This post illustrates a sysudokie human solver technique, the exocet chute lettering table, for the second time in the Unsolvable series. The method was applied to the double exocet of Unsolvable 181 in the post of February 18. Unsolvable 186 is a single exocet. As before, the exocet was first spotted and resolved by JC Van Hay. Here we duplicate in detail his result, as reported in his brief comment in the Weekly Unsolveable page of Andrew Stuart’s site.

The basic solving trace for Unsolvable 186 is short but not sweet. The bypass closes out the 4’s, but no more Mr. Nice Guy in a clueless box marking and a very tough line marking,

leading to

and the question of “Why are we doing this?” I got nowhere with the X-panels, looking to nibble away at a few orphans. But the practiced eye of Van Hay found an exocet in the West stack. I’m hoping JC will send in a comment on how he spots these things so quickly.

Let’s see that exocet stack, alongside a lettering table which enumerates the four different ways that the outsider digits 3 and 8 are arranged in the 9 chutes of the stack, around the exocet base and targets. This is an essential element of the chute table technique.

It may take longer to figure this out than it took to draw it up, but it’s worth it. In this table, the contents of the 9 chutes aligned with the two base cells result from the four different ways that 3 and 8 can occur in the NorthWest box. The arrangements in NW determine the arrangements in the other 6 chutes of the western stack.

We designate the base solution as digits a and b. Actually, placing the 4 and other givens in the table helps us navigate in the table.

The presence of 3 and 8 determines whether each chute requires zero, one or two exocet digits.

The table reveals that fortunately, only the arrangement of the top table allows ‘a’ in one target and ‘b’ in the other, the qualifying condition for a solution via the exocet.

Within that single arrangement, are you wondering if you can interchange c and d in the middle column c2 and have both possibilities to test? One gold star for alertness, but no, you then have to exchange them in row 2 as well, arriving at the same arrangement with interchanged letters. From the lettering, Weekly Unsolvable readers can connect the dots to JC Van Hay’s comments that

“A solution of D2 or E2 excludes the same digit from AC1 and GH3” and

“DE2=ab -> -(ab)AC1.GH3 “ .

So what do you make of “and 0 solution via singles except if ab=95”?

First, let me say that “via singles” does not mean there is a solution requiring only naked singles if DE2 (r45c2) = 95. “Singles” is just guru speak for the puzzle collapsing without notable advanced techniques.

And if you read it to mean that 95 is the only combination of digits, one from {2,7,9} and one from {5,7,9} that brings a collapse, you’re on to what JC is saying. So here is the grid with the NW 3 and 8 candidates in their courtroom seats for the exocet trials. How many trials? Well, 2 combines with {5, 7, 9} in three ways, 5 with 7 and 9 in two more. Then if we are lucky, we get a verdict from a naked pair np79 in r45c2.

Expect three on average, but it could be six.

I leave it for now, half expecting a more diligent student of sudoku to give us a citation to additional conditions that at least limit the testing this particular exocet. But to complete the message of this post, here is a challenge for sysudokie readers:

Here is the Unsolvable grid conditioned for the ab = 59 trial announced by JC Van Hay. Below is a trial trace. It follows the breath first “singles” track of the Sysudoku trial trace, which is the appropriate form for a trial in which you expect a contradiction. The purpose is to document the contradiction graphically on the starting grid with the shortest inference paths.

In case you decide to follow the trace, or duplicate it on your own for a checkpoint, at left is the 3-node XY chain or XY-wing, that is there when the”singles” give out.

Your challenge is to send in a comment with a Sysudoku trial trace of another ab combination that has not already been documented in a comment. You must state the contradiction and document its location. Ties will be credited to all.

Next is another brief review, on Manuel Castillo’s *Only Hard Sudoku*. It’s a “no nonsense” puzzle’s only book of 400 puzzles, but the only challenge is how much you can get out of the bypass. Only one will be traced all the way, so if you do ‘em before reading about it, here it is, Only Hard 82.