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Subject:

Well, my memory is very clear on the point that each nut had all 6

numbers since my solution depended on that fact. But sure, if we can

answer your extended problem all the better.

You mention rotations as a symmetry of a solution, which reminds me of

another kind of symmetry that is relevant to exactly what is meant by

"a set of nuts". Clearly the values of the integers inscribed on the

pieces have no effect of the character of the solution. If someone

broke into your house one night an erased all the 1's and replaced

them with 2's and replaced all the 2's with 1's, they wouldn't have

damadged your puzzle in any way (ignoring that you may have memorized

the solution by number, but that's your fault for chosing a bad way to

remember the solution). So applying any of the 6! permutations of 6

things to the numbers leaves your "set of nuts" fixed (relative to

eachother). The manufacturers's choice of numbering is thus at least

partially arbitrary.