Do a date that needs counting backward: what day was 1 January 2000?

Saturday.

1. Anchor (2000s) = Tuesday (2), so 2000's doomsday = Tuesday (q=r=s=0).
2. January anchor: 2000 is a leap year, so January's doomsday is 1/4 (Tuesday).
3. 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.