2010 AMC 10A Problems/Problem 10

Revision as of 21:24, 11 October 2010 by Sendhil (talk | contribs) (Not-very-elegant solution, but it's a start)
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(E) 2017

There are 365 days in a non-leap year. There are 7 days in a week. Since 365 = 52 * 7 + 1 (or 365 is congruent to 1 mod 7), the same date (after February) moves "forward" one day in the subsequent year, if that year is not a leap year.

For example: 5/27/08 Tue 5/27/09 Wed

However, a leap year has 366 days, and 366 = 52 * 7 + 2. So the same date (after February) moves "forward" two days in the subsequent year, if that year is a leap year.

For example: 5/27/11 Fri 5/27/12 Sun

You can keep count forward to find that the first time this date falls on a Saturday is in 2017:

5/27/13 Mon 5/27/14 Tue 5/27/15 Wed 5/27/16 Fri 5/27/17 Sat

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