Problem 3 · 2008 AMC 8
Easy
Arithmetic & Operations
modular-days
If February is a month that contains Friday the 13th, what day of the week is February 1?
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Answer: A — Sunday.
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Hint 1 of 2
Dates exactly 7 apart land on the same weekday — so the 13th, 6th, and (if it existed) the −1st are all Fridays. Find the nearest Friday to the 1st.
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Hint 2 of 2
To walk back many days, throw away whole weeks first: only the leftover after dividing by 7 matters.
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Approach: jump by whole weeks, then count the leftover
- Subtracting a week keeps the weekday: Feb 13 is Friday, so Feb 6 is also Friday. That puts the Friday right next to Feb 1.
- From Friday the 6th step back to the 1st — that's 5 days: Thu(5), Wed(4), Tue(3), Mon(2), Sun(1).
- Why this transfers: any "what day was X days ago/later" problem — subtract whole weeks (multiples of 7) until you have a tiny number to count by hand.
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