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# Sudoku/Puzzles/Extreme/Nakimoto Extreme/1

< Sudoku‎ | Puzzles‎ | Extreme‎ | Nakimoto Extreme
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Nakimoto 2019 Extreme 1

This puzzle is visible (the first in the book) in the Amazon preview of J.B. Nakimoto, Puzzle Book Extreme Level: Diabolically Difficult Puzzles for Advanced Solvers (2019)

## Contents

Figure 1. SBN r1c5={45}

SBN coloring

• light orange cell: seed cell for chaining
• green: first chain. Convention: lowest digit or Gordonian cell number.
light green: alternate cell candidate within green chain.
• red: alternate chain.
light red: alternate cell candidate within red chain.
• purple: mutual elimination.
• light purple cell: contradiction (multiple in region or empty in color)
• light blue cell: mutual resolution (as only colored candidate in cell)

## Solution

### First coloring

After cleanup, Simultaneous Bivalue Nishio process was begun with r1c5={45} (Figure 1, right). The 4 chain extended well, coming to a contradiction, all candidates were eliminated in r6c9, so r1c5=5.

### Second coloring

Figure 2. SBN r6c7={56}

After cleanup, again SBN on r6c7={56} (Figure 2, left). The 5 chain comes to a contradiction, so r6c7=6.

### Third coloring

Figure 3. SBN r1c9={16}

After cleanup, BSN again on r1c9={16} (Figure 3, right). As the coloring became complex, the shown eliminations were implemented and coloring was continued.

Figure 4. continuation of 3rd coloring

The 6 chain completed the puzzle (Figure 4, below left). The 1 chain was finally contradicted, the mutual resolution of r5c8=9 eliminates a 1 chain colored candidate, therefore the 1 chain contradicts itself. [r9c8=4]