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#722, October 31 - November 6, 2026:
The Weekly 'Unsolvable' Sudoku Puzzle

by Richard Kröger, guest compiler

WARNING: This is the Weekly 'Unsolvable' Sudoku, rated above 'Extreme'.
This is currently unsolvable by my solver, except perhaps with trial and error strategies.
Using the solver will not help you. (much).

Changes March 2026

Due to the introduction of Forcing Nets many Weekly Unsolvable puzzles can now be solved. I have flagged all the Sudoku ones which are solvable. I am struggling to make any new ones so we'll have to see if the Weekly can continue. The point of the Weekly was to provoke discussion and new ideas, so that is progress. But my solution is unlikely to be optimal so alternatives are welcome.

Archive

Each week a new 'unsolvable' will be published and the previous will be accessible here from this archive section. If you like very tough puzzles, these are for you.
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Saturday 31-Oct-2026

... by: Dieter

#722 - initially populated cells: 22 = 27,2 %
No solver used, solver = brain, supported by self-coded EXCEL app.
basics: %

Strategy: numbers 4,6,7,9 occur most frequently, combine two cells with almost same candidates.
combinations of B8 = (1,5,7,9) and E8 = (4,6,7).
B8=1 & E8=6 solve.

Saturday 31-Oct-2026

... by: K9Dr

170 steps, 0.589 seconds, 27 Trials, 21 Errors

Saturday 31-Oct-2026

... by: Serban

# 722 Basics to 22

1. A8=4 & E9=3 solve

2. A8=4 & E3=5 solve

3. A8=4 & B4=2 solve

Saturday 31-Oct-2026

... 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.
Page created on 03-May-2011, last modified on 30-May-2024.
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