How to choose the best answer in puzzles?

Question

I gave my friends a lateral thinking puzzle

There are six eggs in the basket. Six people each take one of the eggs. How can it be that one egg is left in the basket?

My intended answer was

One of them put the egg again inside the basket.

But one of my friend answered

The last person took the basket with the last egg still inside.

Clearly my friend's answer is more creative then my own (as lateral thinking puzzle demands). Now I am confused if I should take his answer for granted (as I should because I found his answer more creative) or should I say that his answer is wrong just because it was not my intended answer?

The definition given by wikipedia on puzzle is: A puzzle is a game, problem, or toy that tests a person's ingenuity or knowledge.

It got to me thinking if puzzles are just to find the intended answer of the question asker or is it to find the most appropriate and reasonable answer. Which one of them would be better? Or is there something I am missing?

Answer 1

^{(Not a guess at any specific answer that the question's poser had in mind.)}

Premise

The more the merrier.   Different solutions have different virtues. Eventually every solution will be appreciated by some puzzle lover.

Solutions have a variety of virtues

Far from being exhaustive or mutually exclusive, these qualities are listed alphabetically within two broad categories. Edits welcome.

More for sport:
  •  approval
  •  brevity
  •  creativity / inventiveness / originality
  •  esoterica / sophistication
  •  firstness
  •   humor   humour  mirth
  •  obviousness
  •  simplicity / ease of calculation
  •  subtlety

•  surprise

More for the long term:
  •  clarity
  •  completeness
  •  education / cross reference
  •  generality
  •  resourcefulness
  •  variety, the spice of life

Brief case study of the kind of puzzle in question

Relabeling two 20-sided dice without changing their total

This puzzle received a wonderful solution that was accepted by the poser, who then proceeded to present the intended solution so that it wouldn't be overlooked.

Three solutions have been posted to date, each with its virtues.

1. A complete solution that transforms the puzzle into algebra

   This solution is so complete, educational, general and sophisticated, who could ask for more?

2. An old-fashioned solution

   This detective-like solution does not require the mathematics or computer employed by the complete solution. Then again, only one of several possible solutions is found and a general solution is only alluded to.

3. The poser's inventive solution

   Quite possibly the poser all along had subconsciously hoped that nobody else would actually think of this gem of an approach, one that even adds to the understanding of the other solutions.

Conclusion

The more the merrier.   As in the case study: a puzzle's creator can acknowledge an unintended excellent solution, someone else can provide an incomplete solution for a different audience, and the poser can present their original solution for posterity and still blow our minds.

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Corollary

Some unexpected solutions simply deserve their own puzzles.   The original puzzle (P) may be restated as two different puzzles tailored differently for the originally intended solution (S) and for the unexpected one (S2).

P 🡒 P1.   There are six eggs  in the basket  on a shelf. Six people each take one of the eggs. How can it be that one egg is left  in the basket  on the shelf?

S 🡒 S1.   One of them put the egg again  inside the basket  on the shelf.
       (Presumably a person cannot take the shelf, or occupy it while holding their egg.)

Chaotic’s answer provides a way to restate part of the puzzle so as to exclude the intended solution.

P 🡒 P2.   There are six eggs in the basket. Six people each take one of the eggs and nobody put it again in the basket. How can it be that one egg is left in the basket?

     S2.   The last person took the basket with the last egg still inside.

Examples of solutions that earned their own puzzles

• Gareth McCaughan’s solution (S2) received its own puzzle, Unreflected infinitely simple polygon reflexivity (P2), because it was brilliantly different from, even if not technically better than, the intended solution (S/S1) to the puzzle restated as Infinitely simple polygon solipsism (P1).

• boboquack’s solution (S2) at New Mathematics forever (P2) was an unforeseen superior solution to the original statement of the puzzle reincarnated as If 6 was 9, or 100 was 64, or M was N (P1).

Answer 2

Suppose it was the opposite: you had the most creative answer, and your friend gave the less creative answer. Then you could:

Clarify your question by saying that six people each took one of the eggs and nobody put it again in the basket.

This way you narrowed the answers to the right one, which is also the most creative one.

I think this is a matter of opinion, but I'm in favor of the most creative answer no matter what, specially for lateral thinking puzzles. So if your question admits more than one answer, you should accept the more creative one.