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2006 AMC 10B Problem 16

Problem 16 of 25IntermediateAlgebraNumber Theory

Leap Day, February 29,29, 2004,2004, occurred on a Sunday. On what day of the week will Leap Day, February 29,29, 2020,2020, occur?

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Solution

From one Leap Day to the next is 3365+366=14613\cdot365+366=1461 days, and 14615(mod7).1461\equiv 5\pmod 7. Over the four cycles from 20042004 to 2020,2020, the weekday advances 45=206(mod7),4\cdot5=20\equiv 6\pmod 7, that is, 66 days forward, which is one day back from Sunday. So Leap Day 20202020 falls on a Saturday. Thus, the correct answer is E.

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Concepts: date and time · modular arithmetic

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.