2006 AMC 10B Problem 16

Below is the professionally curated solution for Problem 16 of the 2006 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 10B solutions, or check the answer key.

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Concepts:date and time modular arithmetic

Difficulty rating: 1340

16.

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

Tuesday

Wednesday

Thursday

Friday

Saturday

Solution:

From one Leap Day to the next is $3\cdot365+366=1461$ days, and $1461\equiv 5\pmod 7.$

Over the four cycles from 2004 to 2020, the weekday advances $4\cdot5=20\equiv 6\pmod 7,$ that is, $6$ days forward, which is one day back from Sunday.

So Leap Day 2020 falls on a Saturday.

Thus, the correct answer is E.

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