Wex 431 Slips by Sue, but is Caught

Finally a Weekly Extreme gets through the Sue de Coq gauntlet. Or so I thought. But after a joyful romp into XYZ-wing technique, and coloring aided by pattern analysis, I get to demonstrate instead another resource of my single alternative Sue de Coq, at the expense of Weekly Extreme 431.

wex 431basic trAfter a very reasonable basic session, . . .




it looks like déjà vu all over again with a Sue de Coq filing at the deadline.

wex 431basic sdcwex 431 verif grid

The Sue de Coq

SEr8 = 8(6+7)(4+9)

is verified when 894 forces two 7’s in c2.

But the removal is indecisive, and 431 gets beyond the grid scan to the bv map scan, conceding only a new bv.

There a regular XYZ-wing collects another bv for me.


WECers, you should know how to systematically find every available XYZ-wing, so let me demonstrate with Weekly Extreme 431:

wex 431 XYZ mapYou start with a table of all the bv. I copy one from the identical bv map used for finding XY-chains. Then you scan top to bottom and left to right for any cell containing the three digits XYZ in two nonmatching bv XY and YZ. You write in the XYZ regardless of where the bv are. Then, on the grid, you look for the unit, or ER,or forcing chain weak links for the wing. When you find both, you look for victims seeing all three Z’s.

wex 431 697-wingIn this case, I found three possible hinges, but could not find ER or forcing chain winks for 58 to 158, or for 47 to 478. But the 697 hinge already had a row wink to 67 and a box wink to 79, and 7r8c9 was caught peeping at three 7’s, one of which is true. He was expelled for that offense, and I got another bv.

Looking at the 431 X-panel was not inspiring, until I noticed the large number of slinks on the 4-panel. My eyes widened a little more at the crossing row and column slinks that hold freeforms to a small number of patterns. Looking back at the grid, I was jolted further at the number of bv sporting a 4 candidate. My regular readers know what’s coming.

wex 431 4-panelsIn the coloring on the left, two clusters cover the strong links dividing the 4-candidates into blue versus green and red vs orange. Only one 4 is left out. On the right, freeforms from the left divide the 4’s into three possible patterns, one pin and two olive. The red freeform is a pink that could not be completed.

On the left, since blue and red see each other, blue and red cannot be both true. In the logic expression I use in slide comments, I have that

!(blue&red) => (!blue | !red) => green | red. i.e. green or red is true, possibly both.

On the right, the single pink pattern has green and red 4’s. The two olive patterns have orange and green (solid) or orange and blue(dashed). One of the three patterns is true.

wex 431orange wreckSo that’s the news from the 4-panel. Back on the grid, orange has a very bad day.

The red/orange cluster expands by slinks into 6, 7 and 9 candidates. And the orange 7 and 9 candidates see 7 and 9 candidates in the same bv. One of the bv candidates is true, and that means all orange candidates are false. In turn, that means that the olive patterns are false. Red and the pink 4-pattern are true.

wex 431final trWith all of that, we still have a long follow up marking to reach the solution. That testifies to the slippery-ness of Weekly Extreme 431.





wex 431 other alternate SdCBut just when I thought that 431 had eluded Sue, the Weekly Extreme Slayer, a revisit of the indecisive Sue de Coq of SEr8 revealed another single alternative formulaton.

The contents of SEr8 can also be described as 8(7+9)(4+6)+864,

the last term applying if 7 and 9 are missing. The verification that it is not missing, shows instead that it is, and spills the solution about as fast as it can be written down. That alone might prompt WECer interest, deadlines being what they are. Here’s the breadth first trial trace that erases any doubts.

wex 431other verif trMoving right along, next post is a highlight report on the fates of Wex 432 and 433.

About Sudent

I'm John Welch, a retired engineering professor, father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. Sudoku analysis and illustration is a great hobby and a healthy mental challenge.
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