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April 11th, 2018, 12:24 AM  #1 
Member Joined: Apr 2018 From: On Earth Posts: 34 Thanks: 0  Days of the Week Question
In a particular month one year, there were an odd number of Tuesdays that fell on oddnumbered days of the month. What are the only possible days of the week that the 18th of the month could have been? Does anyone know how to do this with working? Do you need to use algebra? 
April 11th, 2018, 01:27 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 2,584 Thanks: 1430 
Since the same day appears 7 dates apart we know that they will alternate even and odd dates. Thus there must have been 3 Tuesdays that fell on odd dates. we can get away with this with the first Tuesday being either the 1st or the 3rd since months have no more than 31 days. The 18th appears on friday if the the 1st is a tuesday, and on wednesday if the 3rd is a tuesday. 

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