"Name That Day"

by Jack Sarfaty and Brian Seitz


Given any random date (month, day, year) ,
name the day
of the week that date fell on.

Example: What day did July 9, 1957 fall on?

Answer: Tuesday


We know that in the year 1900, April 4 was a Wednesday.

This means that the day 4/4/1900 was a Wednesday. (THIS IS THE KEY TO THE PROBLEM)

Also, in 1900, the following days were all Wednesdays: June 6, August 8, October 10, and December 8. Each of these days are as important as 4/4. When asked what day you are looking for, you need to know which day of the month was a wednesday. Well, if you notice, these days are 4/4, 6/6, 8/8, 10/10, and 12/12 when written in MM/DD form. There are four other days that we need to concern ourselves with that are equally important to 4/4: 5/9, 9/5, 7/11, and 11/7. Figure out your own method to remember a pattern. All of these days are Wednesdays. Also, notice that we have only dealt with the months of April through December. January through March requires a bit more guile.

Given this information, we are given a date to find the day of the week, say the example from above, July 9th, 1957.

Let's take a look at a second example. Suppose we want to find out what day of the week December 7, 1941 ('a day that will live in infamy'; maybe, you've heard of it). We will repeat the same process from above.

Here's a date where our work gets a bit difficult: Find the day of the week that Valentine's Day fell on in 1903; so we need to find the day of 2/14/1903.

The question now becomes, "Can we determine days from different centuries?" This may be a solution for the reader to determine, but from what we've determined, April 4 of the year 2000 is a Thursday. So all of the key dates that we have to keep track of a Thursdays for the 21st century. Using a bit of the logic we have developed, we can assume that the key dates for the 19th century are Tuesdays, and the key days for the 18th century are Mondays.

So if anyone asks you what day of the week July 4, 1776 fell on, remember Monday is the key day; and 4/4, 6/6, 8/8, 10/10, 12/12, 5/9, 9/5, 7/11, and 11/7 are the key dates.

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