On 8th Feb, 2005 it was Tuesday. What was the day of the week on 7th Feb, 2004?

Concept: In the calendar 'odd days' method, the number of days elapsed between two dates, divided by 7, gives complete weeks (no weekday change) plus a remainder called the odd days. An ordinary (365-day) year contributes 1 odd day; a leap year (366 days) contributes 2 odd days, but only when the span in question actually contains the leap day, 29 February, inside it. Moving forward in time by n odd days advances the weekday by n steps; moving backward subtracts n steps.

Application:

1. Identify the span: from 7 Feb 2004 (day unknown) to 8 Feb 2005 (known to be Tuesday).

2. Split the span into two parts: (a) 7 Feb 2004 to 7 Feb 2005, exactly twelve months, and (b) 7 Feb 2005 to 8 Feb 2005, one extra day.

3. Part (a) contains 29 Feb 2004, since 2004 is a leap year, so this twelve-month span contributes 2 odd days.

4. Part (b) contributes 1 more odd day.

5. Total odd days across the whole span = 2 + 1 = 3.

6. Since 8 Feb 2005 falls 3 odd days after 7 Feb 2004, stepping three weekdays backward from Tuesday gives the day on 7 Feb 2004: Tuesday, Monday, Sunday, Saturday.

7. So 7 Feb 2004 was a Saturday.

Cross-check: Starting from Saturday on 7 Feb 2004 and stepping forward the same 3 odd days gives Saturday, Sunday, Monday, Tuesday, landing exactly on Tuesday for 8 Feb 2005 as given — confirming the result.

Result: Saturday.