More Non-Math Sequences
Purplemath
How can a sequence be culturally specific?
A list can be culturally specific if the answer for the next entry in the list requires knowledge of a particular language or culture. If you have to be familiar with which actors played Doctor Who and in what order, or the names of the days of the week in the Swati language, then the answer has precious little to do with mathematics.
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.
- Find the next number in the sequence: 6, 6, 7, 9, ...
"Sunday" is spelled with six letters.
"Monday" is spelled with six letters.
"Tuesday" is spelled with seven letters.
"Wednesday" is spelled with nine letters.
"Thursday" is spelled with 8 letters.
- Find the next term in the sequence:
F21, S23, T25, T27, S29, M31.
F21: Friday the 21st.
S23: Sunday the 23rd.
T25: Tuesday the 25th.
T27: Thursday the 27th.
S29: Saturday the 29th.
M31: Monday the 31st.
Skipping every other day, the next term must be "Wednesday the 2nd", or "W2" (or maybe "W02").
(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.)
- Find the missing term in the seqence: 325, 446, 567, ___, 709, 820.
This is another math-adjacent puzzler, where you need to pull the numbers apart and deal with the digits for the units, tens, and hundreds places separately:
hundreds digits: 3, 4, 5, ___, 7, 8
tens digits: 2, 4, 6, ___, 0, 2
ones digits: 5, 6, 7, ___, 9, 0
They're adding by one in the hundreds and ones digits, and adding by twos in the tens digit. And, if they get a two-digit answer, they drop the tens digit and keep only the ones digit.
The missing term is 688.
- Find the missing term in the sequence: 127863, 12789, ____, 135, 18
Look at the last two digits of the given numbers.
127863: 6 + 3 = 9
12789: 8 + 9 = 17
_______
135: 3 + 5 = 8
Do you see? They're taking the last two digits, adding them, replacing the last two digits with one zero, and then adding the sum they just found. Completing the pattern:
127863: 6 + 3 = 9: 12780 + 9 = 12789
12789: 8 + 9 = 17: 1270 + 17 = 1287
1287: 8 + 7 = 15: 120 + 15 = 135
135: 3 + 5 = 8: 10 + 8 = 18
Because the pattern does give me the last two values in the list, I'm confident that my answer for the midding value is correct, too. So the missing number is:
1287
Many times (especially on Facebook) you'll see something that looks like this:
2 + 3 = 13
3 + 4 = 25
4 + 5 = 41
5 + 6 = ??
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.
This problem only works in English
Spell the numbers out as words, and count the letters: "one" and "two" each have three letters, and 3×3 = 9. "Three" has five letters and "four" has four; 5×4 = 20. "Five" has four letters and "six" has three; 4×3 = 12. "Seventeen" has nine letters and "twelve" has six, so the missing number is the product of 9 and 6: 54
- Find the next number in the following sequence: 1, 11, 21, 1211, 111221,....
This looks like a "math" sequence, but it isn't really. Instead, each term is a description of the preceding term. The first term is just one "1", or "1 1", which they concatenate as 11. The second term is two "1's": 21. And so forth:
one 1: 11
two 1's: 21
one 2 and one 1: 1211
one 1, one 2, and two 1's: 111221
three 1's, two 2's, and one 1: 312211
So the next term is:
312211
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.
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.
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