Original Manuscript

THE DATING GAME

In “Reader’s Reflections” (1996 April, 267) Arron Eisen discusses his custom of drawing on one or more aspects of mathematics to write the day’s date in a special form for his class. I believe this is a creative and effective way to build “number consciousness,” where by this term I mean a cultivated tendency to search for and recognize special properties of the smallest natural numbers. For example, he mentions writing September 24 as September 4!, thus underscoring that 24 is a factorial. I also practice this bit of number play, although not on a daily basis.

CONSTANTS
I particularly like to present a “constant of the day” when I can. It’s a delight to walk into a class on October 24 (and/or February 10) and write 1K on the blackboard. Certainly March 14 and June 18 suggest and respectively, as do July 22 and August 13; e can be assigned to July 19.

PRIMES
Some dates such as St. Patrick’s Day could be called “particularly prime” since 3, 17 and 317 are all primes. Have students search for other dates in which the month, day of the month and the concatenation of these two are all primes. There are pairs of such dates in which twin primes occur (e.g. 3/11 and 3/13). Both (11, 13) and (311, 313) are prime pairs.

POWERS
On September 8 (August 9 would be better, but school is not in session) I like to write “ONLY SUCCESSIVE POWERS?” on the board. This is an opportunity to inform students that although it is been proven that 8 and 9 are the only square and cube which differ by 1, no one knows if these are the only powers which differ by 1. This is the celebrated Catalan conjecture.

CHRISTMAS
Of course we’re not in the classroom on this day, but the final class day before Christmas vacation might be a good time to point out that 12/25 is very special mathematically, as well as religiously. 1225 is both the square of 35, and the sum of the first 49 numbers, making it a triangular-square number. Have students find the only other triangular-square (aside from the trivial 1) which is less that 1225. What date can it be corresponded with?

INCLUDING THE DAY OF THE YEAR
The day of the year can be incorporated into this game as well, adding to the fun. Students can even be asked to write a program which displays all the days of the year in the form “M/DM/DY” where M stands for month, DM for day of the month, and DY for day of the year. A nice challenge is to ask them to design the program in such a way that it can easily be modified to work for leap years.

Since August 21 is the 233rd day of the year in common years (non-leap years), it probably wins the award for the “most Fibonacci” of the dates. Only one other non-trivial (excluding January dates), Fibonacci date occurs in either a common or leap year.

Traditional Memorial day, May 30, is the 150th day in common years. There is only one other non-trivial, common-year, date where the product of the month and the day of the month is the day of the year, that is M*DM = DY. Appropriately it is the birthday of perhaps the greatest mathematician of all time. If a student is successful in writing the above mentioned program, it can easily be extended to check for such dates. One other date of this type occurs in leap years.

There are a host of other combinations that can be searched for with a program, or without. For example, searching through both types of years, can you find date (s) M/DM/DY:

1. where M, DM, and DY are all squares? all triangular numbers?
2. where M and DM both divide DY? more specially, where M*DM divides DY? Here the programming language’s mod function can be utilized.
3. DY is a power of both M and DM.

VARIATIONS
Variations can include incorporating the year itself into the challenge, and using some the different formats computers use to express dates. One popular format is the “m/d/yy” format. For example here, one could ask for something as simple as the dates in which m*d = yy. For the current year this would include 4/24/96, 6/16/96, 8/12/96 and 12/8/96.

Finally, bringing a digital clock into the classroom and asking similar question about the time, rather than the date, opens up yet another doorway to this entertaining room. Speaking of the incomparable primes, curiously all of the following are prime numbers—1259, 59, 1231, 31. They are respectively

1. the largest number displayed on a digital clock (concatenating hour and minute),
2. the largest number displayed in the minute portion of a digital clock,
3. the largest number formed by concatenating the month and the day of the month and,
4. the largest number representing a day of the month.