Magic Square, No Center

[ijabbott]

(07-30-2018 09:44 PM)Albert Chan Wrote:  Hi, ijabbott:

I am glad you do the puzzle the old fashion way, and not "brute force" it.
How to do grade this puzzle ... Is it good ?

48 is correct ! (3 primary solutions x 16 = 48)

However, some issues before you win the jackpot

1. Why 9-complement symmetries not overlap at the center ? (like the odd-sided zigzag puzzle)
   In other words, can you really recover 48 unique solutions ?
2. When you realized your solutions had overlap, how to you spot it ?
   Checking primary solutions for overlap is a bad idea, as it may not be easy to spot.
3. How to get "reflected" solutions (if not careful, reflection will overlap rotation symmetry)
4. Bonus: you are not fully using 9-complement symmetry, with it, your tests can be cut in half.
5. Bonus: there is an identity you are not seeing. If you spot it, tests can be reduced to 4.
   Hint: calculate B+F and D+H
   

BTW, you might have missed a case, or maybe too trivial to show it.
Tests should be an even number, due to 9-complement symmetry. 19 does not sound right.

(I changed your list to a numbered list for reference.)

1. Because there is no center? (Not sure I understood.)
2. Visually.
3. A rotation is the same as an even number of reflections, so a single reflection will not overlap any rotation.
4. I need sleep!
5. Ditto!
   

I missed "12 (1)7(4)6(2)5(5)6" from my check list.