 of Feb is Mon + 3 = Thu and the 13th of Dec is Mon + 5 = Sat etc.

Note that for both sequences, the numbers 0-6 appear somewhere. So, each day of the week is the 13th of at least one month.

This is true for every day of the month, except the 31st. Even though there are 7 months with 31 days, the 31st never falls on every day of the week in a given year.
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