Mathematic Party Games

Go grab a calendar. Seriously, this will be way cooler with one. Bonus points if it’s for 2012. Got one? Trust me, you’ll want one for this. Still no? Fine, take this one. Open it up and follow along.

Riddle me this: What do 4-4, 6-6, 8-8, 10-10, and 12-12 have in common? Apart from being pairs of the same even number, that is. This is where your calendar comes in. Take a look at 4-4 (that is, April 4th). It was a Wednesday in 2012. How about 6-6 (June 6th)? Also a Wednesday. The same is true for August 8th, October 10th, and December 12th. If you don’t believe me you probably didn’t open up that calendar.

It turns our that these dates (4-4, 6-6, 8-8, 10-10, and 12-12) will always fall on the same key day within a year. In 2012 they are all Wednesdays, and in 2013 they will be Thursdays. This paves the way to a really cool party trick that I like to call “pretending to memorize a calendar”, where all you need to know is the key day for a given year. Have a friend pick a date – say the date the Mayans never said the world will end (December 21) – and in seconds you can tell them the day. In this case we know December is the 12th month, so 12-12 is a Wednesday. A week later is the 19th, the 20th is a Thursday, so the 21st is a Friday. It’s that easy!

But wait, there’s more! Those were just five easy-to-remember months – any chance there’s a similar pattern for the others? It turns out there is. The ninth of the fifth month and the fifth of the ninth month (May 9 and September 5) are also Wednesdays. That’s pretty easy to remember. Also, the eleventh of the seventh month and the seventh of the eleventh month (July 11 and November 7) are also Wednesdays. For those of you who like mnemonics, all it takes to remember that is the sentence: “I work nine to five at 7-11.”

That’s nine months of the year covered. Unfortunately March doesn’t have anything quite as easy to remember for it, but I happen to know that the nerdiest day of the year (Pi day – March 14) also falls on the same day as all these other key dates.

January and February are the only variable ones, because they have that leap day between them and other months. Fortunately enough, no matter what year it is the last day of February will also always be the same day of the week as our other key days, and we can work backwards from there. The only really tricky one is January, and even it has a pretty simple rule: three years out of four (non leap years), the 3rd of January is our key day (so a Thursday in 2013), and on the fourth year out of four (a leap year) it’s the 4th of January (Wednesday in 2012).

You are now literally seconds away from knowing the day of the week of any date for a given year – all you need to know is the one key day! Now go forth and impress people!

Quick recap for key days (within every year these dates will all fall on the same day of the week, no matter what):
January: Either the third (non-leap year) or fourth (leap year)
February: Last day of the month
March: Pi day! (fourteenth)
April: Fourth (even month)
May: Ninth (Nine to five mnemonic)
June: Sixth (even month)
July: Eleventh (7-11 mnemonic)
August: Eighth (even month)
September: Fifth
October: Tenth (even month)
November: Seventh
December: Twelfth (even month)