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Topic
Year & Century Anchors
Question
Work out the doomsday for 1978 step by step.
Answer
1978 → Tuesday.
Century anchor for the 1900s = Wednesday (3). Now YY = 78:
- q = 78 ÷ 12 = 6
- r = 78 − 72 = 6
- s = 6 ÷ 4 = 1
- Sum: 3 + 6 + 6 + 1 = 16, and 16 mod 7 = 2 = Tuesday.
Check: 1978's doomsday is indeed Tuesday. ✓ (So 4/4/1978, 6/6/1978, etc. were all Tuesdays.)
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Topic
Full Method & Practice
Question
Do a date that needs counting backward: what day was 1 January 2000?
Answer
Saturday.
- Anchor (2000s) = Tuesday (2), so 2000's doomsday = Tuesday (q=r=s=0).
- January anchor: 2000 is a leap year, so January's doomsday is 1/4 (Tuesday).
- The date: 1 is 3 days before the 4th: 1 − 4 = −3, and Tuesday − 3 = 2 − 3 = −1 ≡ 6 = Saturday.
Check: 1 January 2000 was a Saturday. ✓ Offsets can be negative — just step backward and wrap around mod 7.
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