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Figure This!


Your answer depends on your date of birth. For example, a student born on December 31, 1986, was born on Wednesday.


Complete Solution:

There are many ways to approach this problem.

A general approach to this problem involves creating a step-by-step procedure for determining the day of the week for a past date. One way to describe such a procedure is with a flowchart. The flowchart given here finds the day of the week for any date from 1900 to 2000 (The Farmer’s Almanac, p. 113).

Alternate Solution:

Another way to find the day of the week of your birth follows: Consider the number of days in a year. Non-leap years have 365 days. Since 365 ÷ 7 gives a remainder of 1, then any particular date moves ahead one day of the week in the following year. Going back a year, each date moves back one day of the week. Since leap years have 366 days, and 366 ÷ 7 gives a remainder of 2, any date moves ahead two days of the week in the year following a leap year.

This means that when going back in time, each date moves back two days of the week for each leap year. (Note: If the current year is a leap year, then only dates after February 29 will have moved two days ahead.)

Suppose that you were born on December 31, 1986. From the hint, you know that January 1, 2000 was a Saturday. That means that December 31, 1999 was a Friday. The year 1986 was 13 years before 1999. The years 1988, 1992, and 1996 were all leap years. That means that the day of the week moves backward 13 + 3, or 16 days. Since 16 ÷ 7 gives a remainder of 2, you should count back two days from Friday to get Wednesday.

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