More Non-Math Sequences

When I was in college, a professor gave this list: 1, 3, 5, 7. He asked what the next number would be. We all said, "Nine", that being the next odd number. He said that, no, he was thinking in terms of a certain (imaginary) cult that worshipped the letter E. The next number which, in its English spelling, contains the letter E is "eight".

That's pretty much what's going on in all of these non-math sequences. I've even seen one that required that you know the kings on England, in order, including if they were deposed and then re-took the throne. That's. Not. Math.

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• Find the next number in the sequence: 6, 6, 7, 9, ...

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• Find the next term in the sequence:
  F21, S23, T25, T27, S29, M31.

(If you're not sure about this, then pull out a calendar and find a month where Friday falls on the twenty-first. See where this leads you.)

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• Find the missing term in the seqence: 325, 446, 567, ___, 709, 820.

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• Find the missing term in the sequence: 127863, 12789, ____, 135, 18

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Many times (especially on Facebook) you'll see something that looks like this:

But these "equations" aren't even true! What they mean is that they have a rule that takes two inputs (such as the 2 and the 3) and some operation (which is being called "addition", even though it's not), and spits out the listed values.

I wouldn't mind so much if they would use a different symbol — ⋇, say — for their operator. But, no; they use "plus", when all they mean is "is combined in some manner with". That's not mathematics; it's just mathiness.

(By the way, the rule for the puzzler above is "multiply the two numbers, multiply the result by 2, and then add 1. So the exercise was kinda mathematical, but not in the way that they said.)

• Given that 1 and 2 yield 9, 3 and 4 yield 20, and 5 and 6 yield 12, find the number yielded by 17 and 12.

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• Find the next number in the following sequence: 1, 11, 21, 1211, 111221,....

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When given a sequence problem in a math class, you would like to think that it is an actual math problem. So always try first (assuming the sequence is of numbers and not of letters) to find a mathematical rule for it. Try to find a polynomial or exponential formula. If that doesn't work, try to find a recursive relationship. If that doesn't work, you're probably out of luck, but try anyway, and see if you can come up with something clever.

In any case, don't feel that these problems reflect badly on you. These kinds of problems have become trendy, with the philosophy being that you like struggling for days with a math problem that turns out to be non-mathematical, because it broadens your horizons and strengthens your innate love of mathematics and.... Well, they get pretty syrupy and emotional at this point.

Anyway, unless you're explicitly studying sequences and series (in precalulus or calculus), you probably don't have the tools for answering these questions, so you shouldn't take it personally if you're not coming up with the expected answers.

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By the way, I would like to add to the above collection of examples (if they're not already listed on this archived collection). If you think you have a good example of a non-mathematical sequence (in particular, a non-math sequence complete with its "answer"), please let me know, and I will consider adding it to this page. Thank you.