### Instruction: January 1, 2000 was on a Saturday. On what day of the week was January 1, 1960?### Response: I know that every year, the day of the week that January 1 falls on shifts by one, except if the previous year was a leap year, in which case it shifts by two.
So I need to figure out how many leap years there were between 1960 and 2000, and how many regular years there were.
A year is a leap year if it is divisible by 4, except if it is also divisible by 100, unless it is also divisible by 400.
So, for example, 2000 was a leap year, but 2100 will not be.
Between 1960 and 2000, there were 40 years, 10 of which were divisible by 4 and also by 100: 1960, 1964, 1968, 1972, 1976, 1980, 1984, 1988, 1992, and 1996.
Of these, only 2000 was divisible by 400, so it was the only exception to the rule.
That means there were 10 leap years and 30 regular years between 1960 and 2000.
So, the day of the week that January 1 falls on shifted by 10 * 2 + 30 * 1 = 50 days.
However, shifting by 7 days is equivalent to shifting by 0 days, since there are 7 days in a week.
So, I can divide 50 by 7 and get the remainder, which is the actual number of days that January 1 shifted by.
50 divided by 7 gives a quotient of 7 and a remainder of 1.
That means January 1, 2000 was one day later in the week than January 1, 1960.
Since January 1, 2000 was a Saturday, January 1, 1960 must have been a Friday.