The New Sudoku Players' Forum

[sfddoc]

4 3 8 1 9 5 6 27 27
569 569 7 2 36 368 89 1 4
1 269 269 7 4 68 89 3 5

2356 4 256 356 7 9 1 256 8
8 5679 569 56 2 1 57 4 3
2356 2567 1 4 8 36 257 9 267

2569 8 2569 36 356 4 257 2567 1
7 1 4 8 56 2 3 56 9
256 256 3 9 1 7 4 8 26[/list]

[Pat]

Chicago Sun-Times 2006.Jan.8
Hard [ 26 clues ]

4 3 8 1 9 5 6 27 27
569 569 7 2 36 368 89 1 4
1 269 269 7 4 68 89 3 5

2356 4 256 356 7 9 1 256 8
8 5679 569 56 2 1 57 4 3
2356 2567 1 4 8 36 257 9 267

2569 8 2569 36 356 4 257 2567 1
7 1 4 8 56 2 3 56 9
256 256 3 9 1 7 4 8 26

the 5 for r2 is in c1 or c2;
the 5 for r9 - likewise;
surely no more 5s can be in these 2 columns!!
thus we have the 5 for r6

(this would be an X-wing,
therefore i'm waiting for someone to provide the simpler explanation!!)

- Pat

[ChrisT]

There are a few box/line interactions that you've missed with the 5s. Once you make those, it should be just singles.

Chris

[ChrisT]

Whoops! Crossed in the post with Pat's message. You can use an x-wing with the 5s, which has the same outcome, but box/line eliminations are perhaps an easier way of attacking it. Either way works fine though.

Chris

[Pat]

You can use an X-wing with the 5s,
but box/line eliminations are perhaps an easier way of attacking it.

yes!
the 5 for r9 is in box 7,
so the 5 for c3 is in box 4,
thus giving us the 5 for r6.

thanks!
Pat

[tarek]

box-line eliminations for 5s should do the trick. The x-wing looks better though

[sfddoc]

thanx for the help, i understand x wing and now see it but what are box/line interactions? thanx.

[Crazy Girl]

For a definition of the terms we use in this forum check out the links below

http://www.angusj.com/sudoku/hints.php or
http://www.simes.clara.co.uk/programs/sudokutechniques.htm

If you are still stuck let us know

[sweetbix]

what are box/line interactions? thanx.

It can be confusing because they are called different things on different solvers. Here they are mostly referred to as locked candidates.

It means that if a candidate must be in one row or column (the intersecting one) in a box, then you can remove it from all the non-intersecting rows/columns in that box.

In box 7 the 5 must be placed in row 9 ( edited : or where r9 intersects with box 7). It is locked into that row, therefore you can remove 5 from all other rows in box 7 ie r7c1 and r7c3.

Also the 5s in c3 in box 4.

[Pat]

what are box/line interactions?

hi sfddoc,
please note that i did not use any such language
- i tried to give the eliminations from basic rules:

the 5 for r9 is in box 7,
so the 5 for c3 is in box 4,
thus giving us the 5 for r6.

if something here is unclear, please specify.

In box 7 the 5 must be placed in row 9

no,
it's the other way around:
in r9, the 5 must be placed in box 7.

- Pat

[sweetbix]

In box 7 the 5 must be placed in row 9 because in row 9 the 5 must be placed in box 7!

[Cec]

In box 7 the 5 must be placed in row 9 (or where r7 intersects with box9).."

"..in r9 the 5 must be placed in box 7.."

Leaving aside sweetbix's reference to "or where r7 intersects with box9" which I find confusing, the above two opinions seem to imply the same explanation for the 5's being locked in r9 box7.
Cec

[Pat]

In box 7 the 5 must be placed in row 9 (or where r7 intersects with box9)

in r9, the 5 must be placed in box 7

the above two opinions seem to imply the same explanation for the 5s being locked in r9 box7.

hi cecbevwr,

i'm sorry to say that sweetbix and i differ on cause-and-effect.

you should be aware that the 2 quotes above are in direct opposition to each other.

i hope this phrasing will clarify my position:

• the 5 for r9 has only 2 cells available -
  and they are both in box 7 - by observation!
  thus, we know that the 5 for r9 will be in box 7
• therefore, we eliminate 5s elsewhere in that box (esp. at r7c3)

In box 7 the 5 must be placed in row 9

no: in box 7 as we observe, the 5 can go in several cells, some of them outside of r9!
after we observe the r9 situation, we can make the deduction which eliminates the 5 elsewhere in that box - this is the result and not the cause.

- Pat

[Cec]

you should be aware that the 2 quotes above are in direct opposition to each other

Can't see why when both quotes reach the same conclusion as to the 5's being locked in r9 box7.
Cec

"..the 5 for r9 has only 2 cells available -
and they are both in box 7 - by observation!
thus, we know that the 5 for r9 will be in box 7.

Agreed
Cec

In box 7 the 5 must be placed in row 9

no: in box 7 as we observe, the 5 can go in several cells, some of them outside of r9!

Not so!. "By observation" of box 7, the 5 cannot "go in several cells... outside of r9" as this would exclude all candidate 5's from r9.

As I see this scenario, we all appear to identify the logic as to why the 5's are locked in r9 box7 but expressing this in a different way.
Cec

[Animator]

This is how I see it:

In box 7 the 5 must be placed in row 9

I read this as: The only possible cells in box 7 that can have the number 5 are in row 9 (read: 5 is not a candidate, before making any elimneations, in r7c1, r7c2, r7c3, r8c1, r8c2 or r8c3). As a result of that I decide to remove all other 5s from row 9 that are not in box 7.

In row 9 the 5 must be placed in box 7

The only cells in row 9 with 5 as a candidate happens to be in box 7. As a result of that I remove the 5 as candidate from all other cells in box 7.

The quotes really are different.

If you explain it as:

"By observation" of box 7, the 5 cannot "go in several cells... outside of r9" as this would exclude all candidate 5's from r9.

Then you ar observing two units. Not one. You are not observing box 7. You are observing box 7 in combination with row 9.

You can never come to that conclusion by looking only at box 7. You can however can come to that conclusion by looking only at row 9.

If you explain it then you should try to limit your observeration to one unit.