How is Halloween the same as Christmas?

The season is appropriate to bring up this interesting relationship. Hopefully it will make you chuckle, pause a moment as you think about it, and then want to tell it to someone else.

Before I expose the answer, let me offer some hints because the revelation hits so much better when you make the connection on your own. That and I can embed and hide the explicit answer in the text so you hopefully do not see it before you want to.

Your first inclination might be to look at the overlapping religious significance of these holidays—but I assure you this is a purely technical/engineering/mathematical relationship that we are looking for here.

So putting aside the social context of these two events—how else could we find a common relationship between them? We can establish a spatial/temporal relationship between these two events by looking at the calendar. Halloween is October 31 and Christmas is December 25. Looking for the answer in the relative distance between these two dates is another red herring. Looking at the absolute placement of these dates on the calendar is also not useful.

So how are these two events the same? As with many technical challenges, being able to look at a problem from multiple and different angles can sometimes yield some interesting relationships that can greatly simplify how to describe and work with the problem.

One of my favorite examples of demonstrating this is teaching people how to quickly add up the numbers from 1 to 100 (or any arbitrary number) in a matter of seconds in your head. While some people might be able to add numbers in a monotonically rising sequence (ie 1 + 2 + 3 + …), most people find it easier to sum up the same number multiple times—say for example 100 + 100 + 100 + … So in this example what is 1 + 99, or 2 + 98, or even 3 + 97, or how about 49 + 51? To get the final answer to our question involves finding an easy number to sum up multiple times and then to add the remaining numbers that are left over—in this example –the number 50. In this example—the sum is 5050.

Another way to look at things from a different angle is to represent them in different notation schemes. For example, you can represent angles in degrees or radians. Each emphasizes slightly different insights into circles. So what if we looked at the dates of these two events in a common way but chose to interpret them slightly different than normal? A common abbreviation for dates is to write the first three letters of the month followed by the day within that month. For example, the Winter Solstice in the northern hemisphere occurs around Dec 21 or Dec 22 each year.

At this point, if you have not figured it out—write out the date of these two events in the same form I finished the last paragraph with and place an equal sign between the two dates. My last hint without actually placing the answer in this text is to interpret what you have written as a mathematical expression rather than as two dates. Remember that the two "words" you have written before each number can be interpreted as a number base, in this case, the less common octal, and the more common decimal number that most of the world uses on a much more regular basis.

Now this last paragraph is here for those people who decided to cheat and jump right to the end of the post to find out the answer. There is no answer here except to encourage you to go back and read the whole post to experience your own epiphany. Hopefully you will enjoy it and want to share it with some equally geeky friend/coworker because we are but a small minority of the people in the world—most of whom will say to such an answer: "Huh?"