In this post, an unbalanced line marked grid is chiseled down some by an unlikely series of 1-ways and ALS chains by the two DIY oriented solvers.
Starting with the bypass grid, with the bypass clues and fill strings in the Bradley Hand ITC script, and the givens in more formal Calibri. The bypass is a game of finding all clues and subsets possible before strong link marking. Two 3-fills are marked with fill strings.
It’s a good result for a Stefan Heine ultrahardcore. Note no givens for value 7.
The basic trace gives a step by step account of the three stages of Sysudoku basic: bypass, box marking and line marking.
The Close completes the marking of lines not completed when the crossing lines were completed.
The Guide (menu bar) explains the goals of each stage. Trace conventions are described there, but experienced solvers can interpret the trace moves when they follow them on their own grid. If that fails, see the Guide for details.
The line marked grid shows the order in which lines were marked with candidates and line slinks. It also shows the fill strings added in line marking.
In UHC 221, candidate values are very unbalanced, with values 1, 2, 4, 6 and 7 prevailing.
There was a naked single for 7 on the third line marked. By following the trace, you can see the state of the grid when the naked single is found.
To start, Beeby finds what it labels a sashimi 1-wing. If either victim is true, columns 1 and 6 require the row 6 position to place a 1. Sudokuwiki sees it as a simple 1 – ANL.
Next, a Sudokuwiki APE is Beeby’s ALS_26.
And one dfc simple 1-way.
If 1r7c6 is true, 1r7c2 is false, but if it is false, the the 1-way AIC makes 1r7c2 false.
Then another 1-way. 7r4c3 is false if 7r1c3 is true or false.
As Sudokuwiki signs off, Beeby does an ALS ANL
And a complex 1-way from 1r2c4 removes 1r2c7, with branching winks along the 1-way AIC removing candidates preventing two slinks in the 1-way AIC. A grouped extension in red extends the 1-way to a second victim. In a complex 1-way, the AIC branches off from candidates the 1-way direction assumes are true if the starting candidate is false.
This AIC is marked by the complex branch as a 1-way rather than an ANL, because the AIC only works in the branching direction. It can start in 7r5c6, but not 7r1c5.
The removal allows . . .
a grouped slink in c5 that could start a boomer eliminating 1 or 6 in r1c5. Then the wink into 7r1c1 makes it a Beeby simple discontinuous loop. What isn’t continuous in this loop is the alternating inference. It’s an almost nice loop (ANL) but a 1-way because in AIC building, we start them on slink partners. The 1-way AIC shows that if 7r1c5 is false, 7r1c1 is false. That along with if 7r1c5 is true, 7r1c1 is false(the wink), proves that 7r1c1 is false.
Let’s end this post with a third complex 1-way. Where does it start? It’s a 1-way aimed at the 6’s seen by 6r3c4. 7r3c1 is suppressed to enable the final slink, and 2r9c3 is suppressed to allow the 2 slink in c3 needed to get there.
The SEc9 boxline follows the removal.
This intense session leaves a lot more for next week, with a rare finned starfish, and a series of ALS chains to be found.
Systematic Sudoku 