How to choose the answer to accept in a multi-question puzzle?

Similar question but not extremely useful because this time is about multi-question puzzles rather than the answers quality.

I recently posted this puzzle which was composed of multiple questions of the form: can you do [something] for $$n=6$$? And for $$n=8$$? For which value of $$n$$ [the same thing] can be done? Which is the best way to do it? I thought it was fine to include all these questions on the same post because they were highly correlated.

However I received 5 answers (which I think is a lot): the quickest users just answered the first few questions because it was a relatively simple problem. Then someone else answered the last non-obvious question without answering the first question because "an answer was already posted" (I agree with them on this point).

So (TL;DR)

How do I choose the answer to accept if there are a few satisfactory answers but none of them answers all the questions in the original post?

You choose whichever answer you think most deserves the glorious green checkmark.

You can use whatever criteria you find appropriate. First to answer anything. First to answer everything. First to answer whatever was answered last. (On the grounds that presumably that was hardest.) Clearest answer. Cleverest answer.

Unless you're doing something 100% unreasonable like accepting only answers from your friends, or accepting answers that are flat out wrong, you have total discretion.

If you find it difficult to decide what to accept, why then that's a sign that asking lots of separate questions produces a puzzle that doesn't fit so well with the way PSE works. What some people do is to ask one question, and then attach labels like "Bonus" or "Extra credit" or "Warmup" to the other things they want to ask, so it's clear which bit determines what gets accepted. If you feel that other answers need an extra reward, you can always do it with the bounty system, though that's not as flexible as you might like.

Other options available to you, if you don't want to accept something that isn't a complete answer to all your questions:

• Encourage solvers to make a single answer that integrates the best features of the others. (You might suggest that whoever's answer you like the best be edited to include the other bits; or that they write up a new one; or that there be a new community-wiki answer to which everyone can contribute.)
• Write a single answer of your own and accept that. (This may annoy some solvers.)
• Just leave the question with no accepted answer even though the given answers, collectively, solve it completely. (This will annoy some solvers, and others too. You're absolutely allowed to do this, but I urge you not to.)
• Not accepting an answer at all is also (pardon the pun) acceptable. Commented May 9, 2020 at 20:19
• It is, though strongly deprecated (at least by me) if the answers given do actually answer the question(s) posed completely. There are some other options available if you want to make sure there is One True Answer, which I will edit into my answer here.
– Gareth McCaughan Mod
Commented May 9, 2020 at 23:47
• +1 for the Wiki-summary-answer suggestion. It makes for the best solution for future readers of the site. It also allows for background-info chipped in by the puzzle author. If you want to give out rep, you can do this with additional bounty. An example where I've done this: Commented Jun 9, 2020 at 7:31