## Reviewing a Truly Extreme Collection

This post and the next initiate a review of Sudoku Puzzle Book, Extreme Level by J. B. Nakamoto, with Nakex 3. The review combines moves by Andrew Stuart’s Sudokuwiki solver with Sysudoku alternatives, while reporting and interpreting moves in accordance with the Sysudoku Guide to  systematic human solving.

Nakex 3 Sysudoku Basic portends an extreme level, with a total of four clues and six fully claimed cells.

The line marked grid offers two hidden unique rectangles of type 1, in which one UR value is slinked along both lines from the corner opposite the single extra free cell. The other UR candidate in the opposite cell must be false, because otherwise, the slinks force a reversible solution on the rectangle corners.

The hidden UR removal 1r5c1 enables a BARN, which Sudokuwiki labels a WXYZ wing. The Bent Almost Restricted n-Set applies to other values of n. Here, and most commonly, n = 4. The single value set 3 that is not restricted to a single unit must contain a true value, and is therefore toxic to any outside candidate seeing the whole set.  This one brings W3 and SW3 clues.

Moving on to the X-panel methods, two grouped X-chain ANL follow:

When a coloring cluster in the South stalls, Sudokuwiki steps into AIC building with the  AIC boomerang below. On the diagram are the slinks that you would examine as boomerang starters. These you would scan, looking for slink terminals that see another slink candidate. In this case, r6c4 is the first successful starting cell, and it takes two 8 nodes, a cell wink, a 7 node, and an XY node to reach a 9 seeing into the starter cell.

It is a good idea to leave AIC building results in place, even if unsuccessful, because they are often extended by later removals and clues.

In this case, the 9r6c4 removal leaves an XY node extending the 5r2c6 boomer 2 to the 8-chain.

The new XY node also enables the 5r3c7 boomer 3. This time the next node is the ALS 289 internal slink between 8 and 9 value sets to reach an XY node back into starting cell r3c7.

The boomer’s removal 1r3c7 expands the cluster and allows the AIC grouped ANL, with follow up

,

with coloring traps in r1, a naked quad and naked pair in r4.

The naked pair 12 in r4 sets up a Type 4 unique rectangle. The slink across the floor guarantees that one slink partner is true, which guarantees that both UR partner 1-candidates must be false. The 5r4c3 removal also permits the grouped 5 slink of the almost nice loop.

It’s good to look at new aligned pairs for UR, and line removals for new grouped slinks.

The story is getting long, and perhaps you’d like to take full advantage of added coloring to shorten the Sudokuwiki solution path, which continues in AIC Building mode.  Those results are reported next week.