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Printjmc
number theory senior
Problem
Lucy was born on Wednesday, December 1st, 2004. That Wednesday was the first day of her life. Her parents held a party for her on the th day of her life. On which day of the week was the party?
Solution
Since there are 7 days in a week, Lucy's 1st day, 8th day, 15th day, 22nd day, etc. were on Wednesday. When is divided by , the remainder is . Therefore, the 1002nd day was a Wednesday (since 1002 is one more than a multiple of 7). So the 1000th day, was two days earlier on a .
Final answer
\text{Monday}