July 2018 little math problem

[Albert Chan]

(07-27-2018 01:30 AM)Valentin Albillo Wrote:  your last (12th) solution can be derived from it by simply 10-complementing it (and in your case, reversing the digits), like this:

      [13, 391847256 ] -> [30-13, (10-3)(10-9)(10-1)...(10-2)(10-5)(10-6)] -> [17, 719263854]

and after reversing the digits we get: 17 458362917, which is your 12th solution indeed.

Hi, Valentin,

Nice catch. That shorten my hand calculations by half. :-)

For this puzzle, center (sum = 15) has no solution, so N-complement symmetry has a clean cut.

But, if center has solution, and other symmetries are involved, it is hard.

A sure way is to build all the center solutions first, go through the list, and remove its N-complement.
Unfortunately, it may be hard to spot, possibly mask by other symmetry.

Each center solution has to check if it's N-complement equivalent had already shown.
That may be more trouble than it is worth ...

Note: zigzag side must have the same length, otherwise N-complement symmetry is gone.