## help with colors on this puzzle

Post the puzzle or solving technique that's causing you trouble and someone will help

### help with colors on this puzzle

I don't understand how colors can eliminate the '1' in R2C2 in this puzzle:

Code: Select all
`14  7    5   | 248  289  289 | 3    6    123   16   146 | 24   5    7   | 129  129  82   9    8   | 6    1    3   | 7    5    4-------------+---------------+-------------9   126  7   | 5    268  268 | 4    3    1218  3    126 | 9    7    4   | 126  128  548  5    246 | 23   236  1   | 269  289  7-------------+---------------+-------------6   8    3   | 7    4    5   | 12   12   97   12   12  | 38   389  89  | 5    4    65   4    9   | 1    26   26  | 8    7    3`

And that took me so long to write.
Thanks.
mikebot

Posts: 4
Joined: 13 May 2006

### Re: help with colors on this puzzle

mikebot wrote:I don't understand how colors can eliminate the '1' in R2C2 in this puzzle:

Code: Select all
`a14  7    5   | 248  289  289 | 3    6   A12 3  -16   146 | 24   5    7   | 129  129  8 2   9    8   | 6    1    3   | 7    5    4--------------+---------------+------------- 9  A126  7   | 5    268  268 | 4    3   a12-18  3    126 | 9    7    4   | 126  128  5 48  5    246 | 23   236  1   | 269  289  7--------------+---------------+------------- 6   8    3   | 7    4    5   | 12   12   9 7   12   12  | 38   389  89  | 5    4    6 5   4    9   | 1    26   26  | 8    7    3`

r2c2 & r5c1 see both an 'a' and an 'A', therefore they cannot be a 1. Turns out that since r1c1 is the only 1 left in column 1, 'a' must be true and 'A' must be false as well.
Myth Jellies

Posts: 593
Joined: 19 September 2005

There are different coloring methods you can use. One is a form of advanced coloring, which i express as a chain here:
r1c1<>1 => r5c1=1 => r4c2<>1 => r4c9=1 => r1c9<>1 => r1c1=1
So r1c1 must be 1.

I hope, others will show you alternative methods [edit: just done by MJ

You can see, that there are [edit:] 4 strong links in this chain.
Those pairs of them can be used for eliminations:
r1c1-r1c9 and r4c9-r4c2 eliminate 1 in r2c2 and r5c1 (Myth's)
r1c1-r5c1 and r4c2-r4c9 eliminate 1 from r1c9]
Last edited by ravel on Tue Jun 06, 2006 7:11 am, edited 1 time in total.
ravel

Posts: 998
Joined: 21 February 2006

### Re: help with colors on this puzzle

mikebot wrote:I don't understand how colors can eliminate the '1' in R2C2 in this puzzle:

Code: Select all
`14  7    5   | 248  289  289 | 3    6    123   16   146 | 24   5    7   | 129  129  82   9    8   | 6    1    3   | 7    5    4-------------+---------------+-------------9   126  7   | 5    268  268 | 4    3    1218  3    126 | 9    7    4   | 126  128  548  5    246 | 23   236  1   | 269  289  7-------------+---------------+-------------6   8    3   | 7    4    5   | 12   12   97   12   12  | 38   389  89  | 5    4    65   4    9   | 1    26   26  | 8    7    3`

And that took me so long to write.
Thanks.

I just read angusj's explanation on coloring in Simple Sudoku. For a laugh, I'm going to try and answer your question.

First off, the whole thing hinges on assigning alternating colors to a candidate that appears only twice in a row/column/block.

If you examine row 1, column 9, and row 4, you'll see that the value '1' appears twice as a candidate in each.

Now, color r1c1 blue and r1c9 green. This results in r4c9 being blue and r4c2 being green.

Now, cell r2c2 can not have a '1' value because it's in the same block as the blue cell r1c1 and it's in the same column as the green cell r4c2.

In other words, r2c2 is a buddy to both a blue cell and a green cell. Therefore, it can't have '1' as a candidate.

As to why this is so, ask yourself what would happen if r2c2 was '1'. It then simultaneously eliminates '1' as a candidate from r1c1 and r4c2. This then forces two cells -- r1c9 and r4c9 -- to both be '1'. This can't happen!!!
Last edited by daj95376 on Tue Jun 06, 2006 11:53 am, edited 1 time in total.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Colors are a special case of Nice Loops. Here is another one:

Code: Select all
` *--------------------------------------------------* | 14   7    5    | 248  289  289  | 3    6    12   | | 3    16   146  | 24   5    7    | 129  129  8    | | 2    9    8    | 6    1    3    | 7    5    4    | |----------------+----------------+----------------| | 9    126  7    | 5    268  268  | 4    3    12   | | 18   3    126  | 9    7    4    | 126  128  5    | | 48   5    246  | 23   236  1    | 269  289  7    | |----------------+----------------+----------------| | 6    8    3    | 7    4    5    | 12   12   9    | | 7    12   12   | 38   389  89   | 5    4    6    | | 5    4    9    | 1    26   26   | 8    7    3    | *--------------------------------------------------*`

[r2c4]=2=[r2c78]-2-[r1c9]-1-[r4c9]=1=[r4c2]-1-[r5c1]=1=[r1c1]=
=4=[r2c3]-4-[r2c4], => r2c4<>4 and the puzzle is solved.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

### Re: help with colors on this puzzle

daj95376 wrote:Now, someone else will explain to you why my explanation is full of s**t.

Just fine, should make it clearer. Note, that also r5c1 is a buddy to the same blue/green cells.
ravel

Posts: 998
Joined: 21 February 2006

Thanks ravel for pointing out r5c1. Simple Sudoku didn't highlight this cell (or remove the '1') when I cross-checked my answer to mikebot. Until yesterday, I hadn't investigated Coloring. It was on my To-Do list after rewriting my solver to use Buddy Lists.
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

thanks for the help everyone...i think i'm starting to understand colors a little better.
mikebot

Posts: 4
Joined: 13 May 2006

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