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Purple Comet 2009 MS Question 3

Source:

July 28, 2011
Purple Comet

Problem Statement

The Purple Comet! Math Meet runs from April 27 through May 3, so the sum of the calendar dates for these seven days is 27+28+29+30+1+2+3=120.27 + 28 + 29 + 30 + 1 + 2 + 3 = 120. What is the largest sum of the calendar dates for seven consecutive Fridays occurring at any time in any year?
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