... by: Arthur Lurvey, Tucson, AZ, USA
Load Sudoku:
329000000507320098840907023400592371795103082132780905900200030670030259253679814
Even/Odd Path Length
This is a more interesting example of the even/odd path length strategy.
Looking at the above board, we see a pair chain of 4,6 located at: E5,E7,F8,A8, since there is both an even and odd number of steps from E5 to A5, the 4,6 at A5 can be eliminated. Your puzzle solver eliminates the (4,6) at A5 by applying simple coloring twice.
Using the solver further, we eliminate 1 at B6 using:
X-CYCLE on 1 (Discontinuous Alternating Nice Loop, length 6):
1[r2c6]-1[r2c2]=1[r7c2]-1[r8c3]=1[r8c6]-1[r2c6]-
- Discontinuity is two weak links joined at R2C6, 1 can be removed from that cell
Now we can apply the even/odd chain length strategy again to eliminate the 4,8 at B7. There is an even path from F6 to B7 (F6==>B2==>B7) and also an odd bath from F6 to B7 (F6==>F8==>E7==>B7).
At this point, the puzzle is easily solved.
Your solver uses Box-Line Reduction
LBR: 6 exists only in box 3 and row A, can remove from B7
LBR: 6 exists only in box 3 and row A, can remove from C7
Followed by Simple Coloring
SINGLES CHAIN (Type 2): Removing 4 from R1C4
SINGLES CHAIN (Type 2): Removing 4 from R1C8
SINGLES CHAIN (Type 2): Removing 4 from R2C7
SINGLES CHAIN (Type 2): Removing 4 from R5C7
SINGLES CHAIN (Type 2): Removing 4 from R6C6
SINGLES CHAIN (Type 2): Removing 4 from R7C5
SINGLES CHAIN (Type 2): Removing 4 from R8C3
This even/odd strategy may be a specialized case of the simple coloring methods, but it does look at the problem from a different perspective; i.e., counting the lengths of the chains.
Love your solver. Enjoy your holiday.