Number Construction Puzzles: What Constitutes a Duplicate?

Question

User Dmitry Kamenetsky posted some puzzles today (here and here) that I enjoyed working through - they were simple enough anyone could attempt them, but the matter is complex enough that some cleverness goes into finding the optimal solutions.

But, I think this begs the question, "At what point is it considered a duplicate question when the only thing that changes is the number to be composed?" It seems to me that the spirit of the problem is found within the rules of composition, not the number itself (though there may be cases were the given exercise is substantially different for some esoteric number theoretic property).

I imagine there may be some level of subjectivity in dealing with the issue, we frequently have old puzzles of the style raised to life with each new year, some composition of the next year number. But obviously it would be bad form to just keep changing the numbers and reproducing identical puzzles.

I appreciate your thoughts on this.

Answer 1

The general rule is that a new question is a duplicate of an existing one if an answer to the existing question would also answer the new question — even if no such answer has yet been given, if it’s obvious both questions are asking substantively the same thing such that an answer to one is an answer to both.

Marking a question a duplicate is essentially saying, “Somebody already asked this. If that other question doesn't solve your problem, please clarify your question to explain how it's different.”

There are cases where the numbers don’t matter. We see various reformulations of the water jugs problem that differ in the sizes of the containers and the starting/goal amounts of water, for example. But a general solution exists for these puzzles and has been posted as an answer, so basically any of the standard formulations of such puzzles can be closed as a duplicate of that one.

Other puzzles, such as the more or less yearly “form the values 1 to 100 from the digits of the new year, using only $(set of operations)” ones, don’t have a general solution. The rules tend to differ slightly (digits in order or not? initial concatenation allowed or not? concatenation allowed as an operator? which operators are allowed?) and the solutions depend on the usable digits. A solution for 2012 may work in 2021, but we weren’t around then :) so it’ll be a long while yet (2051!) before we land on a year whose digits are a reshuffling of a year that’s been used in a formation-of-numbers puzzle so far, or (2023->2032) is likely to be in the future.

Since these questions thus are not answered by another question, there’s no reason to mark them as duplicate.

Having said that, genre fatigue happens when too many of the same type of formulaic-looking puzzles are posted in too short a time. They are, usually correctly, viewed as being low-effort rehashes of the same type of puzzle with no effort required by the poster beyond exchanging one value for another. Downvotes are the inevitable result, and probably the correct one. So, as @GentlePurpleRain noted in a comment, these indeed tend to be self-correcting problems.

Answer 2

I accidentally stumbled across this question and was rather surprised to see a discussion about my puzzles.

In general I agree. We don't want to see puzzles that are too similar, even if they are not exact duplicates.

With most of my puzzles I usually post two versions. I begin with a simple version. Once that gets solved then I post a harder version. Often the harder version requires new or different insight to be solved, but this is not always the case. I cannot be sure how things will play out.

In this particular case, the first puzzle was about the new year 2020. For the second version I wanted something considerably harder, but also something with many divisors. I couldn't think of any special number, so 123456 seemed as good as anything. But I agree it was rather an arbitrary choice. I believe the two puzzles are sufficiently different and it seems that people have enjoyed them. I wouldn't want to make a third version in genre, unless it uses completely different rules.

I've also had cases where the first version of a puzzle gathers many votes, while the second version gathers few votes (or even negative votes). I guess in those cases people think that the second version is too similar. I cannot predict this beforehand, but the negative votes actually do help me to calibrate my puzzle making.

So in conclusion, I do try to keep puzzles different as much as I can. If I make a mistake, well so be it - my puzzle will be punished with negative votes which is fair. So it does end up as a self-calibrating system, which is good.