(Not a guess at any specific answer that the question's poser had in mind.)
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
within two broad categories.
More for sport:
• creativity / inventiveness / originality
• esoterica / sophistication
• simplicity / ease of calculation
More for the long term:
• education / cross reference
• variety, the spice of life
Brief case study of the kind of puzzle in question
Relabeling two 20-sided dice without changing their
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.
A complete solution that transforms the puzzle into
This solution is so complete, educational, general and sophisticated,
who could ask for more?
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.
The poser's inventive
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.
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.
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.)
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?
The last person took the basket with the last egg still inside.
Examples of solutions that earned their own puzzles