Thanks for your efforts but I think you need to understand how these puzzles are supposed to work. It should not be about making assumptions using symmetry. We should be able to determine where things go using logic. The end result here is a nice picture but it cannot be solved logically. The idea is that through a process of elimination we can determine which squares are definitely black or white and that will lead on to other logical steps until the puzzle is complete. Unfortunately with this puzzle, that is not possible. When you create a puzzle you are able to test it to check that it can be solved using logic.
A first step of 'logic' is to see if there is any symmetry. In this case the pattern is mirrored. This logically leads to needing to solve one half of the puzzle. This in turn reduces the options for exploration - one persons intelligent guessing another's hypothesis, conjecture, theory etc. All logic has to be applied, albeit sometimes to a theoretical problem. In a Hanjie it is in drawing a picture, so some of the 'pure' logical ambiguities can be absolutely resolved in creating a coherent picture, though sadly not all.
There is a big difference in making an assumption about symmetry and using logic. Logic is rigorous. You can say with certainty for example 'This square has to be black'. I could create a puzzle that has a recognisable pattern that appears to be symmetrical but isn't. The assumption of symmetry would be false. Basically, symmetry is an educated guess based on patterns and experience. Using logic requires no assumptions. There is a more rigorous definitive possibility/impossibility which leads to deduction.
Robaharrison - I challenge you to create a puzzle where the numbers on the left are palindromic, the numbers at the top are symmetrical, the puzzle is logical... and the puzzle itself is not symmetrical.
I have to agree with Robaharrison. If you have to assume something (e.g. symmetry) then it is not logical. Logic implies there is a yes/no answer and each point can be defined by the puzzle without guessing the start.
Not one which can be solved by using logic. As for symmetry, fold down the middle so that what is on the left is the opposite of the right (or vice versa).
Baggy T: Thanks for the impossible challenge :) I am trying to describe the difference between recognising (assuming) symmetry and using logic. To be clearer, when I said I could make a puzzle which had a recognisable pattern that appears to be symmetrical, I did not mean that it had to be palindromic on the left hand side nor did I mean that the whole puzzle was entirely symmetrical. I just meant for example that you could recognise, say, if the top 5 rows were as follows: row 1 having 1 black, row 2 having a row of 3, row 3 having a row of 5, row 4 a row of 7, row 5 a row of 9 etc etc is highly likely to be horizontally symmetrical. It is perfectly feasible to have row 6 be a row of 11 shifted to the left or right and not continue the symmetry. The only point I was making is that you don't know that it is symmetrical but are assuming. Logic doesn't require assumptions.
I took up your challenge anyway. It is not entirely palindromic obviously but it demonstrates what I was talking about anyway.
Robaharrison: I know what you mean. But I have a very strong suspicion that, just like in this puzzle, if one side of numbers is completely symmetrical and every set on the opposite side is palindromic, then symmetry is no longer an assumption, but a logical necessity. The logic lies in identifying the pattern with the numbers.
Logic implies there is a yes/no answer and each point can be defined by the puzzle without guessing the start.
I took up your challenge anyway. It is not entirely palindromic obviously but it demonstrates what I was talking about anyway.