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Stuck in the Past

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

2013 is the only year before 2015 in which each date will fall on the same day of the week as it did in 2002.
Year 2002 2003 2004 2005 2006 2007 2008
1st January Tue Wed Thu Sat Sun Mon Tue
2009 2010 2011 2012 2013 2014 2015
Thu Fri Sat Sun Tue Wed Thu
So two of the years before 2015 start on a Tuesday. But each date has to fall on the same day and since 2008 is a leap year but 2002 wasn't, it must be excluded.

This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.