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.
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
To find the day of the week, we calculate the number of odd days:
2192÷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÷7=1 odd day
Starting from Saturday (January 1, 2000) and adding 1 day:
Saturday + 1 day = Sunday
Therefore, January 1st, 2006 was a Sunday.