2006 AMC 10B Problem 16

Moving a date forward one ordinary year adds $365 = 52 \cdot 7 + 1$ days, which pushes the weekday forward by $1$. If the year crossed contains a February $29$, the jump is $366$ days and the weekday moves forward by $2$.

From February 29, 2004 to February 29, 2020 is $16$ years. The leap days passed along the way are February 29 of $2008$, $2012$, $2016$, and $2020$: four of them (none of these years is a century exception). So $4$ of the $16$ yearly steps shift by $2$ and the other $12$ shift by $1$:
$$12 \cdot 1 + 4 \cdot 2 = 20 \equiv 6 \pmod 7.$$

Six days after Sunday is Saturday (equivalently, one day back).

The answer is $\boxed{\textbf{(E)}\ \textrm{Saturday}}$.

Weekday problems are counting mod $7$, and a year is "one extra day" (two for a leap year) rather than $365$ days, which avoids big numbers. The only thing to get right is how many leap days lie strictly after the start date and up to the end date; here the target date is itself a leap day and counts.

Count days: $16 \cdot 365 + 4 = 5844 = 7 \cdot 835 - 1$, so the date moves one weekday backward from Sunday to Saturday.

• Counting 3 leap years instead of 4 (the leap day of 2020 itself is inside the interval), landing on Friday.
• Adding $16$ days without any leap adjustment ($16 \equiv 2$, giving Tuesday).