A color wrap kills half the candidates in a cluster, and promotes the other half into clues. If you took up the challenge to color Maestro 40, I’m confident that you discovered the color wrap. That is a removal or marking that shows one of the two colors of a cluster to be false. In this case a 3-candidate in r8c7 is being forced to green when there already is a green 3 in c7. Since the column can have only one 3, and a color is all true, or all false, green is thereby false, and blue is true. This large influx of clues dooms Maestro 40.
If this is not your result, check the box and line marks carefully. The most frequent error is assuming a wink to be a slink, and extending the cluster where it shouldn’t go.
Having two candidates of the same number and color in a unit is the typical color wrap. Having no candidate of a number and color in a unit would also prove the color to be false. When there are multiple clusters, both wraps and traps are a little more complex. The merging of two clusters into one is called bridging. We’ll do a blow-by-blow example of bridging multiple clusters shortly.
A color wrap on first coloring of a cluster, as in the Maestro 40 example above, is not rare, but more often there is a series of candidate removals, gradually extending the cluster until the wrap occurs. In the most frequent removals, the removed candidate
- sees its number in both colors, or
- has both colors assigned to other candidates in its cell, or
- sees its number in one color and has the other color in its cell.
Actually the wrap of Maestro 40 was a removal of the third type. It became a wrap because this removal left only a green candidate in the cell.
So let’s go trapping. Here are the solving actions which bring Maestro 50 to the point of coloring:
XY-chain 89498 beginning in r9c2 removes 8 in r9c6. Extending this chain, 949859 beginning in r8c1 removes 9 in r8c9. XY-chain 8498 beginning in r7c2 removes 8 in r7c5.
xyt-chain 59765 beginning in r1c5 removes 5 in r9c5 =>S5m=>SW5.
Sue de Coq SEc7 = 5(1+4)(6+7) removes 4 in r4c7.
4-wing r47 removes candidates in r5c8 and r8c8.
Kraken analysis of the finned 8-swordfish r458 yields no victims. It requires a “both fin and victim OK ” argument to be complete. All of this leaves the following grid for coloring.
Start with blue 5 in r3c1. Carry on until you get a wrap. It takes a second set of removals in the extended cluster to get it. A checkpoint is coming Thursday in my next post.
On Maestro 4, my line marking trace reads:
4f: c3=>SWns4=>Sr7np45=>S3=>(SE3t, Nt3, S1=>(SE1m, N1=>NW1, Sc5np89=>(N8m,C9=>(W9m, C4m=>W4m))), Cc6np56).
4f: r2=>nt237=>N6=>(NW6m, N7=>NE7m=>NEns5=>N5m).
3f: r1. 3f: c5 4f:r7, r8=>np89=>np26=>SE8m .
5f: r3, r4, r9, c4, c8, c9, 7f: r5 8f: r6 Close:c1, c2, c6.
I wind up with this grid:
For a checkpoint in the extra Thursday post, you can whip through the bv scan and X-panel. I found an XY nice loop eliminating two candidates, a surprisingly meager haul for so many bv. A swordfish brought three more eliminations.