What was the day of the week on 1st January, 2006?

To find the day of the week on January 1st, 2006, we'll use a reference date and count the odd days.

Taking January 1, 2000 as the reference date, which was a Saturday.

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Counting the days from January 1, 2000 to January 1, 2006:

Year 2000: Leap year = 366 days

Year 2001: Regular year = 365 days

Year 2002: Regular year = 365 days

Year 2003: Regular year = 365 days

Year 2004: Leap year = 366 days

Year 2005: Regular year = 365 days

Total days = 366 + 365 + 365 + 365 + 366 + 365 = 2192 days

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To find the day of the week, we calculate the number of odd days:

$2192 \div 7 = 313$ with remainder $1$

Alternatively, counting odd days for each year:

2000 (leap): 2 odd days

2001: 1 odd day

2002: 1 odd day

2003: 1 odd day

2004 (leap): 2 odd days

2005: 1 odd day

Total odd days = $2 + 1 + 1 + 1 + 2 + 1 = 8$ days

$8 \div 7 = 1$ odd day

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Starting from Saturday (January 1, 2000) and adding 1 day:

Saturday + 1 day = Sunday

Therefore, January 1st, 2006 was a Sunday.