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# Sudoku/Methods/Advanced/Simultaneous Bivalue Nishio/Sudoku Addicts Workbook/149

## Contents

## Introduction[edit]

- Raw puzzle.
- SW Solver: Extreme grade, overall score 842.
- Stephens' estimated times: Improver: N/A, Expert: 354 mins, Genius: 118 mins.

## Solution[edit]

### First pair: Contradiction[edit]

See **Figure 1** on the right.
Seed pair is r2c3{38}. Red chain contradiction in c8{9}. Therefore r2c3=3.

(to aid working on the chains, multiple proposed resolutions in a region are marked with lighter versions of the chain colors.)

### Second pair: Contradiction[edit]

See **Figure 2** on the left. Seed pair r39c2{2}. Green contradiction, 4s in r8c27. Therefore r8c2=2.

### Third pair: Contradiction[edit]

See **Figure 3** on the right. Seed pair r8c7{48}. Contradiction in r4c9, candidates exhausted in red chain. Therefore r8c7=4.

### Fourth Pair: Contradiction and Resolution[edit]

See **Figure 4** on the left. Seed pair r1c4{76). Red chain contradiction in r9, two positions for {9}. Therefore r1c4=6. Resolving that, it was singles or easy to full resolution.

## Comments[edit]

As might expected, this puzzle required more bifurcations than the previous three of the "Fearsome Five." However, solution time is approximating "Genius" time. It simply takes care, patience and persistence. The alternative, of searching for the truly fearsome number of advanced "logical strategies" needed, many of which actually use similar techniques, will be, except for a true savant, more time-consuming. SBN generates steady progress, almost always. (A very non-productive pair, leading to impasse with no resolutions, only creates progress in terms of identifying a pair not to use, at least from that state!)

SBN may, of course, be combined with advanced strategies. "Impasse" merely means that I did not find a strategy, and I deliberately did not search for non-obvious strategies. If one can find one, it will speed up full resolution. SBN merely makes the other difficult-to-identify advanced strategies unnecessary.