## Guide 775 Concluded

Here we continue with Gordon Guide 775, going through Sysudoku advanced methods, but trying particularly to invoke those brought up in the Guide.

Last week, we found a regular XYZ-wing, a 231-wing to be exact, generating 11 new clues and as many marks. Updating our XYZ and bv maps, there is a sysudokie ER 192-wing that cuts another wide swath. It’s outside of the Guide repertoire, because the victim needs “Empty Rectangle” vision to see both toxic 2’s. ER is shown here as a forcing chain.

There is one UR (Gordonian rectangle) opportunity, with corner cells on this grid. It requires both 5r2c7 and 9r3c7 to be removed. I tried several candidates before realizing that 5 and 9 cannot both be removed from NEc7, because cell r9c7 would then have to supply both.

An XY-chain relates to Gordon’s bivalue graph, except here it results in almost nice loops, , not a nice one. The black chain makes the same elimination as the ER 231-wing, and the red branch adds more. The railroad bv map made these jump out at us.

Guide 775 has a very interesting ending from here. The follow up trace .  .  .

leaves a near BUG, with all bv except for 129r3c4. Coloring, a trap of 2r3c4 leaves an impossibly twisted BUG, and no solution, because the cluster proves both green and blue false.

That suicidal war means that 2r3c4 cannot be removed, and its installation as a clue, brings a solution, mixing blue and green candidates.

This is the situation Andrew Stuart had in mind with his BUG rule in The Logic of Sudoku, to promote the candidate appearing three times in a row.

The final trace is below

If you are among the readers enjoy my struggles with the hardest puzzles, you have to be disappointed with my selection of Longo puzzles for this review. Why not select from the last 100? I would turn around and do that, except that Frank has given me a better plan. His later puzzle book, The Nastiest Sudoku Book Ever, is replete with the inferno cover and the charming warning that “only the most skilled Sudoku Experts should try these mind-blowing puzzles”. I had to buy it, only to discover it is a mix of his Mensa Guide and Absolutely Nasty Sudoku IV puzzles. What would you do?

Here’s my plan: After the great stuff  already announced, I promise to review Nastiest. That’s relying on Frank to have picked the most wicked from his two hardest sets. I’ll exclude any Nastiest that I’ve already reviewed from the Guide and Absolutely Nasty IV collections. Maybe the Nastiest collection will get up to the KrazyDad Insane level. Another candidate collection is the consecutive string of Weekly Extremes coming up shortly.

Next we review the More Extreme Sudoku collection of Antoine Alary. This collection book follows his Extreme Sudoku. I’m doing the second book, which Antoine says is identical in scope. More Extreme Sudoku does reach an extreme level occasionally, but the most interesting feature for me is how the puzzles react to the newly introduced two-stage version of box marking. The puzzles can be generous , or very stingy, in basic solving. You can get a feel for the generous side from More Extreme 64, but you may need touch of advanced technique to finish it off. Be sure and start with the bypass.