## Fireworks 4 Stretches the Matched Elbow Rule.

After a challenging basic, we get two matched pairs on two values again, but this time, linked by a single bv. The second challenge is the application of the matched elbow rule of the last post in a more hypothetical situation. The fireworks result is not an immediate collapse, and we get  interestingly  parallel solution paths of ALS_XZ and BARN.

The basic is easier tracked than performed.

The 1-wing removals are made in line marking, before X-panels are constructed.

Doing the X-panels for the fireworks elbows scan, we note the dead swordfish joining the now dead 1-wing, but what is the significance of having four matched elbows nested around the center cells of four boxes? I’ll say at the end of the post, but more on topic is the two matching elbow pairs on 2 and 8.ic is the two matching elbow pairs on 2 and 8.

Plotting the matching pairs on the grid with curves, there’s a 28 bv on the row and column between the cuff cells of the two matched pairs of elbows.

By the matched elbow rule, at least one cuff cell on each matching pair solves to  2 or 8.  The bv switches the true 2 or 8 to the opposite true value, so the cell on the other end must have neither 2 nor 8. By the matched elbow rule, that means the opposite cuff cell has 2 or 8, and the bv forces it to be the same as the true 2 or 8 we started with.  Regardless of which cuff cell we start with, corner cells r1c9 and r9c1 are limited to 2 or 8.

Limiting two neck cells to two values is not necessarily decisive. But solver Beeby takes us through some interesting steps to a solution. 8r1c5 is removed by ALS_98 (in black), or a BARN on 2789.

The 8’s attack continues with an ALS _28, or if you prefer, a BARN on 2368.

The cherry on top is another ALS_28,

and a rare 5 – pole BARN on 23578, for C8 =>(NW8, SW8).

Then Beeby supplies a finned swordfish.

Asked for another fish, Beeby gets a “sashimi X-wing” with fin at r1c5. I shoulda asked for a simple AIC.

Finally, the collapse. In the solution, you can verify what you concluded from the four matched elbows on the 1-panel. One set of opposing necks are 1.

Next time, we examine Hanabi, proponent shye’s fifth fireworks example in http://forum.enjoysudoku.com/fireworks-t39513.html.

It suggests there are additional ways in which combinations of elbows can be used to find candidate removals. There are no matching elbows, but elbows of four values share the same box and intersection cell. And there is a firework sharing this cell which is not an elbow.