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TGHamilton
New kid on the Grid

Joined: 01 Dec 2006
Posts: 1
Location: USA

Posted: Fri Dec 01, 2006 10:10 pm    Post subject: Braids with coloring

I have been toying with combining the braid analysis method with coloring, kind of hard to do in David Bird's Excel spreadsheet, but easy enough on paper. You can color digits that are off the actual sudoku grid, based on how they must travel N or Z. The idea is:
1. List the braiding possibilities, or copy braid chart from SudoCue tool.
2. Select a band or stack.
3. Choose a digit there that must be going in one of two directions.
4. Assign colors to digits on the chart (N or Z).
5. Examine implications on intersecting stacks or bands.
6. Find a contradiction and eliminate a digit.
This is Friday's DN after Simple Sudoku has made basic eliminations:

 Code: *-----------*  |.93|.52|..6|  |8..|...|.1.|  |24.|.7.|...|  |---+---+---|  |...|...|..7|  |.17|3..|9.5|  |...|.2.|...|  |---+---+---|  |..9|.3.|..1|  |...|.6.|8.3|  |5..|...|64.|  *-----------*

 Code: *-----------*  |.93|.52|..6|  |8..|...|.1.|  |24.|.7.|...|  |---+---+---|  |...|...|..7|  |.17|3..|925|  |...|.2.|...|  |---+---+---|  |..9|.3.|..1|  |...|.6.|8.3|  |53.|...|64.|  *-----------*

 Code: *-----------------------------------------------------------------------------*  | 17      9       3       | 148     5       2       | 47      78      6       |  | 8       567     56      | 469     49      3469    | 23457   1       249     |  | 2       4       156     | 1689    7       13689   | 35      3589    89      |  |-------------------------+-------------------------+-------------------------|  | 39      2568    24568   | 14569   149     14569   | 134     368     7       |  | 46      1       7       | 3       48      468     | 9       2       5       |  | 39      568     4568    | 15679   2       145679  | 134     368     48      |  |-------------------------+-------------------------+-------------------------|  | 467     2678    9       | 2458    3       458     | 257     57      1       |  | 147     27      124     | 12459   6       1459    | 8       579     3       |  | 5       3       128     | 12789   189     1789    | 6       4       29      |  *-----------------------------------------------------------------------------*

For the bands the braiding possibilities are shown below. Asterisk will indicate a digit going in a known direction. Letters "a" and "b" are different parities or truth-states for digit 1.

 Code: N       Z 678     46 2*1a45  1b379 39      58 1467*   3468 59      2*59 3468    146 1a27    1b25 58      789 246*9   24

By doing the same with the stacks, adding bridges, and continuing in this way one can eventually ascertain whether the "a" or the "b" set is true, since one of them must be.
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