# Number-Sequence Puzzles: What (Not) To Do?

Similar to Code Puzzles: What (Not) To Do? as this is a genre which I feel also drastically needs improvement.

1, 6, 3, 8, 5, 10, 7, 12, ?, ?

What are the next two numbers in this sequence?

I have seen far too many of these and they make up the quite a lot of the puzzles.

There are some great number-sequence puzzles. But not one of them looks like the above. I feel a lot of these puzzles are either homework or belong on the maths site.

At the time of this post, the two most recent posts are at -10 and -7 are almost exactly the same as the fake copy above. I don't want the site to get bogged down as such.

Now instead of just watching get closed, downvoted into oblivion and eventually deleted, I want the poster of the puzzle to understand why and learn how to make a good one.

I have seen a post requesting a ban, but I don't think that's the answer to this problem. If people know how to make one, then we should have less of this issue in the future.

This will hopefully set the standard when it comes to these puzzles.

• As a first step towards analysing what makes such a puzzle good or bad, can you (or anyone else) come up with an example of a really good number sequence puzzle? Commented Dec 31, 2016 at 14:52
• @randal'thor I'll have a look through the tagged puzzles Commented Dec 31, 2016 at 15:04
• @randal'thor Here's a link to the current top voted pure [number-sequence] question puzzling.stackexchange.com/q/20135/31384 Commented Dec 31, 2016 at 15:04
• And here is the highest voted puzzle tagged number-sequence Commented Dec 31, 2016 at 15:18
• @randal'thor Back in the old days I had a teacher who instructed us to close our eyes, and try to guess the general formula of a number sequence, which started as 1, 2, 4, 8, 16, ..., and then 33 (what a surprise!) instead of 32, as everyone expected. I find this a most amusing number sequence puzzle. But I don't think that something like this is a good fit for this site. Hint: oeis.org/A004149 . Commented Dec 31, 2016 at 16:24
• This is another well-received number-sequence puzzle, even though it's not tagged as such. Commented Jan 1, 2017 at 4:50
• or belong on the maths site $\to$ No. Not ever are such questions well received on MSE. Garbage is garbage. No matter what the average person thinks what mathematics are. Commented Sep 19, 2019 at 22:20

Simple as that:

Search OEIS for that sequence.

If it appears there, the puzzle is very likely to:

• be boring (if that is the intended answer),
• be closed for being too broad (if not).

To improve add some clues in the puzzle. These may hint a connection to properties of this sequence or link to another sequence. It is not needed that the text is in a format. It can be any other puzzle or simple text that would make the challenge innovative, interesting and unambiguous.

• Yes, this is one very good test (+1). However, there must be more to it than that. Perhaps you could expand on this answer, or make it community wiki so that others can? Commented Jan 2, 2017 at 12:50
• Indeed there should be other restraints. If I come up with some magical sequence not in OEIS, then I can make it a valid sequence by fitting it to a polynomial, which would make for a crappy number sequence puzzle. Commented Jan 7, 2017 at 21:17
• This is a good litmus test, but I'm not sure it works as a complete guide.
– user20
Commented Jan 11, 2017 at 7:13

Providing a sequence of numbers, with little to no context, and asking for either missing values in the sequence or the rule by which the sequence is generated, is typically a bad puzzle. The reasons are:

1. Such a sequence is guaranteed to be non-unique. For any finite sequence of n real numbers, it is possible to create infinitely many polynomials that generate that sequence, in addition to any number of other possible generating functions and/or algorithms.
2. If the generating method is sufficiently general and/or well-known, it is likely that the sequence is already listed in a database such as the OEIS.
3. If the generating method is sufficiently specific and/or obscure, then with no context there is no way of knowing what kind of process the asker had in mind.
4. All of the above, combined, mean that any such question reduces to a guessing game where the asker continually rejects apparently valid but not intended solutions, which is a sign of a poor puzzle.

For example:

What's the next number? 1, 2, 4, ???

8 is an obvious answer (powers of 2), but a little searching will show that there are valid arguments for 10 ("left factorials"), or 16 (raise 2 to the previous number in the sequence), or 7 (number of pieces you get when you cut a circle with n lines, or numbers with an odd number of 1s in their binary expression), and if you want to be a dick then you can construct arbitrarily many other solutions.

This is on a par with asking:

What's the missing word? CAT, RAT, DOG, ???

and then rejecting a host of attempted solutions (ANT, MOUSE, OWL, AMOEBA) because they aren't the "right" solution you were thinking of.

Some things that you can do to help improve the question include:

1. Providing sufficient numbers in the sequence to reduce ambiguity. While you can't completely remove all alternative ways to generate the sequence, you can make it so that the intended method is immensely simpler than any other.
2. Giving additional contextual information to lead towards the intended solution. If the solution relates to the way the numbers are spelled, then at least put in a cryptic "I won't spell it out for you, but ..." or something. If it's about Pascal's triangle let people know "You might have to look at some combinations of things".
3. Checking the OEIS to make sure the sequence doesn't already appear there in some form. If you're feeling particularly thorough, use their SuperSeeker email address to check whether your sequence is related to one they have (e.g. your sequence might be the prime numbers squared minus the next prime number, and if that weren't a sequence in their database already - which it is - it would still give you the breakdown of where it comes from).
• Great example: smbc-comics.com/index.php?id=4071 Fun fact (unverified): there are 69,869 different integer sequences beginning with '1, 2' on OEIS. Commented Oct 18, 2023 at 14:07

Third answer. I could not find this in the two previous answers.

CAUTION: This post may contain spoilers.

Please make sure that it is a sequence, not a set.
If you can swap a few distinct terms and the pattern still works, that's a set.

For example, this one is a sequence.

0 32 15 3 9 5 4 2 6 7 13 110 174 155 314 2120 5360 24671 119546 193002 240820 274454 153700 1397287 17916598 26245242 8880928 7320921 14726415 42969065 35308126 14978764 68756682 ...

Because if you swap some terms, the pattern...

The number $$a_{n-1}$$ first occurs at the $$a_n$$th decimal digit of $$\pi$$.

will no longer work.

Some "sequences", like this, are actually not sequences, but rather "sets", which should be
better tagged .