## Color Wraps and Color Traps

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. 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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### 2 Responses to Color Wraps and Color Traps

1. Sudent says:

A subtle color trap, wrap, and merge of clusters are illustrated in the post of April 2, 2013.

2. Big says:

John, I got totally fascinated with Medusa 3D Coloring. I think it will be my favorite advanced technique. I spent last several days trying to learn it and been looking at your site – particularly on the Maestro 40 Puzzle – My education involved me trying to understand how to come up with the graph. It does not seem to matter the exact paths you take so I was able to chain one somewhat efficiently. I also created a PDF of my own map using FoxitPDF software I have. I wish I could post my PDF to go with the following chain representation in text. What I am doing here is like the trace you take when solving a puzzle. This is a trace for the color graph to show in what order the paths were done. Thinking about your 2D trace and thinking about something more compact I created a Tables view – however it does not seem to ‘flow’ like the chain view. I wanted to get your comments on my work if you have time. Here is my Chain View of the Maestro 40 Medusa Coloring:

Maestro 40 Puzzle – Medusa Coloring -ala John Welch May 22, 2012 post
Color-wraps-and-color-traps
red chain by Richard Goodrich email: richardgoodrich@gmail.com 2013.04.10
01 r1c2=4y
02 r1c2=5g —-> 41 r2c1=4g (yellow stub)
03 r2c1=5y
04 r2c9=5g
05 r2c9=2y
06 r1c8=2g
07 r1c8=5y
08 r9c8=5g
09 r9c8=4y
10 r9c2=4g
11 r9c2=2y
12 r3c2=2g blue chain
13 r3c2=9y ——————————————> 31 r3c5=9g
14 r2c3=9g 32 r3c5=1y yellow stubs
15 r2c3=7y green chain 33 r1c6=1g
16 r1c3=7g —————–> 27 r1c7=7y 34 r9c6=1y —-> 42 r9c7=18
17 r1c3=1y 28 r1c7=6g 35 r7c5=1g —-> 43 r7c5=3y
18 r3c1=1g 29 r2c7=6y 36 r7c9=1y
19 r3c1=2y black chain 30 r2c7=7g 37 r6c9=1g
20 r8c1=2g –>24 r8c7=2y 38 r5c7=1y —-> 44 r5c7=3g
21 r8c1=4y 25 r9c7=2g 39 r5c3=1g —-> 45 r5c3=9y
22 r8c9=4g 26 r8c7=3g !# 40 r6c1=1y
23 r8c9=5y

Here is my Table View of the same information. I will email my PDF to you – It is the picture view of all this. Things get messed up because I can only post in text. I will put this and the pretty picture on my Sudoku site and give you a reference.

Maestro 40 Puzzle – Medusa Coloring -ala John Welch May 22, 2012 post
Color-wraps-and-color-traps

Alternate View to Chains (no longer accurate)
(Purpose is to show structure vs chain representation – very flexible
in that the width of the text will be much less than some 2-D
type trace presentations)

Table of Cells
—————————-
from to
—————————-
01 r1c2=5g r1c2=4y r2c1=5y r2c1=4g
=4y Start r1c2=5g
02 r1c3=7g r2c3=7y r1c3=1y r1c7=7y
=1y r1c3=7g r3c1=1g
03 r1c6=1g r3c5=9g r9c6=1y
=
04 r1c7=6g r1c7=7y r2c7=6y
=7y r1c3=7g r1c7=6g
05 r1c8=2g r2c9=2y r1c8=5y
=5y r1c8=2g r9c8=5g
06 r2c1=4g r1c2=5g r2c1=5y
=5y r2c1=4g
07 r2c3=9g r3c2=9y r2c3=7y
=7y r2c3=9g r1c3=7g
08 r2c7=7g r2c7=7g end
=6y r1c7=6g r2c7=7g
09 r2c9=5g r2c1=5y r2c9=2y
=2y r2c9=5g r1c8=2g
10 r3c1=1g r1c3=1y r3c1=2y
=2y r3c1=1g r8c1=2g
11 r3c2=2g r9c2=2y r3c2=9y r3c5=9g
=9y r3c2=2g r2c3=9g
12 r3c5=9g r3c2=9y r3c5=1y
=1y r3c5=9g r1c6=1g
13 r5c3=1g r5c7=1y r5c3=9y r6c1=1y
=9y r5c3=1g
14 r5c7=3g r5c7=1y
=1y r6c9=1g r5c7=3g r5c3=1g
15 r6c1=
=1y r5c3=1g end
16 r6c9=1g r7c9=1g r5c7=1y r9c7=1g
=
17 r7c5=1g r9c6=1y r7c5=3y r7c9=1y
=3y r7c5=1g
18 r7c9=
=1y r7c5=1y r6c9=1g
19 r8c1=2g r3c1=2y r8c1=4y
=4y r8c1=4y r8c9=4g
20 r8c7=
2y r8c1=2g
21 r8c9=4g r8c1=4y r8c9=5y
=5y r8c9=4g end
22 r9c2=4g r9c8=4y r9c2=2y
=2y r9c2=4g r3c2=2g
23 r9c6=
=1y r1c6=1g r7c5=1g
24 r9c7=1g r6c9=1y end
=
25 r9c8=5g r1c8=5y r9c8=4y
=4y r9c8=5g r9c2=4g