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csc · Joined: 03 May 2007 Posts: 14

I got as far as this. Could someone please render assistance. I've tried using all the techniques I know, but to no avail.
Thank you for the help.
Regards
scchua

|78| -6-|278|12---| -4-| -3- | 5 |17| -9-|
----------------------------------------------------------------------------
| 5 | -1-| -9-|68---| -7-|68- | 4 | 2-| -3- |
---------------------------------------------------------------------------
| 3 |27-| -4-|125--|129|159| 8 | 6-|17-|
----------------------------------------------------------------------------
| 6 | -3-|578| -9- |12- |15- |27|18| -4 |
----------------------------------------------------------------------------
| 2 | -4-| -1-|78-- | -3- |78- | 6 | 9-| -5 |
---------------------------------------------------------------------------
| 9 |78-|578|1256|126| -4-|27| 3-|18-|
---------------------------------------------------------------------------
| 4 | -5-| -6-|17-- |189|19- | 3 |78| -2- |
---------------------------------------------------------------------------
|78| -9-|278| -3-- | -5-|267| 1 | 4 |678|
---------------------------------------------------------------------------
| 1 |278| -3-| -4- |68-|267| 9 | 5 |678|

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Hi Scc,

I see three possible lines of attack:

1)Look at r3c9 r6c9 and r6c2 - what do you see ?

2)Look for a skyscraper on 7's

2)Look for a strong links eliminartion on 1's (two string Kite)

If this doesn't make sense to you let me know.

csc · Joined: 03 May 2007 Posts: 14

Hello Mogulmeister
Thanks for your reply.
It was smooth sailing after the xy-wing you pointed out.
I tried your other 2 lines of attack. I found a skyscraper on 7, and a 2 string kite on 1, after reading that excellent article on strong links from Havard (thanks Havard). However, I got no further than following:

|78| -6-|278|12---| -4-| -3- | 5 |17| -9-|
----------------------------------------------------------------------------
| 5 | -1-| -9-|68---| -7-|68- | 4 | 2-| -3- |
---------------------------------------------------------------------------
| 3 |27-| -4-|125--|129|159| 8 | 6-|17-|
----------------------------------------------------------------------------
| 6 | -3-|578| -9- |12- |15- |27|18| -4 |
----------------------------------------------------------------------------
| 2 | -4-| -1-|78-- | -3- |78- | 6 | 9-| -5 |
---------------------------------------------------------------------------
| 9 |78-|578|256|126| -4-|27| 3-|18-|
---------------------------------------------------------------------------
| 4 | -5-| -6-|17-- |189|19- | 3 |78| -2- |
---------------------------------------------------------------------------
|78| -9-|278| -3-- | -5-|267| 1 | 4 |68|
---------------------------------------------------------------------------
| 1 |278| -3-| -4- |68-|267| 9 | 5 |678|

ie. after eliminating 7 from r8c9, and 1 from r6c4 (looks like I still need the xy wing?). Could I trouble you to point out the alternative route?
Thanks a lot.
regards
scchua

Mogulmeister · Joined: 03 May 2007 Posts: 1151

cc,

Have a look at all the strong links on 8's. You can eventually build a series which will elimin8 the 8 in r9c5 !

PS please read Marty's thread on how to post a better grid ! Smile

It's here: http://www.dailysudoku.co.uk/sudoku/forums/viewtopic.php?t=1885

csc · Joined: 03 May 2007 Posts: 14

Dear M,
I'm such a novice at strong links that even with your hint on the 8's, I can't make it work, but not for want of trying. Thus, all (I think) of the strong links on 8's are:

(1) r1c1 - r8c1
(2) r1c1 - r1c3
(3) r6c2 - r9c2
(4) r4c3 - r4c8
(5) r2c4 - r2c6
(6) r2c4 - r5c4
(7) r5c4 - r5c6
(8) r7c5 - r7c8
(9) r7c5 - r9c5
(10) r2c6 - r5c6
(11) r4c8 - r6c9
(12) r4c8 - r7c8

Potentially useful pairs of strong links are:
(1) and (3)
(2) and (4)
(3) and (4)
(3) and (9)
(3) and (11)
(4) and (8)
(8) and (11)
(9) and (12)

But none of the above are profitable, ie. none results in an elimination! Am I misunderstanding the concept of strong links?

Thanks for your patience (hopefully your response will serve also for 8 Dec, where I'm now stuck for the moment, but haven't given up yet).

p.s. repeating the grid below, using ascii code:

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Look at this cc,

You will see if you follow the true/false path of these 8's. Green is true and orange is false or the other way round if you prefer - either way r9c5 is toast. Smile

csc · Joined: 03 May 2007 Posts: 14

M, thanks.
finally got what you mean.
regards
scchua

Marty R. · Posted: Sun May 27, 2007 3:18 pm Post subject:

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Marty - look at the two pincers at r7c5 and r9c2. Start with either one and set it to true or false. Whatever you do there is always a "true" looking at r9c5.

Marty R. · Posted: Sun May 27, 2007 7:32 pm Post subject:

Post deleted.

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Whoops - Marty you're right - the extra 8 on row 6 means that this doesn't work quite the way I had anticipated/shown. However I'm working on something that hopefully will show that 8 is a fruitful eliminand!

Mogulmeister · Joined: 03 May 2007 Posts: 1151

Yes multicolouring is correct Marty- I wasn't expansive enough but let's look at the deterministic proof:

Let us consider setting r9c2 to TRUE (green) and look at the effect that this has on the state of all the links.

Let us now consider setting r9c2 to FALSE. Notice that because r9c2 is set to FALSE (orange) this means that either r8c1 or r8c3 is TRUE which in turn makes r8c9 FALSE.

Notice that as well as our candidate cell (important to blowing the puzzle)
being eliminated, we could also eliminate cells:
r4c3 r6c9 r7c8

Which remained FALSE throughout ! Smile

csc · Joined: 03 May 2007 Posts: 14

Dear Mogulmeister and Marty,
I too saw the "extra" 8 in r6c3, but it was ignored based on the following logic:
Strong links r6c9 - r4c8 and r4c8 - r7c8 and r7c8 - r7c5 all together form a "long" strong link (generalisation: odd number of strong links connected end to end are equivalent to a strong link). If you take this "long" link and pair it with the link r6c2 - r9c2, then 8 can be eliminated in r9c5 which is a common peer to r7c5 and r9c2.
Question: would there be a case in which my logic above wouldn't apply.

regards
scchua

Marty R. · Posted: Mon May 28, 2007 4:04 am Post subject:

MM,

You saw my comment about multi-coloring before I deleted it, because I incorrectly thought it was incorrect, again getting tripped up by that extra 8 in row 6.

CSC,

You have described a multi-coloring example. You have two separate T-F chains, each with an even number of cells, weakly linked in row 6. Since both in row 6 can't be true, then one or both of the pincers has to be true.

While it is true that each chain has an odd number of strong links, most people think in terms of the chains having to be an even number of cells, which forces the start and end of the chain to be of opposite polarity.

Mogulmeister · Joined: 03 May 2007 Posts: 1151

CSC and Marty,

Just to put a footnote on this to highlight what we've all noticed about multicolouring:

There are as you said two clusters of conjugate links and in the recommended fashion (Sudopedia) I have coloured one set Green and orange and the other set blue and pink.

Notice that an 8 MUST be in either blue or pink and as these both point at an orange square we can deduct that orange is false. We can therefore eliminate 8 from ALL orange squares.