Heine’s left page ultrahardcore 265 is solved in two posts. This post follows the alternative methods of the review solvers Beeby and Sudokuwiki until they converge on a long series of AIC in the second post.
Here is the grid after the bypass clues and subsets and box marking strong links defined by boxes.
We always have the basic trace, showing the sequence of moves. The Guide explains them, but the trace conventions become clear when you see the moves and and the trace notation that reports them at the same time.
In the line marked grid, line slinks and bv are marked, and fill strings are shown. The trace records the order of line marking, in increasing order of unplaced cells. The Sysudoku grid places candidates on corners and edges to distinguish slinks in boxes, rows and columns.
The order recommended here for DIY solving is spelled out in the Guide: obvious UR and remote pairs first, then a scan over boxes for bv, SdC and BARNs, then make a bv map and find the bv railways for XY ANL, then scan a XYZ map for regular and irregular XYZ. Then make the X-panels and scan value by value for X-chains and fish, and the edges for easy pattern analysis. As bv accumulate, build colorng clusters. If still necessary, explore all AIC, including ALS nodes. All else failing, map ALS and and mark singles and aligned value sets for ALS_XZ
On the ultrahardcore review, I’m applying two human oriented solvers to this order, mixing Sudokwiki’s fixed order of methods with Beeby’s menu of options for fish, ALS, and AIC methods. The result is characteristic alternatives along a consistent solving path.
For UHC 265 the review path starts with two X-panel results, a finned 1-wing from Beeby and a 6-chain ANL by Sudokuwiki.
The fin is 1r1c9, and the victim 1r2c7 is in the fin box. None of the potential kraken victims 1r2c1, 1r8c1, and 1r8c7 see the fin via forcing chains.
Boxline NEr1 removes 6r1c6.
Next is Beeby’s finned 6-wing removing 8r7c5 and a Sudokuwiki ANL confirming 6r2c5, to the same effect.
The removal of 9r7c8 brings a hidden dublex of 9’s in c79 and
A third finned X-wing or 4-chain removes 4r1c4, and 8r2c8 is removed by Sudokuwiki’s 348-wing or Beeby’s equivalent ALS_48.
The 4r1c1 removal allows another finned 4-wing removing 4r2c7, but Sudokuwiki leaps ahead with a grouped 4 – ANL and a green extension to remove two more.
Beeby pulls ahead with this pair of hidden UR’s on the left, a short one for a go-ahead 9 clue and a long one to get one of the NE 4’s.
That leaves a 4 – ANL for the other one.
A Sudokuwiki boomer from 9r5c7 duplicates the E9 clue and the solvers are on the same grid again.
Next time we’ll report a long series of Beeby’s simple chain AIC that get us to a third hidden UR and a coloring wrap of UHC 265. Want to do it first?
Systematic Sudoku 