PaulIQ164 wrote:Well, I've studied it a bit, and I remain unconvinced. Seems to me you're still trying two possible sets of places for the sixes, and rejecting the one that leads to an error.
You don't quite understand it. "Coloring" has a long history in recreational mathematics that pre-dates the Sudoku.
One of the most well known puzzles and simplest is this one:
You are given an 8x8 grid of squares with two opposite corners removed and 31 dominos, each of which will exactly cover two squares. You are challenged to cover the board completely with the dominos. Though there are many ways to solve the problem, including brute force search, the simplest is to color the board like a checkerboard with light and dark squares. The board will have 30 squares of one color, 32 to of the other. Since a domino will always cover exactly one of each, the task is impossible. It doesn't matter which squares are colored dark or light, only that they follow the pattern.
When coloring, either the board or the Sudoku grid, nothing is "assigned" to the light or dark cells, they are merely colored according to a pattern. When the coloring is in place, a direct conclusion can be made. No hypothesis is required. The solution becomes *visable*. We can *see* that there are more squares of one color than the other. We can *see* that two cells in the same row, column or box have the same color or polarity.
And by the way:
there are two 6's with the same sign in box 6 -- they both can't be 6, so they both must NOT be 6.
PaulIQ164 wrote:The two 6s in box 6 have the different signs. The only unit that has two sixes of the same sign that I can see is column 7. Is this what was meant.
Thanks. I fixed it. "New Math" syndrome.:
...
From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)...
And so you've got thirteen tens
And you take away seven,
And that leaves five...
Well, six actually...
But the idea is the important thing!
...
