If August 12, 2004, fell on a Thursday, on which day of the week did August 12, 2008, fall?

The correct answer is Tuesday.

Step 1: Understand the time period
We need to determine the day of the week for August 12, 2008, given that August 12, 2004, fell on a Thursday.

The total duration between August 12, 2004, and August 12, 2008, is exactly 4 years.

Step 2: Calculate odd days for each year in the interval
An ordinary year consists of 365 days (52 weeks + 1 odd day).
A leap year consists of 366 days (52 weeks + 2 odd days).

Let us analyze each 1-year period:

1. From August 12, 2004 to August 12, 2005: 1 ordinary year = 1 odd day (Note: February 29, 2004 passed before August 12, 2004).
2. From August 12, 2005 to August 12, 2006: 1 ordinary year = 1 odd day.
3. From August 12, 2006 to August 12, 2007: 1 ordinary year = 1 odd day.
4. From August 12, 2007 to August 12, 2008: 2008 is a leap year and February 29, 2008 is included in this range = 2 odd days.

Step 3: Calculate the total number of odd days

$\text{Total odd days}=1+1+1+2=5$

Step 4: Count forward from the original day
We add 5 odd days to Thursday:

Thursday + 1 day = Friday
Thursday + 2 days = Saturday
Thursday + 3 days = Sunday
Thursday + 4 days = Monday
Thursday + 5 days = Tuesday

Therefore, August 12, 2008, fell on a Tuesday.