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July 27th, 2013, 05:49 PM  #1 
Member Joined: May 2013 From: Phnom Penh, Cambodia Posts: 77 Thanks: 0  Logic
Prove that for all years, there is at least 13th Friday.

July 31st, 2013, 01:51 AM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  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 06 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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