... by: Serban

# 722 Basics to 22

1. A8=4 & E9=3 solve

2. A8=4 & E3=5 solve

3. A8=4 & B4=2 solve

... by: Norman Powell

AS's solver:
1) X-Cycles 7E9
Forcing Nets 2) 9H6, 3)9J2, 4)2A5, 5) 5A6, 6) 5C9 7) 2E5, 8) 3E5, 9) 7E6

My Solver:
Finned Swordfish CFH169 Fin F8 for value 7 - Eliminate other 7E9 [AS#1 by X-Cycles]
[I have Finned Swordfish before X-Cycles in my list of methods, since for me it is a much faster search]
Forcing Network First Pass: 2A5 [AS#4] 2E5 [AS#7] 3E5 [AS#8], 9H6 [AS#2], 9J2 [AS #3]
Forcing Network Complement finds the last two eliminations 9H6 [AS#2], 9J2 [AS #3], from being held OFF when 7B2 is both ON and OFF. An alternative method I test for in the same pass, but is redundant in this case.
Forcing Network Second Pass 5A6 [AS#5]
Forcing Networks Third Pass 5C9 [AS#6], 7E6 [AS#9]
Cell Forcing Networks - When each of the possibilities in tested for ON in cell B2, Value 5C3 is always forced OFF so eliminate. [This is a Forcing Network routine inspired by Cell Alternative Inference Chains, where Cell is abstracted to include possibilities in a Cell or single values in Rows, or Columns or Boxes, I thought it was clever when I wrote it, but this is one of the rare occasions it has been triggered, it is quite a long search.]
Forcing Network Fourth Pass: 1A2, 1B2, 8F8, 9F8, 8H4.
Forcing Network Complement finds the two eliminations 8F8 & 9F8, from being held OFF when 1E5 is both ON and OFF. An alternative method I test for in the same pass, but is redundant in this case.
Confined to Box: Value 1 is confined to Box 1 and Column 1, Eliminate all other ones in Column 1, i.e. 1F1.
Forcing Networks Fifth Pass finds a solution [Equivalent to AS's Bowman's Bingo] when testing 1A5 as ON.

A long solve path [182seconds, more if the graphical clean ups are included on my solver VBA in Excel with lots of graphical calls]. Exotic routines Finned Swordfish, Complementary Forced Networks [redundant to the regular forcing networks], Cell Forcing Network [a rare outing], but ultimately Forcing Network based methods do most of the work and find the solution.