The New Sudoku Players' Forum

by **JEAGoodman** » Thu Mar 16, 2006 4:16 am

Ok, I'm stuck. Why are the blues excluded here?

*-----------------------------------------------------------*
| 3 4 29 | 6 58 7 | 158 15 29 |
| 1 79 5 | 2 4 89 | 78 3 6 |
| 8 2679 269 | 15 3 19 | 57 4 29 |
|-------------------+-------------------+-------------------|
| 2 36 346 | 8 1 5 | 46 9 7 |
| 9 1 46 | 7 2 3 | 46 8 5 |
| 5 8 7 | 9 6 4 | 12 12 3 |
|-------------------+-------------------+-------------------|
| 7 35 13 | 4 9 12 | 25 6 8 |
| 6 59 189 | 15 7 128 | 3 25 4 |
| 4 25 28 | 3 58 6 | 9 7 1 |
*-----------------------------------------------------------*

by **ronk** » Thu Mar 16, 2006 4:37 am

JEAGoodman wrote:Why are the blues excluded here?

Because either pink or amber will ultimately be true, and at least one blue "sees" a pink and at least one blue sees an amber.

Ron

by **JEAGoodman** » Thu Mar 16, 2006 5:18 am

I think I get it. You don't happen to have another puzzle with a two color solution like that for me to try to get on my own, do you?

Thanks so much!

Jeanne

by **emm** » Thu Mar 16, 2006 11:22 am

One of angusj’s – colour the 5s

Code: Select all: *-----------------------------------------------------------* | 5 16 7 | 2 9 16 | 3 4 8 | | 2 168 3 | 4 578 168 | 156 17 9 | | 4 168 9 | 15 578 3 | 1256 127 57 | |-------------------+-------------------+-------------------| | 1 5 6 | 7 2 4 | 8 9 3 | | 9 7 2 | 8 3 5 | 4 6 1 | | 8 3 4 | 19 6 19 | 7 5 2 | |-------------------+-------------------+-------------------| | 3 2 15 | 6 4 89 | 159 178 57 | | 7 4 15 | 359 58 289 | 1259 1238 6 | | 6 9 8 | 35 1 7 | 25 23 4 | *-----------------------------------------------------------*

and another – colour the 3s

Code: Select all: *--------------------------------------------------* | 9 56 13 | 45 47 37 | 8 2 16 | | 7 2 4 | 1 6 8 | 9 3 5 | | 13 56 8 | 9 35 2 | 7 4 16 | |----------------+----------------+----------------| | 123 4 6 | 8 23 9 | 13 5 7 | | 8 9 135 | 45 47 37 | 13 6 2 | | 23 7 35 | 6 235 1 | 4 9 8 | |----------------+----------------+----------------| | 5 8 7 | 3 9 6 | 2 1 4 | | 6 3 2 | 7 1 4 | 5 8 9 | | 4 1 9 | 2 8 5 | 6 7 3 | *--------------------------------------------------*

and one shamelessly stolen from Jeff - colour the 7s.

Code: Select all: +----------------+----------------+----------------+ | 6 47 3 | 5 1 47 | 2 8 9 | | 8 257 27 | 6 9 3 | 4 57 1 | | 457 1 9 | 28 27 478 | 6 3 57 | +----------------+----------------+----------------+ | 1 8 6 | 9 3 5 | 7 2 4 | | 47 247 5 | 28 6 78 | 1 9 3 | | 9 3 27 | 4 27 1 | 5 6 8 | +----------------+----------------+----------------+ | 25 9 8 | 7 4 6 | 3 1 25 | | 3 57 4 | 1 8 2 | 9 57 6 | | 27 6 1 | 3 5 9 | 8 4 27 | +----------------+----------------+----------------+

by **JEAGoodman** » Thu Mar 16, 2006 1:32 pm

Thanks for your help Em, but I'm still not there. Let's take the 3s example you gave. I don't understand why r4c5 and r5c3 weren't eliminated but r4c1 was!

by **ronk** » Thu Mar 16, 2006 1:58 pm

JEAGoodman wrote:I don't understand why r4c5 and r5c3 weren't eliminated but r4c1 was!

Maybe you haven't yet seen these write-ups by Angus Johnson.

Ron

by **emm** » Thu Mar 16, 2006 5:53 pm

OK, JEAGoodman, I see where you’re coming from - it’s not enough to intersect just any old Aa with any old Bb ie r4c5 and r5c3.

First, one from each colour must also share a group = A and B in r5
therefore one or both of their conjugates must be true
therefore any cell that intersects both their conjugates must be false.

Code: Select all: . . 3A| . . 3a| . . . . . | . . . | . . . 3a . | . 3 . | . . . ---------+---------+----- 3* . . | . 3 . | 3b. . . . 3 | . . 3A| 3B. . 3 . 3 | . 3 . | . . . ---------+---------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . .

r4c1 is the only cell that 'sees' both conjugates (a and b) of two cells that share a group (A and B).

by **JEAGoodman** » Fri Mar 17, 2006 8:17 pm

Ok, good. That helped A LOT, EM. But can you help out with one more?

In this one...

Code: Select all: *-----------------------------------------------------------* | 5 16 7 | 2 9 16 | 3 4 8 | | 2 168 3 | 4 578 168 | 156 17 9 | | 4 168 9 | 15 578 3 | 1256 127 57 | |-------------------+-------------------+-------------------| | 1 5 6 | 7 2 4 | 8 9 3 | | 9 7 2 | 8 3 5 | 4 6 1 | | 8 3 4 | 19 6 19 | 7 5 2 | |-------------------+-------------------+-------------------| | 3 2 15 | 6 4 89 | 159 178 57 | | 7 4 15 | 359 58 2 | 159 138 6 | | 6 9 8 | 35 1 7 | 25 23 4 | *-----------------------------------------------------------*

using your notation * is the one that is excluded, c is a candidate and ? is the one that I just don't get why it's NOT excluded

Code: Select all: . . . | . . . | . . . . . . | . 5a . | 5A . . . . . | * c . | c . c -------------------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . -------------------- . . c | . . . | c . c . . c | c ? . | c . . . . . | 5b . . | 5b . .

Jeanne

by **emm** » Sat Mar 18, 2006 12:23 am

You’ve got it, Jeanne - it is excluded. I really like Havard’s threads on Strong links and Skyscrapers for a simple way of visualising this stuff.

Code: Select all: . . . | * . . | . . . . . . | . a----|-A . . . . . | * . . | . . . --------+---------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . --------+---------+------ . . . | . * . | . . . . . . | . * . | . . . . . . | b-------|-B . .

Skyscraper is a good technique to use on the 3rd puzzle with the 7s.

by **alrocks** » Mon Mar 20, 2006 2:05 am

Here's a nice one. It needs a couple colorings:

Code: Select all: *-----------------------------------------------------------------------------* | 79 8 6 | 1249 5 12479 | 39 14 3479 | | 579 345 349 | 1469 8 14679 | 69 146 2 | | 2 1 49 | 469 3 4679 | 5 8 4679 | |-------------------------+-------------------------+-------------------------| | 46 7 5 | 8 46 3 | 2 9 1 | | 3 2 8 | 469 1 469 | 7 46 5 | | 46 9 1 | 7 2 5 | 8 3 46 | |-------------------------+-------------------------+-------------------------| | 15 6 234 | 12345 9 124 | 13 7 8 | | 8 345 7 | 123456 46 1246 | 1369 25 369 | | 159 35 239 | 12356 7 8 | 4 25 36 | *-----------------------------------------------------------------------------*

by **QBasicMac** » Mon Mar 20, 2006 2:13 am

alrocks wrote:Here's a nice one.

Why did you put this in this thread? It looks like a new thread.

Mac

by **JEAGoodman** » Mon Mar 20, 2006 1:34 pm

QBasicMac wrote:
Why did you put this in this thread? It looks like a new thread.

Mac

That is because I had asked for more examples above.

So Em, thanks to you I think I'm 96% there. Now my only question is how do you know when something is an A or an a. When I look at the code you just entered, I think that I could have missed it by putting the A on the left.

Jeanne

by **QBasicMac** » Mon Mar 20, 2006 3:35 pm

JEAGoodman wrote:That is because I had asked for more examples above.

Oops! Sorry all

Mac

by **JEAGoodman** » Mon Mar 20, 2006 3:58 pm

No worries, Mac.

Wait, I think I've got it and I got what was bothering me before. The A and B are defined because of their relationship not only to their own pairs, but their relationship to one another? They're not quite a pair, but yet, they're connected. Yes?

by **ronk** » Mon Mar 20, 2006 6:37 pm

JEAGoodman wrote:The A and B are defined because of their relationship not only to their own pairs, but their relationship to one another? They're not quite a pair, but yet, they're connected. Yes?

'A' and 'a' are strongly linked. If one is true, the other is false. If one is false, the other is true.

[edit: As shown on em's diagram,] 'A' and 'B' are weakly linked. If one is true, the other is false. But if one is false, the other may be either true or false.

That the colors in one column are both upper case ("AB") has no meaning. The reasoning would be the same if the colors were "Ab", "aB", or "ab".

Ron

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