## color wing

Advanced methods and approaches for solving Sudoku puzzles

### color wing

In a Brainbasher puzzle I came across a technique called color wing by sudocue.

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`..63.45...2.....3.3..9.2..75.7.6.9.2...7.9...8.9.4.7.39..6.1..4.3.....7...14.72.. *--------------------------------------------------------------------* | 17     9      6      | 3      178    4      | 5      2      18     | | 17     2      458    |*1-8    1578   6      | 148    3      9      | | 3      58     458    | 9      158    2      | 1468   1468   7      | |----------------------+----------------------+----------------------| | 5      14     7      |*18     6      3      | 9     *14-8   2      | | 2      146    3      | 7     *1-8    9      | 1468   14568  1568   | | 8      16     9      | 2      4      5      | 7      16     3      | |----------------------+----------------------+----------------------| | 9      7      58     | 6      2      1      | 3      58     4      | | 4      3      2      | 5      9      8      | 16     7      16     | | 6      58     1      | 4      3      7      | 2      9      58     | *--------------------------------------------------------------------*color wing`

The 8 in r4c4 has a strong link in row, column and box.

Can you always say:

A cell with strong links for the same digit in row, column and box can be set with that digit? Or do I not get color wing?

dan
Last edited by ArkieTech on Thu Jul 31, 2008 9:30 am, edited 1 time in total.
dan

ArkieTech

Posts: 2976
Joined: 29 May 2006
Location: NW Arkansas USA

I dont know color wings, but starting with r4c4 there is a cycle for 8's with 4 strong links connected by 3 weak links. Therefore r4c4 must be 8.
r4c4=8=r4c8-8-r7c8=8=r9c9-8-r1c9=8=r1c5-8-r2c4=8=r4c4
iow: r4c4<>8 -> r4c8=8 -> r9c9=8 -> r1c5=8 -> r4c4=8

For sure you cant say, that you can pin a number just because it has 3 strong links to others. This only means, that either the number is true or all 3 others. But as you can see above, in this case e.g. r4c8=8 implies r1c5=8, i.e. then the other two (r2c4 and r5c5) cannot be 8.
eleven

Posts: 1873
Joined: 10 February 2008

eleven said
For sure you cant say, that you can pin a number just because it has 3 strong links to others. This only means, that either the number is true or all 3 others. But as you can see above, in this case e.g. r4c8=8 implies r1c5=8, i.e. then the other two (r2c4 and r5c5) cannot be 8.

In this puzzle r4c4 must be 8 the cells with the strong relationship (r2c4, r5c5 and r4c8) must be something other than 8. r4c8 does not have strong relationship in the box or column. What am I missing?

dan
dan

ArkieTech

Posts: 2976
Joined: 29 May 2006
Location: NW Arkansas USA

ArkieTech wrote:In this puzzle r4c4 must be 8 the cells with the strong relationship (r2c4, r5c5 and r4c8) must be something other than 8. r4c8 does not have strong relationship in the box or column. What am I missing?

eleven wrote:For sure you can't say that you can pin a number just because it has 3 strong links to others. This only means that either the number is true or all 3 others.

===== ===== ===== ===== ===== =====

Sudopedia says that Color Wing is the same thing as Multi-Colors, but this PM must need more than two colors because Simple Sudoku doesn't find [r5c5]<>8. I'm pretty sure the following fish can be expressed using three colors.

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`finned Franken Swordfish r14b9\c589 w/fin [r1c5]  <> 8  [r5c5]`

Your approach using the strong links has a practical side that I've used in the past. Set the non-common cells true and check their impact. It often, but not always, leads to a contradiction.

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`[r2c4]        -8- [r1c5] =8= [r1c9]  \                                       contradiction! => [r4c4]=8[r4c8]|[r5c5] -8- [r5c7] =8= [r23c7] /`

Also, the elimination is found with X-Colors (or an X-Chain).
Last edited by daj95376 on Thu Jul 31, 2008 10:39 am, edited 2 times in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

daj95376 has already referred to the Color Wing. Here is a Grouped Turbot that achieves the key elimination.
Code: Select all
`(8): r1c5=r1c9-r23c7=r5c7  leading to r5c5<>8`
Glyn

Posts: 357
Joined: 26 April 2007

daj95376 said:
but not always

Thanks daj. It did not take me long to find an a "not always":
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`000059060010000008069000410000610002007000300200035000024000530900000020080570000 *-----------------------------------------------------------* | 48    47    28    | 1     5     9     | 27    6     3     | | 5     1     23    | 347   46    367   | 279   79    8     | | 37    6     9     | 2378  28    378   | 4     1     5     | |-------------------+-------------------+-------------------| | 48    3     58    | 6     1     47    | 79    579   2     | |*16    45    7     | 29    29    48    | 3     58   *16    | | 2     9     16    | 78    3     5     |*16    78    4     | |-------------------+-------------------+-------------------| | 167   2     4     | 89    89    16    | 5     3     167   | | 9     57    156   | 34    46    136   | 8     2     167   | | 3-16  8     136   | 5     7     2     |*16    4     9     | *-----------------------------------------------------------*remote pair(16)`

Look at r6c7 both the 1 and 6 have strong links in row, column and box. It is hard to set the cell to both.
color wings need more study.

It is part of a remote pair that solves the puzzle.

dan
dan

ArkieTech

Posts: 2976
Joined: 29 May 2006
Location: NW Arkansas USA