What are the doomsday dates for January and February — and why do they depend on the year?

They shift by one in leap years: January is 1/3 (common) or 1/4 (leap); February is the last day, 2/28 (common) or 2/29 (leap).

• January: 3rd in common years, 4th in leap years. (Mnemonic: "the 3rd 3 years in 4, and the 4th in the 4th.")
• February: always the last day — 2/28 or 2/29.

Because the leap day sits inside this stretch (end of February), the dates before it shift when the year is a leap year — which is exactly Jan and the Feb anchor.