Fun with math - Doomsday Rule. Coolest trick EVER: Guess what day of the week a person was born.

THE DOOMSDAYS:

I have taught classes from Pre-Algebra up to AP Stats and most in between. Although solving equations, calculating derivatives, and performing regression analysis are all fine and dandy, the thing students tend to be impressed with is learning the Doomsday trick, which is how to guess what day of the week someone was born. I will attempt to teach it to you, in 5 easy steps. The most difficult math involved is dividing by 2, adding 11, and knowing some multiples of 7. Not too bad!

First, the Doomsday Rule has it's own Wikipedia page for those of you interested in learning more: https://en.wikipedia.org/wiki/Doomsday_rule

Second, you can actually guess any day for centuries back and forward, but we will focus on the 1900s and 2000s for ease.

Third, the steps are simple, but it takes a bit of time to practice. Arthur Benjamin is the best at it: https://www.youtube.com/watch?v=M4vqr3_ROIk

In the steps below we will try to figure out what day of the week Dec 10, 1964 and Jan 15, 2007 were. in order to use specific examples for illustration purposes.

Without further ado, here goes:

1. You first need to know that for the year 1900, the "Doomsday" was a Wednesday and for 2000, the "Doomsday" was a Tuesday. Therefore if someone asks you to guess the date for either of those 2 years, you will be able to skip steps 3 and 4 below! For any year aside from those, we need to figure out how many days (1-7) they are away from those and use all 5 steps.
2. What is a Doomsday? It's just the name given to certain dates that are the same day of the week as the Doomsday every month of every year. The Doomsdays are based on the calendar at the top of this post. They may seem complicated to remember, but they really aren't. Notice that 4/4, 6/6, 8/8, 10/10, and 12/12 are Doomsdays. Easy. She works 9/5, and so naturally 5/9 are as well. Slurpees at 7/11 are tasty, and hence 11/7 is a Doomsday too. This is a math trick, so Pie Day 3/14 is a Doomsday. Finally Jan and Feb have 2 options. Leap years fall every 4 years, so if you're trying to guess a date from a leap year (one divisible by 4) then 1/4 is a Doomsday, if not 1/3 (the other 3 years in the cycle). And finally the last day of Feb, either 2/28 or 2/29, are Doomsdays. What this means is that once you know what day of the week the Doomsday is, then all of those dates each month would be a the same day of the week. We will figure those out in steps 3 &4. But if we calculate the doomsday to be a Saturday, then 1/3 or 1/4, 2/28 or 2/9, 3/14, 4/4, 5/9, 6/6, 7/11, 8/8, 9/5, 10/10, 11/7 and 12/12 would ALL be Saturdays. 
3. Now ready for the math? You take the last 2 digits of the year someone is born. For the example Dec 10, 1964 you take 64. If that 2 digit number is even, divide by 2. (so 64/2 = 32). If the 2 digit number is odd, first add 11 then divide by 2. For the example Jan 15, 2007 you add 11 to 07 and divide by 2 to get 9. Once you have divided by 2, if the result is even you will use that 2 digit number in step 4 (like 32 in the first example). If the resulting number is odd (like 9 in the 2nd example) you add 11 again and STOP (so here we would use 9 + 11 = 20).
4. Based on the answer you achieved in step 3 (the 32 for Dec 10, 1964 or 20 for Jan 15, 2007), find the multiple of 7 (because there are 7 days a week) that is closest to our number from step 3, but just over it. So for 32 we would use 35 (7x5) and for 20 we would use 21 (7x3). Calculate the difference between big number and number from step 3 (so 35-32 = 3 for Dec 10, 1964 or 21-20 = 1 for Jan 15, 2007) and that tells you what your specific year's Doomsday is. For the 1964 example the Doomsday is 3 days past Wednesday (recall from step 1 that 1900 base is Wednesday) which means Saturday. For the 2nd example it would be a Wednesday, because that is 1 day past the 2000s Doomsday of Tuesday.
5. Final step: Now that you know that all of those key days are the same day of the week, figure out where the specific date you are searching for falls relative to the weekday found in Step 4. For Dec 10, 1964, we know that 12/12 would be a Saturday, so Dec 10 being 2 days before that would be a Thursday. In the case of Jan 15, 2007, we know that Jan 3 would be a Wednesday (because 2007 is not a leap year of course), so Jan 10 would also be a Wednesday. Jan 15 being 5 days later, it should therefore have fallen on a Monday.

Finally you should do a big reveal. Make a show of it, and tell your guest that Dec 10, 1964 was a Thursday and/or Jan 15, 2007 was a Monday. You can generally get a laugh if you claim that it was partly cloudy, rainy or snowy, depending on how you feel at that moment. 

I hope that this is a fun little trick for you to learn. It doesn't take that long to master the 5 steps, although it does take a little bit of practice to do it mentally. Initially you can try writing the numbers down (not necessarily the Doomsday dates, but the dividing by 2, adding 11, etc...) I am confident that within an hour or so you can actually have it mastered by doing it all mentally. A little trick would be to ask for the year first (as does Arthur Benjamin in the video above) in order to take care of steps 3 & 4 with minimal distraction. Then you ask for the month and date in order to take care of step 5. 

Have fun with this, give it a go, and please let me know how it went...