Fun Math Games
A way to pass the time
I sometimes entertain myself with mental computation. This is a silly thing to do, as the existence of calculators and later cell phones has long since automated the activity. Nevertheless, I persist. And who truly knows what is useful? I showed off occasionally by doing wacky computations in my head when I taught an SAT class, and one of the students referred me for my first software job.
That’s right. You heard it here first. Play my strange games, and ascend the economic ladder. What could go wrong?
The one rule: you have to do them in your head.
Prime Finder
The classic. Start with some number - 100 if you’re new, 1000 or 2000 if you’re a veteran - and figure out what the next prime is. If you have a friend to play with, first of all, I seethe with jealousy, but anyway you can either race or take turns. Overall, this game is pretty easy, even for high numbers. I will give you some pro tips:
You only have to check for divisibility of all the primes up to the square root of each candidate number. The square root of 1000 is less than 37, so that means you only have to check the numbers up to 31 if you start there.
You can check for divisibility by 3 by adding up the digits and dividing by 3. Combined with the fact that divisibility by 2 or 5 is immediately obvious, you can skip most numbers immediately.
This one may be hard to follow, but the mechanism I find easiest for seeing if some number divides some other number is adding (or subtracting) whatever multiple will make it end in 0, then dividing by 10, and repeating until the answer is obvious. I’ll do an example.
Suppose we want to see if 1016 is divisible by 7.
7 does not go evenly into 11, so 1016 is not divisible by 7. If you didn’t follow that, these games may not be for you. Alternatively, I may be bad at explaining math. I sure was as a kid; just ask my family.
Find the Factors
This is a variant of the previous game, but this time our mission is to find the full prime factorization of each number in sequence, starting with some moderately high number. Lower than for the last game, though. I recommend about 200. Using 200 as an example:
Etc.
This one is most fun with some time pressure. I usually play it when driving on an interstate, trying to factor each mile number before the mile ends. It’s less cognitively intense than “find the primes” and is extra good when the numbers get higher over time.
It’s also fun with bigger numbers, like 2886, because you have to hold more things in your head as you go. (For example, you add the digits and notice it’s divisible by 3, then divide by 3 in your head and get 962, but now you need to figure out what 962 is divisible by while also holding in your head that your answer includes a 3. Thrilling!)
Long Division
You just do long division in your head. Pretty straightforward. The trick here is that any long division problem will eventually start repeating decimals, so even though the result may be infinite you can always come up with a definite answer. This isn’t the most fun version of this particular game, though. That would be…
Long Division in a Different Base
Now we’re talking! By “base” here I mean alternatives to “base 10.” In base 8, for example, you count 1, 2, 3, 4, 5, 6, 7, 10, and 77 + 1 = 100. To do long division in a different base, you have to do all the computations in your chosen base.
Actually, I’ve kind of skipped some steps here. To warm up for this one, first you should try doing some simpler mental math in a different base. Like, say, multiplying two-digit numbers in base 8. For example, let’s do 17 * 23.
The fun thing about this warm up game is you can check your work by converting both the question and answer back to good ol’ fashioned base 10.
17 in base 8 is 8 + 7, which is 15, and 23 in base 8 is 16 + 3, which is 19. 15 * 19 in base 10 is 300 - 15, which is 285. So to check our work:
Tada!
So anyway, you do that, but with long division. Good luck! Next time I do zany computation-posting, we’ll get to one of my favorite mathematical diversions: a mysterious world where 2 + 2 = 10300. But that shall have to wait.
I'm only liking this because of the cool "your brain on math" AI image.
For factoring, I would definitely start by removing all the 2s. It's easy, it's always instantly obvious if you're done, and for any even number it'll make the number smaller effectively for free. After 2s are 5s for the same reason.