SudoCue Users

Posted: **Sun Aug 27, 2006 8:22 am**

Here is an idea for a variation in solving a Killer - Tag Killer - the 'tag' being like in 'tag-team' wrestling - one person starts, then another takes over.

Below is the code for a Killer I made which is "Ruudiculous" - ie very hard and quite possibly is not solvable logically (Sumocue's dancing algorithms go crazy just finding the solution).

3x3:d:k:5376:5376:5378:5378:5378:5378:5378:5639:5639:5376:5642:4619:4619:5133:5133:5133

5639:5376:5642:5642:4619:5133

3607

2320:5376:5916

2845:5407

8225:8225

2852:5916

6695:5407

8225

2851

5916:5916:6695:5407:5407:8225

2357

6695:6695:6695:5434

8225:8225

4415

3648:5434:5434

3643

4167:4415:4415:5450:5450:5450:5450:5450:4167:4167:

[/code]

But perhaps together we can solve it. So, here is my suggestion for how we can collaborate.

1) I've followed Sumocue's "hints - F8" to get the puzzle "marks" to the "no more hints" spot below. [edit to include SumoCue's hints from start of puzzle to No More Hints (NMH) #1 -

Start of puzzle
1)Candidate 9 locked in cage 22(3) in N3
2)Candidate 9 locked in cage 22(3) in N1
3)45 test eliminates in 2 outies of r9
4)45 test eliminates in 2 outies of c1 (Edit:{13} only in r19c2 ->no 1or 3 elsewhere in c2)
5)45 test eliminates in 2 outies of r89
6)Unplaceable candidates in cage 14(4) in N89
7) Unplaceable candidates in cage 17(3) in N7
8)45 test eliminates in 3 innies of N69
9)Killer pair {1,3} found in r1
10)Killer pair {6,9} found in N7
11)Killer pair {8,9} found in N7
12)Killer pair {1,3} found in r9
13)Eliminations in innie/outie difference in N689
No more hints #1

2) Now, if anyone can see how to progress the puzzle further, tell us what your idea is - and use Sumocue's hints to find the consequences of your idea.

3) Post the marks of the new "No more hints" point (this will make sure we are all talking about the same thing).

4) In order to let others absorb that step - just post one idea and consequences at a time. If you have another idea of how to get past the next "no more hints" spot - wait at least until after the next full day to post. This will give others a chance to digest and get another idea. My hope is that a range of posters will be giving ideas (hence the 'tag' Killer).

It would be really helpful if Sumocue can "read" the Marks code from someone elses post - does anyone know if this is possible? If it is, how do you do it? If it's not possible then it is going to be a bit laborious manually entering the marks

but....

Any-way - I've called this puzzle "Uluru" - a famous rock in Northern Territory in Australia.

Anyone want to play?

Code: Select all

.-----------------------.-----------------------------------------------------------.-----------------------.
|&#40;21&#41;                   |&#40;21&#41;                                                       |&#40;22&#41;                   |
| 245678      13        | 12345678    123456789   123456789   123456789   12345678  | 56789       56789     |
|           .-----------+-----------------------.-----------------------------------+-----------.           |
|           |&#40;22&#41;       |&#40;18&#41;                   |&#40;20&#41;                               |&#40;9&#41;        |           |
| 12345678  | 56789     | 12345678    123456789 | 123456789   123456789   12345678  | 123456    | 56789     |
|           |           '-----------.           |           .-----------------------&#58;           '-----------&#58;
|           |                       |           |           |&#40;14&#41;                   |                       |
| 12345678  | 56789       56789     | 123456789 | 123456789 | 12345678    12345678  | 123456      123456    |
|           &#58;-----------.-----------'-----------+-----------&#58;           .-----------'-----------.-----------&#58;
|           |&#40;23&#41;       |&#40;11&#41;                   |&#40;21&#41;       |           |&#40;32&#41;                   |&#40;11&#41;       |
| 123456789 | 2456789   | 12345678    12345678  | 123456789 | 12345678  | 123456789   123456789 | 23456789  |
&#58;-----------&#58;           |           .-----------&#58;           |           |           .-----------&#58;           |
|&#40;11&#41;       |           |           |&#40;26&#41;       |           |           |           |&#40;11&#41;       |           |
| 12345678  | 2456789   | 12345678  | 123456789 | 123456789 | 12345678  | 123456789 | 23456789  | 23456789  |
|           |           '-----------&#58;           |           '-----------&#58;           |           &#58;-----------&#58;
|           |                       |           |                       |           |           |&#40;9&#41;        |
| 12345678  | 2456789     123456789 | 123456789 | 123456789   123456789 | 123456789 | 23456789  | 12345678  |
|           &#58;-----------------------'           &#58;-----------.-----------&#58;           '-----------&#58;           |
|           |                                   |&#40;21&#41;       |&#40;14&#41;       |                       |           |
| 123457    | 2457        123457      123457    | 56789     | 45678     | 123456789   123456789 | 12345678  |
&#58;-----------+-----------------------.-----------'           |           '-----------------------+-----------&#58;
|&#40;17&#41;       |&#40;14&#41;                   |                       |                                   |&#40;16&#41;       |
| 5678      | 5689        5689      | 456789      456789    | 1234567     1234567     1234567   | 12345678  |
|           '-----------.-----------'-----------------------'-----------------------.-----------'           |
|                       |&#40;21&#41;                                                       |                       |
| 689         13        | 123457      123456789   123456789   123456789   12345678  | 2456789     2456789   |
'-----------------------'-----------------------------------------------------------'-----------------------'

Posted: **Sun Aug 27, 2006 10:51 pm**

It's actually completely solvable by logic--try a more powerful solving program like JC Godart's, which nails it down without a problem.

Posted: **Mon Aug 28, 2006 12:19 pm**

Thanks udosuk for making these versions of the puzzle for me.

My brother's family has just returned from Uluru and they were utterly transfixed by it - though it looks a lot redder/purpler than in udosuk's version - but hey, anything in green and gold is fine by me (our Australian national sporting colours).

http://img245.imageshack.us/img245/4070/uluruip8.png

Code: Select all

Uluru&#58; a diagonal puzzle &#40;X&#41;
.-----.--------------.-----.
|21   |21            |22   |
|  .--+-----.--------+--.  |
|  |22|18   |20      |9 |  |
|  |  '--.  |  .-----&#58;  '--&#58;
|  |     |  |  |14   |     |
|  &#58;--.--'--+--&#58;  .--'--.--&#58;
|  |23|11   |21|  |32   |11|
&#58;--&#58;  |  .--&#58;  |  |  .--&#58;  |
|11|  |  |26|  |  |  |11|  |
|  |  '--&#58;  |  '--&#58;  |  &#58;--&#58;
|  |     |  |     |  |  |9 |
|  &#58;-----'  &#58;--.--&#58;  '--&#58;  |
|  |        |21|14|     |  |
&#58;--+-----.--'  |  '-----+--&#58;
|17|14   |     |        |16|
|  '--.--'-----'-----.--'  |
|     |21            |     |
'-----'--------------'-----'

Posted: **Mon Aug 28, 2006 12:47 pm**

It's actually completely solvable by logic

That's great news ND. Thanks.

Finally found something to get this puzzle going.

From the "No more hints" #1:
“45” on N7-> 4 innies = 14 = {1247}{2345} = 24{17/35}
ie, 2 & 4 are locked in these 4 cells.

We know that“45” on N689 means that the difference between the one innie and one outie is 0 ->r7c4 = r9c3
-> 2 & 4 must be in r7c1234, since if 2 or 4 is in r9c3 they must also be in r7c4.
->2 and 4 cannot be elsewhere in r7
->4 is eliminated from r7c6 -> no 9 in r7c5 (since the two outies of r89 = 13)
-> 9 in r7 is locked in N9 in r7c78
-> no 9 elsewhere in N9 or 32(6) cage in n89
but 9 cannot go in r7c8 because this would mean no 9's in N6 since the 9 in N3 would have to be be in c9 when 9 is in r7c8
->r7c7=9

Plugging this into SumoCue -
From r7c7=9
14)hidden single digit 9 in N1
15)unplaceable candidates in cage 18(3) in N12
16)unplaceable candidates in cage 23(4) in N4
17)unplaceable candidates in cage 14(4) in N89
18)unplaceable candidates in cage 14(2) in N7
19)Eliminations on innie/outie difference in N6
20)Obsolete candidate 5 in cage 9(2) in c9
21)Obsolete candidate 7 in cage 9(2) in c9
No more hints #2

the "No more Hints" #2 spot is here.

OK - someone else want to take it from here?

Code: Select all

.-----------------------.-----------------------------------------------------------.-----------------------.
|&#40;21&#41;                   |&#40;21&#41;                                                       |&#40;22&#41;                   |
| 245678      13        | 12345678    123456789   123456789   123456789   12345678  | 56789       56789     |
|           .-----------+-----------------------.-----------------------------------+-----------.           |
|           |&#40;22&#41;       |&#40;18&#41;                   |&#40;20&#41;                               |&#40;9&#41;        |           |
| 12345678  | 5678      | 12345678    3456789   | 123456789   123456789   12345678  | 123456    | 56789     |
|           |           '-----------.           |           .-----------------------&#58;           '-----------&#58;
|           |                       |           |           |&#40;14&#41;                   |                       |
| 12345678  | 9           5678      | 12345678  | 12345678  | 12345678    12345678  | 123456      123456    |
|           &#58;-----------.-----------'-----------+-----------&#58;           .-----------'-----------.-----------&#58;
|           |&#40;23&#41;       |&#40;11&#41;                   |&#40;21&#41;       |           |&#40;32&#41;                   |&#40;11&#41;       |
| 123456789 | 245678    | 12345678    12345678  | 123456789 | 12345678  | 12345678    12345678  | 23456789  |
&#58;-----------&#58;           |           .-----------&#58;           |           |           .-----------&#58;           |
|&#40;11&#41;       |           |           |&#40;26&#41;       |           |           |           |&#40;11&#41;       |           |
| 12345678  | 245678    | 12345678  | 123456789 | 12345678  | 12345678  | 12345678  | 23456789  | 23456789  |
|           |           '-----------&#58;           |           '-----------&#58;           |           &#58;-----------&#58;
|           |                       |           |                       |           |           |&#40;9&#41;        |
| 12345678  | 245678      23456789  | 123456789 | 123456789   12345678  | 12345678  | 23456789  | 1368      |
|           &#58;-----------------------'           &#58;-----------.-----------&#58;           '-----------&#58;           |
|           |                                   |&#40;21&#41;       |&#40;14&#41;       |                       |           |
| 123457    | 2457        123457      123457    | 5678      | 5678      | 9           1368      | 1368      |
&#58;-----------+-----------------------.-----------'           |           '-----------------------+-----------&#58;
|&#40;17&#41;       |&#40;14&#41;                   |                       |                                   |&#40;16&#41;       |
| 5678      | 568         689       | 456789      456789    | 123456      123456      123456    | 12345678  |
|           '-----------.-----------'-----------------------'-----------------------.-----------'           |
|                       |&#40;21&#41;                                                       |                       |
| 689         13        | 123457      123456789   123456789   123456789   12345678  | 245678      245678    |
'-----------------------'-----------------------------------------------------------'-----------------------'

Posted: **Tue Aug 29, 2006 6:01 am**

First, please excuse my ignorance, what is a diagonal puzzle? Do you mean that the two diagonals also have all the digits 1-9?

I'm not into Sumocue since I'm not interested in solving puzzles by software. However I'll try to throw in a few thoughts just using my old brain.

In the diagram posted in the previous message, R8C9 should be 1234 rather than 12345678 by applying the 45 rule to R9 making R8C19 total 9.

Clearly R19C2 are {13} as in the diagram by applying the 45 rule to C1. For whichever of these two squares has the 1, the 21(5) cage immediately to the right of it will be {23457}.

In the previous message it says 4 is eliminated from R7C6 so no 9 in R7C5; wouldn't it be better to make the more general statement that 4 is eliminated from R7C56 so no 9 in R7C56? This is more precise and still leads to the same conclusion that the 9 in R7 in locked in N9.

Hope these few thoughts help. I only started looking at this puzzle, intermittently, a few hours ago so I haven't yet tried to work out all the eliminations from the originally posted grid as I started from the basic killer grid. Similarly I haven't yet had time to think why one pair of {59} has been eliminated from the 14(2) cage in N7; I still have them both as 59/68.

Assuming that my assumptions about the diagonals is correct, then R7C7=9 prevents the 9 in the 22(3) cage in N1 from being in either R2C2 or R3C3 so it must be in R3C2 as in the diagram in the previous message. Hopefully I'll be able to work out the other fixings and eliminations that have appeared in that diagram before I think about adding any more to this thread.

Posted: **Tue Aug 29, 2006 8:16 am**

Do you mean that the two diagonals also have all the digits 1-9?

Yeah - spot on. I should have made that clearer.

I'm not interested in solving puzzles by software.

Neither am I - have never used the hints button on Sumocue before this puzzle. But I like the fact that it only gives hints that are relatively straighforward.

R8C9 should be 1234 rather than 12345678 by applying the 45 rule to R9

This is a good example of Sumocue's solver being basic - it seems to only give each hint once, even when the same move can be used later.

I stayed absolutely to the hints so that others can follow the same route.

Clearly R19C2 are {13} as in the diagram by applying the 45 rule to C1. For whichever of these two squares has the 1, the 21(5) cage immediately to the right of it will be {23457}.

Thats why 1 and 3 can be eliminated from r1c1 and r9c89 - I think the technical name for this elimination move is "Killer pair".

wouldn't it be better to make the more general statement that 4 is eliminated from R7C56 so no 9 in R7C56?

The 4 in r7c5 had already been eliminated in the "No more hints #1" pic because no 9 is possible in a 14(4) cage that r7c6 is in. Then combined with 2 outies of r89 = 13, therefore minimum value possible in r7c5 is 5 (with 8 in r7c6).

why one pair of {59} has been eliminated from the 14(2) cage in N7

because 9 has been placed in r3c2 after the 9 is placed in r7c7. Because r7c7 is on the Diagonal\, 9 is eliminated from r2c2 and r3c3, leaving r3c2 as a hidden single in N1.

Posted: **Wed Aug 30, 2006 2:54 am**

I've followed Sumocue's "hints - F8" to get the puzzle "marks" to the "no more hints" spot below

It think it would have been helpful if you could have said which steps had been taken to reach the first "no more hints" spot.

Clearly it has eliminated digits that are impossible in the basic cages such as 1 from 11(2) and 9 from 14(4); I missed the latter last night as I was up late and, as I said, starting from the basic grid rather than from the first "no more hints" spot.

Then it applied the 45 rule to C1 to get R19C2 = {13} so 1 and 3 are eliminated from all other squares in C2.

This makes R89C1 = 14 or 16 = {59}, {68} or {79} and R8C23 = {59} or {68} so R89C1 must contain either 8 or 9 with the other in R8C23, eliminating 8 and 9 from the other squares in N7.

If R8C23 = {59} then R89C1 must be {68} while if R8C23 = {68} then R89C1 may be either {59} or {79}. Either way 6 is eliminated from the other squares in N7.

Those seem to me to be all the easy initial steps. What else have I missed that has been done before the first "no more hints" spot? This has R9C1 = {689} but from the above I have {56789}. Why have 5 and 7 been eliminated from R9C1 or is that a typo?

Also why is R7C5 given as {56789} rather than {456789}? Aren't R7C5 and R8C45 all {456789} at this stage? I don't see that the 4 is eliminated until the message that starts after the "no more hints" spot.

R9C7 is given as {12345678}. Should it be {123456789} at this stage, the same as R9C456?

Thats why 1 and 3 can be eliminated from r1c1 and r9c89 - I think the technical name for this elimination move is "Killer pair".

OK I've worked that out now! The 21(5) in the same row as the 1 (of R19C2) must be {23457} while the 21(5) in the same row as the 3 must be {12459}, {12468} or {12567} so must contain {12}. Therefore you can go slightly further in the "no more hints" spot 2 and eliminate 1, 2 and 3 from R1C1 and R9C89.

I hope other forum members don't feel that I'm going into this at too basic a level but I'm just trying to establish the basis of the first "no more hints" spot.

Also once this puzzle has been completed, assuming that it can be done by human brainpower, I think it would be a good idea for sudokuEd to post the complete walkthrough including how the first "no more hints" spot was reached. That is another reason why I am going into so much detail.

Starting from the first "no more hints" spot, subject to my queries above, and applying the steps given in Monday's message including elimination of 9s from the diagonal I then got to the second "no more hints" spot with the following exceptions

R2C4 = {3456789} but I still have {123456789}
R6C3 = {23456789} but I still have {123456789}
R6C9 = {1368} but I still have {123468}
R7C89 = {1368} but I still have {135678}

Were there hints from Sumocue between "no more hints" spot 1 and "no more hints" spot 2?

I realise that sudokuEd set up this thread on the basis of using Sumocue. Am I the only person who is looking at this puzzle without having downloaded Sumocue which I have no plan to do?

I'm sure it would make this thread more meaningful to everyone if the hints from Sumocue and resulting steps were included in this thread.

I'll wait to read sudokuEd's reply to this message before posting anything else in this thread. If it is thought that I'm spoiling it for others because I'm not using Sumocue then I won't post any more on this puzzle and just try for myself to make progress after others post their messages and progress.

Posted: **Wed Aug 30, 2006 10:26 am**

I think it would have been helpful if you could have said which steps had been taken to reach the first "no more hints" spot.

Good idea. I've added SumoCue's hints to each post they belong to. No trouble at all to include those - in fact, a number of the hints do involve some interpretation and possibility of error.

I've been through everything again and I can't find any mistakes in the puzzles pics.

The clues added should answer all your questions Andrew. If they don't, ask again.

I realise that sudokuEd set up this thread on the basis of using Sumocue.

but then included the picture/text pic version - so that everyone has the opportunity to get involved!

Anyway - been too busy to do much solving the last 2 days - but think I've found the next move. Hopefully can post later.

Posted: **Wed Aug 30, 2006 2:27 pm**

The only thing I can find to make any progress is a short contradiction move. Has a whiff of T& E about it so not real happy – but...getting desperate!

Complex innies/outies on r1 -> sum of cages + 2 innies (r1c12) – 1 outie (r2c9) = 45
-> 2 innies – 1 outie = 2
min 1 outie = 5 -> min 2 innies = 7.
Since max r1c2 = 3 -> min r1c1 = 4 -> no 2 in r1c1

Also, when 1 in r1c2, only 6 or 8 can be in r1c1 ( not 7 since this is taken in the 21(5) cage in r1 which can only be {23457} when r1c2 = 1)

Also, when 1 in r1c2, r9c2 must = 3.
->r89c1 can only be [59] – not {68} because this would leave no 6 or 8 in r1c1.
-> the 6 & 8 can be eliminated from the 17(3) cage in N7

-> the only combinations in the 17(3) cage in N7 are [179/359] with both combinations having 9 only in r9c1 [edited]

->r9c1=9
-> r6c3 = 9

Plugging these moves into Sumocue, the following hints come up

After placing 9 in r9c9 and r6c3
22)Candidate 2 locked in cage 23(4) in N4
23)Candidate 6 locked in cage 14(2) in N7
24)Candidate 9 locked in c6
25)Obsolete candidate 1 in cage 18(3) in N12
26)Obsolete candidate 2 in cage 18(3) in N12
27)Obsolete candidate 6 in cage 23(4) in N4
28)All candidates 9 in row 8 locked in cage 21(3)
29)Unplacable candidates in cage 11(3) in N45
30)Unplacable candidates in cage 11(3) in c1
31)Unplacable candidates in cage 26(5) in N578
32)Unplacable candidates in cage 11(2) in N6
33)Unplacable candidates in cage 16(3) in N9 (extra – made r8c9 = {24} since r8c19=9)
34)Candidate 7 locked in N9
35)all candidates 3 in r8 locked in cage 14(4)
36)Eliminations in innie/outie difference in N689
37)All candidates 7 locked in N8 locked in cage 21(3)
38)Candidate 5 and 9 locked in cage 21(3) in N8
39)Naked subset of size 3 found in r8
40)Candidate 5 locked in N9
41)Unplaceable candidates in cage 21(5) in r9
No More Hints #3

And the NMH#3 marks pic is:

Code: Select all

.-----------------------.-----------------------------------------------------------.-----------------------.
|&#40;21&#41;                   |&#40;21&#41;                                                       |&#40;22&#41;                   |
| 45678       13        | 12345678    12345678    12345678    123456789   12345678  | 56789       5678      |
|           .-----------+-----------------------.-----------------------------------+-----------.           |
|           |&#40;22&#41;       |&#40;18&#41;                   |&#40;20&#41;                               |&#40;9&#41;        |           |
| 12345678  | 5678      | 345678      345678    | 12345678    123456789   12345678  | 123456    | 56789     |
|           |           '-----------.           |           .-----------------------&#58;           '-----------&#58;
|           |                       |           |           |&#40;14&#41;                   |                       |
| 12345678  | 9           5678      | 345678    | 12345678  | 12345678    12345678  | 123456      123456    |
|           &#58;-----------.-----------'-----------+-----------&#58;           .-----------'-----------.-----------&#58;
|           |&#40;23&#41;       |&#40;11&#41;                   |&#40;21&#41;       |           |&#40;32&#41;                   |&#40;11&#41;       |
| 1345678   | 24578     | 1345678     123467    | 123456789 | 12345678  | 12345678    12345678  | 23456789  |
&#58;-----------&#58;           |           .-----------&#58;           |           |           .-----------&#58;           |
|&#40;11&#41;       |           |           |&#40;26&#41;       |           |           |           |&#40;11&#41;       |           |
| 1345678   | 24578     | 1345678   | 2456789   | 12345678  | 12345678  | 12345678  | 3456789   | 23456789  |
|           |           '-----------&#58;           |           '-----------&#58;           |           &#58;-----------&#58;
|           |                       |           |                       |           |           |&#40;9&#41;        |
| 1345678   | 24578       9         | 12345678  | 12345678    12345678  | 12345678  | 2345678   | 1368      |
|           &#58;-----------------------'           &#58;-----------.-----------&#58;           '-----------&#58;           |
|           |                                   |&#40;21&#41;       |&#40;14&#41;       |                       |           |
| 12347     | 457         123457      1234      | 57        | 68        | 9           1368      | 1368      |
&#58;-----------+-----------------------.-----------'           |           '-----------------------+-----------&#58;
|&#40;17&#41;       |&#40;14&#41;                   |                       |                                   |&#40;16&#41;       |
| 57        | 68          68        | 579         579       | 1234        1234        1234      | 24        |
|           '-----------.-----------'-----------------------'-----------------------.-----------'           |
|                       |&#40;21&#41;                                                       |                       |
| 9           13        | 1234        123468      123468      123468      1245678   | 5678        5678      |
'-----------------------'-----------------------------------------------------------'-----------------------'

Posted: **Thu Aug 31, 2006 4:14 am**

I think it would have been helpful if you could have said which steps had been taken to reach the first "no more hints" spot.

Good idea. I've added SumoCue's hints to each post they belong to. No trouble at all to include those - in fact, a number of the hints do involve some interpretation and possibility of error.

Thanks for including SumoCue's hints. As you say they do involve some interpretation and possibility of error, especially the possibility that one might not eliminate all unplaceable candidates.

One thing I like about SumoCue's hints is that they make one look at rows, columns, nonets and cages that one might not think of considering at that stage, in particular they make one revisit them when it is not always obvious that one should look there again as the result of making changes elsewhere in the puzzle. I must learn to do that as a matter of habit. It's clearly a matter of practice and I'll hopefully improve with experience.

In the initial set of hints I must admit that I hadn't spotted the Killer Pair in hint 10 even though I had spelled out the relevant options in yesterday's message, admittedly with two of these options given in {} when they should have been given in [] because of hint 3. I've deliberately left this comment fair vague in case anyone isn't looking at the hints.

I suppose the reason why {5678} were not eliminated from R8C9 was because hint 3 was only applied at the time and not retrospectively later on when the number of candidates in R8C1 had been further reduced. However it appears that hint 5 had been retained and applied again after hint 6.

When Sumocue found the Killer pairs {1,3} in R1 and R9, one would think that it would also have found that 2 was locked in the adjacent 21(5) cages since it must have analysed these cages to find the Killer pairs {1,3}. The 2s in R1C1 and R9C89 have now been eliminated in NMH3.

I've been through everything again and I can't find any mistakes in the puzzles pics.

The clues added should answer all your questions Andrew. If they don't, ask again.

They did indeed answer all my questions and the puzzle pics were correct.

I would suggest that you move the hints for NMH2 to before the diagram; they are before the diagrams for NMH1 and NMH3.

Moving on to the next message.

That's a neat argument to prove that R9C1=9! Can I suggest that after the sentence … you insert “and when R9C2=1, then R89C1 = [59]” to make this logic more obvious.

I'm still struggling with some of the latest hints leading up to NMH3. I assume that hints 24, 34 and 40 mean that the number is locked in a particular row or column of a nonet; that is consistent with diagram NMH3.

In hint 31, I have eliminated 1 from one of the cells of the cage. Is that all at this stage or are there more unplaceable candidates in this cage?

At the moment I don't agree with hint 37 as I haven't yet eliminated {489} from this cage. Have I missed something?

I'm happy to receive replies to these queries about the hints before NMH3 on the forum or by Private Message. If I get a good reply by the latter method, I'll edit out the later part of this message once I understand all these hints.

Posted: **Thu Aug 31, 2006 4:47 am**

Starting from the NMH3 diagram.

As stated in one of my earlier messages and in sudokuEd's latest message, one of the 21(5) cages in R1 or R9 must be {23457}. This must be the one in R1 because the cage in R9 now only had {57} in one cell.
-> R1C2=1, R9C2=3
Eliminating {23457} from the other cells of R1 gives R1C1=R1C9={68}, R1C8=9, R2C9={57}, R2C6=9

{124} are locked in the 21(5) cage in N789 so the only two placeable candidates are {68} making this cage {12468}
-> R9C89={57}, R8C9=4, eliminate 4 from the other cells of N9, R8 and C9
-> R8C678={123}, R7C6=8, eliminate 8 from the other cells of N8, R7 and C6
-> R9C7=8, eliminate 8 from the other cells of C7
Because 8 has been eliminated from R7C9, eliminate 1 from R6C9
-> The 1 in the 32(6) cage in N69 is locked in N6 eliminating 1 from R7C8
The 2 in N9 is locked in R8C78 eliminating 2 from R8C6

I think that's as far as I can go at the moment. May I please ask sudokuEd to enter these changes into SumoCue, posting the next set of hints that result from these changes and the resulting diagram. I would guess that it will have a lot less candidates than in NMH3

Posted: **Thu Aug 31, 2006 11:34 am**

Well done Andrew - you got us to the end!

Here are the last batch of hints - nothing fancy among them - mostly naked and hidden singles.
42)Naked single 5 in r8c1
43)Hidden single digit 5 in N 8
44)Hidden single digit 8 in N9 - [edit note - redundant since Andrew had already pointed this out]
45)Hidden single digit 8 in N3
46)Naked single 6 in r1c1
47)Naked single 5 in r2c9
48)Naked single 6 in r8c2
49)Naked single 8 in r8c3
50)Naked single 7 in r9c9
51)Naked single 8 in r2c2
52)Naked single 5 in r3c3
53)Naked single 5 in r9c8
54)45 test forces a placement in an innie of c9
55)Hidden single digit 1 in N2
56)Candidate 2 locked in cage 9(3) in N3
57)Hidden single digit 2 in N9
58)Hidden single digit 1 in N9 & r8c6=3
59)r23c8 =[26]
60)r7c89=[36]. R6c9=3
61)Hidden single 6 in N2
62)45 test forces a placement in an innie of c89
63)Candidate 7 locked in cage 21(5) in c1
64)11(3) cage in c1 now {128} only
65)r456c2 now {257} only
the rest are basically naked and hidden singles.

However it appears that hint 5 had been retained and applied again after hint 6.

SumoCue seems to have some eccentricities and personality - keeps you from trusting it too much!

I would suggest that you move the hints for NMH2 to before the diagram; they are before the diagrams for NMH1 and NMH3.

For some reason the site would freeze up whenever I tried to post it above so I'd have to log out

Can I suggest that after the sentence … you insert “and when R9C2=1, then R89C1 = [59]” to make this logic more obvious.

Good suggestion.

I assume that hints 24, 34 and 40 mean that the number is locked in a particular row or column of a nonet;

That's it.

In hint 31, I have eliminated 1 from one of the cells of the cage. Is that all at this stage or are there more unplaceable candidates in this cage?

I think I also eliminated 3 from the same cell. I must admit a developing aversion to this type of combination nit-pickery - too easy to make a mistake. Absolute last ditch desperation move only.

At the moment I don't agree with hint 37 as I haven't yet eliminated {489} from this cage. Have I missed something?

Can't remember - it is worded funnily; but it made sense at the time. Perhaps the only 7's in N8 are in that cage so any combination for that cage must have 7?

Any-way - it's done. I enjoyed it. Will definately think of doing it again sometime.

Sure wish SumoCue had a Paste Marks capability though.

The puzzle resolved too quickly for my liking after the initial key moves. I like 'em to resist to the end. Perhaps I'll have to use smaller cages to get that.

Posted: **Sat Sep 02, 2006 12:11 am**

Here is the walk-through for this puzzle. It's the short-cut route - rather than just mirroring the way we actually went. SumoCue's hints about unplaceable candidates were not needed (

).

Just a quick reminder - this is a diagonals puzzle!
Step 1
22(3) cages [edited] in N1 and N3 must have 9
“45” on c1 -> two outies = 4 = {13}
->17(3) cage in N7 = {179/359/368} = {6/9, 8/9....}
14(2) cage in N7 = {59/68} = {6/9, 8/9} -> Killer pair on both 6 and 9, 8 and 9 with 17(3) cage
-> no 6, 8 or 9 elsewhere in N7.
“45” on N689 -> the difference between the one innie and one outie = 0 ->r7c4 = r9c3
-> r7c4 cannot have 6, 8 or 9 since these have been eliminated from r9c3.
“45” on N7 -> 4 innies = 14 = {1247}{2345} = 24{17/35}
ie, 2 & 4 are locked in these 4 cells.
-> 2 & 4 must also be in r7c1234 because r7c4 = r9c3! (If 2 or 4 are in r9c3, they must also be in r7c4)
->2 and 4 cannot be elsewhere in r7
“45” on r89 -> two outies = 13 -> r7c56 = {58/67}
-> 9 in r7 locked in r7c78 -> no 9 elsewhere in N9 or 32(6) cage in N89
but 9 cannot go in r7c8 because this would mean no 9's in N6 since 9 in N3 would have to be in c9
->r7c7=9 and r3c2 = 9

Step 2
A short contradiction move is required at this point. Feels a little like T&E – but can't see any other way to make any real progress....caught between a rock and a hard place (couldn't resist the pun!)

Complex innies/outies on r1 -> sum of cages + 2 innies (r1c12) – 1 outie (r2c9) = 45
-> 2 innies – 1 outie = 2
min 1 outie = 5 -> min 2 innies = 7
Since max r1c2 = 3 -> min r1c1 = 4
We already know that r19c2 = {13}
Now, when r1c2 = 1
-r1c1 can only be 6 or 8 ( not 4,5 or 7 since these are taken in the 21(5) cage in r1 which can only be {23457} when r1c2 = 1)
-3 must be in r9c2
-r89c1 can now only be {59} – not {68} because this would leave no 6 or 8 in r1c1 which would be a bit of a problem!
-> 6 & 8 can be eliminated from the 17(3) cage in N7
-> the 17(3) cage is only {179/359} = 9{17/35} with 9 only in r89c1.
“45” on r 9 -> two outies = 9 -> no 9 in r8c19
->r9c1=9, r6c3 = 9 (9 cannot go in 11(3) cage in N45 ->hidden single N4), 14(2) cage in N7 = {68}, r8c1 = {57}

Step 3
“45” on N6 -> 2 outies = 9 -> r7c89 = hidden 9(2) cage = {18/63} = {6/8...}
“45” on r9 -> 2 outies = 9 -> r8c9 = {24} -> r9c89 = {57/68}, but {68} conflicts with hidden 9(2) cage in N9
-> r9c89 = {57} ->r8c19 = [54], r19c2 = [13]
r8c45 now {79} -> r7c56 = [58], r9c7 = 8 (h single N9)
r7c89 = {36} -> r8c78 = {12} -> r8c6 = 3
r67c9 = {36} -> r45c9 = {29}, r3c9 = 1 (h single c9)

Step 4
In r1, the 21 (5) cage is now {23457} only
->r1c189 = [698], r2c9 = 5, r9c89 = [57], r8c23 = [68], r2c2 = 8, r3c3=5, r23c8 = [26], r8c78 = [21], r7c89 = [36], r6c9 = 3, r56c8 = {47}, r4c8 = 8

Step 5
“45” on c2 -> r7c2 = 4
r456c2 = {257}
r234c1 = {347} -> r7c1 = 2 (hidden single c1)
Naked triple on {234} on \diagonal in N5
the rest is basically naked and hidden singles with a few cage combination singles thrown in.
Thanks Andrew for your helpful suggestions to make some points clearer.

Posted: **Sun Sep 03, 2006 4:06 am**

Hope people don't mind if I tidy up on some of my earlier comments.

As I said in an earlier message I was taking part in this without using SumoCue. I've now learned, from off-group discussions with sudokuEd, that one has to completely solve each hint before going on to the next one. Obviously that makes sense but since I wasn't using SumoCue there were a few hints that just seemed to be statements of things already done so I just moved on instead of looking for an alternative meaning about what the hint really meant.

In hint 31, I have eliminated 1 from one of the cells of the cage. Is that all at this stage or are there more unplaceable candidates in this cage?

I think I also eliminated 3 from the same cell. I must admit a developing aversion to this type of combination nit-pickery - too easy to make a mistake. Absolute last ditch desperation move only.

Yes, it was necessary to eliminate the 3 from the same cell but not from the other cells in that cage. I agree with you about this type of combination elimination of candidates.

At the moment I don't agree with hint 37 as I haven't yet eliminated {489} from this cage. Have I missed something?

Can't remember - it is worded funnily; but it made sense at the time. Perhaps the only 7's in N8 are in that cage so any combination for that cage must have 7?

It was actually hint 35 that was critical. This was another misleading hint that seemed to be stating something that had already been done. However when I looked at it in more detail I found that it actually eliminated 7 from R7C6 because it is not possible to have R8C678 = {124} as that would be inconsistent with the {24} in R7C9 which is in a different cage not mentioned by the hint. This is neat and at the same time sneaky! The hint should have been expressed better. After eventually working out what hint 35 meant then hint 37 was fine as 7s had been eliminated from the other squares in the nonet as suggested by sudokuEd in his answer.

Apologies for a typo in my previous message. R9C2 should have been 3. I've edited that now.

An interesting final thought from sudokeEd. Smaller cages might have made the puzzle last longer. However it might also have made an easier puzzle to solve. I certainly find that puzzles with large cages are harder to solve.

Posted: **Mon Sep 04, 2006 1:18 pm**

The final walk-through has been edited to fix up some typo's and make some points clearer. Thanks Andrew for the suggestions.

The new (solver) version of SumoCue looks great Ruud and ND. It is picking up the complex innie-outie opportunities. It is revisiting all parts of the puzzle as necessary. It is picking up the sub-sets - including on the diagonals (that I miss nearly everytime).

The result for this puzzle was that the solver needed 1 less No More Hints spot to get to the end. Very nice indeed.

Still doesn't appear to paste copies of marks though

SudoCue Users

Ruudiculous tag Killer - Uluru

Ruudiculous tag Killer - Uluru