Assassin 60 - the rejected pattern

[Ruud]

Here is a cage pattern that I tried over and over again, but failed to create a suitable Assassin.

The only puzzle I could come up with was this 24-carat piece.



3x3::k230433304869:4869:5639:56395642:564238524869:4869:5639:5138:5642:4372:437233425145:5639:5138437238702848:5145:5145:5138310033682848:5931:51454142:41423368:4402:4402:5931:59313629:41423632:44023644:5931:64634161:4161:6979:69794678:4678:6463:6463:6463:4161:4161:6979:6979:4678:4678:

Good luck. You'll need it.
Ruud

[rcbroughton]

This is a real tough nut.

20 steps, no placements and nothing obvious from here.

Any suggestions gratefully received . . .


0a Cage 9(3) n1 no 7/8/9
0b. Cage 20(3) n14 = {389}/{479}/{569}/{578} - no 1/2
0c. Cage 11(3) n56 - no 9
0d. Cage 14(4) n47 = {1238}/{1247}/{1256}/{1346}/{2345} - no 9

1. Cage 22(3) n1 = 9{58}/9{67} - 9 locked for n1

2. Cage 27(4) n89 = 9{378}/9{468}/9{567} 9 locked
2a. no 9 in r9c45

3. 45 Rule on n9 - innies r7c9 r9c7 total 13 - no 1/2/3

4. 45 Rule on r12345 - innies r5c8 minus outies r6c5 equals 4
4a. no 1/2/3/4 r5c8
4b. no 6/7/8/9 r6c5

5. 45 Rule on r89 - innies r8c27 total 4 = {13} - locked for r8

6. combo {248}/{257} not valid in 14(3) n9
6a 1/3 cannot be in r7c78

7. combos {1359}/{1368} blocked in 18(4) n9 by r8c8=1/3

8. 45 Rule on c89 - innies r27c8 total 7 - no 7/8/9
8a. no 4/6 at r2c8 because no 1 in r7c8

9. 45 Rule on c6789 - outies r8c5 minus innies r5c6 equals 4
9a. no 6/7/8/9 r5c6
9b. no 4 at r8c5

10. 45 Rule on c1-5 - innies r568c5 total 17
10a. r56c5 must total 8=[71]/[62], 9=[63]/[72], 10=[91]/[82]/[64], 11=[83]/[74], 12=[93]/[84]
10b. no 1/2/3/4 at r5c5
10c. no 5 at r6c5

11. 45 Rule on r6-9 - outies r5c568 total 17
11a. r5c56 must total 9=[63]/[72]/[81], 10=[91]/[82]/[64] ,11=[92]/[83]/[74] , 12=[93]/[84]
11b.no 5 r5c6
11c. no 9 r5c8
11d cleanup no {157}/{256} in 13(3) n5

12. 45 Rule on n5689 - outies r3c8 r8c3 total 8 - no 8/9
12a. no 5/7 at r3c8

13. 14(3) n9 - {239} - 9 must be at r7c7, {149} 9 must be at r7c7, {347} 7 must be at r7c7
13a. no 2/4 r7c7

14. revisit step 9 - no 9 at r8c5

15. 45 Rule on r123 - innies r3c1348 total 22
15a. {1489} - 9 only at r3c4
15b. {1579}- 9 only at r3c4
15c. {1678} - 1 ar r3c4 -> {78} at r3c13, but this is blocked by 22(3) n1
15d. {2389}- 9 only at r3c4
15e. {2479}- 9 only at r3c4
15f. {2569}- 9 only at r3c4
15g. {2578} - no placement with 2 at r3c4
15h. {3469}- 9 only at r3c4
15i. {3478}, {3568}, {4567} - no 1,2
15j no 1,2 at r3c4

16. Further analysis of 15.
16a. {3478} - 4 at r3c4 -> {78} at r1c13 but this is blocked by 22(3)n1
16b. {4567} - 4 at r3c4 -> {57} at r1c13, but this is blocked by 22(3)n1
16c. no 4 at r3c4

17. 45 Rule on n23 - innies r3c48 minus outies r1c3 equals 8
17a. no 8 r1c3

18. 45 Rule on n1 - innies r13c3+r3c1 total 14 = h14(3)={158}/{167}/{248}/{347}
18a. {149}/{239} - not possible - no 9
18b. {257} - blocked by 9(3)n1
18c. {356} - blocked by 9(3)n1

19. 45 Rule on c123 - innies r1348c3 total 17
19a. {1268} - 6 at r1c3 -> r34c3={18} - not possible because of 17(3)n124
19b. {1367} - 6 at r1c3 -> r34c3={13} - not possible because of 17(3)n124
19c. {2456} - 6 at r1c3 -> r3c3=2/4/5 - not possible because of h14(3) from step 18
19d. No 6 r1c3

20. 45 Rule on n5 - innies r4 c6+r6c46 total 17 = h17(3)

21. 45 Rule on n5 - innies r6c46 minus outies r45c7 equals 6
21a. outies total 3,5,6-10, so innies total 9,11,12 to 16 ({13} in outies blocked by r8c7)
21b. innies total 9={53} - {18} blocked because r4c6 would be 8
21c. innies total 11,12 to 16 - no 1
21d. no 1 at r6c46

Code: Select all

.-------------------------------.-------------------------------.-------------------------------.
| 123456    123456    123457    | 123456789 123456789 123456789 | 123456789 123456789 123456789 |
| 123456    56789     56789     | 123456789 123456789 123456789 | 123456789 1235      123456789 |
| 345678    56789     12345678  | 356789    123456789 123456789 | 123456789 12346     123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 3456789   123456789 123456789 | 123456789 123456789 12345678  | 12345678  123456789 123456789 |
| 3456789   123456789 123456789 | 123456789 6789      1234      | 12345678  5678      123456789 |
| 12345678  123456789 123456789 | 23456789  1234      23456789  | 123456789 123456789 123456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 12345678  12345678  123456789 | 123456789 123456789 123456789 | 56789     2456      456789    |
| 2456789   13        24567     | 2456789   5678      456789    | 13        2456789   2456789   |
| 123456789 123456789 123456789 | 12345678  12345678  3456789   | 456789    123456789 123456789 |
'-------------------------------.-------------------------------.-------------------------------'

Rgds
Richard

[mhparker]

This is a real tough nut.
...
Any suggestions gratefully received . . .

I agree. My only real suggestions are that we document the misery, be thankful for every candidate we've managed to pick off, pack our bags and go home**!


**OK, let's not be pedantic, maybe we already are at home! Just meant it in the idiomatic sense of course...

I can only offer a few mere morsels (4 candidates in 5 moves, to be precise). A drop in the ocean, as it were:

22. Complex hidden pair on {13} in n9:
22a. Only other place for {13} in n9 apart from r8c7 is 18(4) n9
22b. -> 18(4) n9 = {(1/3)..}
22c. -> {2457} combo blocked

23. r45c2 cannot contain both of {13} due to r8c2
23a. -> no 8 in r5c3

24. r45c7 cannot contain both of {13} due to r8c7
24a. -> no 7 in r4c6

25. Outies r1: r2c1789+r3c9 = 18(5)
25a. min. r2c1789 = 10
25b. -> max. r3c9 = 8
25c. -> no 9 in r3c9

26. I/O difference r1: r1c89 - r2c178 = 4
26a. -> no 9 in r2c7 (otherwise min. r2c178 = 12 -> 16 needed in r1c89 - impossible, because 9 in n9 already taken in r2c7)

[mhparker]

Another small step for mankind...

27. From step 18, only combo with a 3 for n1 innies h14(3)n1 = {347}
27a. -> If r3c1 = 3, then (from step 15) r123 innies (r3c1348 = 22(4)) must be [3496] or [3784]
27b. However, [3496] is blocked by 17(3) at r3c3 ({449} not possible)
27c. and [3784] requires 4 in r8c3 (step 12) -> clash w/ 4 in r1c3
27d. Summary: no 3 in r3c1

[CathyW]

If it's any consolation, JSudoku can't solve it!

[Para]

I don't know if this puzzle is going to be any fun to solve. Sometimes uniqueness might not be the only good constraint for a puzzle.

This puzzle for example is also unique(even without the diagonal constraint). It was the result of an attempt to create a proper 5-cage diagonal Killer-X puzzle(based on Ruud's Killer-X special No4). But i don't think there is any proper way of solving this puzzle.



PS:

3x3:d:k:2560384251243589:46153593358551244615513735933585:5124:4615513736023593512451373866:5156:5156:5156:51565161:5161:5161:5161:5165:516511540:51693379:4404:4404:516511540516911540440426243906:51693643337928733906:516928842630:

Haven't seen a solver that can do anything but place a 5 in the middle. It just shows that puzzles can be too hard.

I'll have a look at the Ass 60 RP next week. But just feel it will be too hard a battle to enjoy.

greetings

Para

[sudokuEd]

If it's any consolation, JSudoku can't solve it!

True - but only after 200 Ctrl D before DNF (had the pic hidden of course). Which means it's an absolute grinder. Not worth the effort.

Here's just a couple more for the record before the (emoticon here with white flag).

28. no 6 r3c1. Here's how.
28a. 6 in r3c1 -> from h14(3)n1 r13c3 = {17}.
28b. -> h17(4)r1348c3, r48c3 = 9 = [36]/{45}
28c. -> only 7 can go in r3c3 since 1 in 17(3) can only have {79}
28d. only combination in 17(3) with {345} is {467} -> 4 in r4c3 and 6 in r3c4
28e. but this means 2 6's in r3
28f. -> r3c1 !=6

29. no 4 in r4c3. Here's how.
29a. "45" n47: r3c1 + 3 = r48c3.
i. r3c1 = 4 -> r48c3 = 7 -> no 4 possible in r4c3 (no 3 r8c3)
ii. r3c1 = 5 -> r48c3 = 8 -> no 4 possible in r4c3
iii. r3c1 = 7 -> r48c3 = 10 = [46] only. But from h14(3)n1, 7 in r3c1 -> r13c3 = {16/34} only which both clash with r48c3
iv. r3c1 = 8 -> r48c3 = 11 = [47]. But when r3c1 = 8 -> r13c3 = 6 = [15] (cannot be [51] because of 17(3)) -> r34c3 = [54] = 9 -> r3c4 = 8. But this means 2 8's in r3
29b. -> no 4 in r4c3

Deflated
Ed

[mhparker]

deleted

[mhparker]

BTW, anyone (apart from me) on this forum old enough to remember postal chess, long before the Internet and e-mail was ever invented?

Never played it myself, but an uncle of mine did. It was a painfully slow process, involving sending the next move to one's opponent via mail and waiting for his or her response (again via mail). That way, a simple game of chess used to drag on for months!

Get the analogy?

At this rate, we should be finished by Christmas (if we have a clear run!). Perhaps it would be a good idea to ask for that white flag as a Christmas present...

[Andrew]

Yes. I used to play postal chess, as well as over the board chess, when I was a postgraduate student in London. Later, when I moved to Edinburgh, I took it up again and played once in the Scottish Postal Chess Championship having qualified through the previous year's Candidates tournament. I also played for Scotland against England and Wales and had an unbeaten record in those matches. It was interesting playing for Scotland against England because I'm English although I prefer to think of myself as British first and English second.

I'll admit this message is totally OT. I was just replying to Mike's question. Edited so I could use an emoticon that I hadn't seen before.

[Ruud]

When Michael Mepham posted his first series of unsolvables, they could not be solved with the existing techniques. Now the first and second series of "unsolvables" no longer deserve this epithet. The Sudoku community has learned a lot since then.

A60RP may be unsolvable at this moment, but a lot of progress has been made in the Killer community, so I expect this puzzle to fall at the hands of a skilled player at some time in the future.

There is no value in trying to solve A60RP with guesses. It will still be there when new solving strategies have emerged.

If you cannot wait, there is a new emoticon which you can use:

Ruud

[Glyn]

The eliminations I took a long time to find were in fact erroneous, thanks for pointing that out Mike, applied one of your eliminations twice once with transposed row and column so my starting board was up the creek.



Hope we don't throw in the towel yet as hopefully it is not intractable. Anyone who would like 'good' news about some critical placements can have a look at the following (no values are given though), but I haven't found anything to force any of them yet. This is where we need one of Ruuds undiscovered neat moves.

Any correct placement within the 4 innies of r123 allows JSudoku to proceed to a solution.

Perhaps we need to collect all these unsolvables together, as we have a much smaller sample set of Killers to work with than vanilla Sudokus.

Best of luck

Glyn

[mhparker]

Hi Glyn,

Nice to hear from you again! That itself is another "positive" to be salvaged from this thread!

I admire your perserverence on this one. But let's face it, the situation looks pretty bleak.

30. If r3c3=7 innies n1 require Sum(r1c3+r3c1)=7 only combo is [25] blocked as cage 22(3) must contain 5|7.
Conclusion r3c3<>7.

Are you sure? What about [34]?

This is where we need one of Ruuds undiscovered neat moves.

Agreed.

Let me provide another analogy. In my spare time, I do quite a lot of cycling. Like most keen cyclists, I have a watch with a heart rate monitor, capable of recording one's maximum pulse. The problem is, just how does one measure that (without risking collapsing with a heart attack afterwards!)? Now, if you ask most people how to do it, they will maybe suggest finding a good steep hill and battling up it. However, this is the wrong answer. The correct answer (surprisingly enough) is to take a flat(-ish) piece of road and do a prolonged sprint.

Get the analogy again? Make a parcours too difficult, and what happens is that instead of the contestants' performance increasing as expected, they just end up pacing themselves and losing form. This is clearly visible on this forum. Up to a point, the moves we make get more and more ingenious as the difficulty of the puzzle increases. But go beyond that threshold, and the quality of the moves tends to rapidly decrease again.

IMO (and I'm saying this with my puzzle setter hat on), the best puzzles are the ones that hit the above-mentioned threshold, without exceeding it. In other words, the ones that stretch the solvers, yet without over-strectching them.

We should not IMO fall into the trap of thinking we can and should solve every puzzle. Even if we could do the A60RP, it's not the end of the road, by any means. There are other - bigger - hills to climb beyond. Puzzles that are even more intractable than this one. For example, the A60RP looks like child's play in comparison to this one, which I came across when looking for a suitable A61X. The image shown represents the final grid state (as reached by JSudoku before it waved the metaphorical white flag):




3x3:d:k:4096:4096:4354:43545125:5125:5127:5127:4096:5130:4354:43545125:51255127:6674:5130:5130:462946313088:4378:6674:6674:4629:4629:4631:4631:4631:4378:4378:4644:6674:667431117722:7722:4378:4644:4644:5423:5423:54233378:7722:7722:46442872:542333783901:7722338341624164390126234162:41624164:4164:3901


In total, the latest and greatest JSudoku managed to eliminate a grand total of 76 candidates here (in comparison to the 130 it managed with the A60RP). This means that an average of less than 1 candidate per cell could be eliminated! Note that there are no bivalue cells, and no cages with fixed combinations. So, in view of all this, it's hardly surprising that JSudoku couldn't find a single chain either!

And yet, despite the veritable forest of candidates remaining, this puzzle has a unique solution and, as such, is a valid Killer. So, it goes almost without saying that there's plenty of room for Ruud to tighten the thumbscrew even further in the future...

[Glyn]

I thought I would post the list of remaining candidates especially having made a cock up of my moves 30-34, especially if this one is getting put on hold pending a miracle.


Amended to include all earlier eliminations

Code: Select all

+-------------------------------+-------------------------------+-------------------------------+
|   123456    123456    123457  | 123456789 123456789 123456789 | 123456789 123456789 123456789 |
|   123456    56789     56789   | 123456789 123456789 123456789 |  12345678   1235    123456789 |
|    4578     56789    12345678 |   356789  123456789 123456789 | 123456789   12346    12345678 |
+-------------------------------+-------------------------------+-------------------------------+
|  3456789  123456789  12356789 | 123456789 123456789  1234568  |  12345678 123456789 123456789 |
|  3456789  123456789  12345679 | 123456789    6789      1234   |  12345678    5678   123456789 |
|  12345678 123456789 123456789 |  23456789    1234    23456789 | 123456789 123456789 123456789 |
+-------------------------------+-------------------------------+-------------------------------+
|  12345678  12345678 123456789 | 123456789 123456789 123456789 |   56789      2456     456789  |
|  2456789      13      24567   |  2456789     5678     456789  |     13     2456789   2456789  |
| 123456789 123456789 123456789 |  12345678  12345678  3456789  |   456789  123456789 123456789 |
+-------------------------------+-------------------------------+-------------------------------+

Having rechecked my moves none of the 4 candidates taken out would have gone if the starting grid had been correct. Thanks Mike for checking it.

The technique I used was to try every value of r3c1 and follow the logical conclusions of the following constraints to the bitter end.
Innies r123=22, innies c123=17, outties n5678=8, considering only the conflicts in r3, c3, n1, and 17(3) cage of n124 which was common to all.

There are 14 arrangements of the innies that work.

In the erroneous calculation 3 of these arrangements vanished and the remaining 11 sets had 4 candidates that were no longer required.
I started with each of those 4 'superflous' candidates as a given and found shorter chains to eliminate them more succintly.

[rcbroughton]

Note that there are some additional eliminations over and above Glyn's pic that were done in the first post. I'll redo marks pic when I've got a mo.

In the meantime here are a couple of moves we should have seen . . .

Step 30 No 1 in r9c123 as it eliminates all placement in 16(4) n78
30a. 1 in r9c123 -> no 1 in 16(4)n78 = {2347}/{2356}
30b. 1 in r9c123 -> r8c2=3 -> r8c7=1 -> 3 locked in r9c89 for r9 -> no 3 in 16(4)n78

31. No 3 in r9c123 as it eliminates all placement in 16(4) n78
31a. 3 in r9c123 -> no 3 in 16(4)n78
31b. 3 in r9c123 -> r8c2=1 -> r8c7=3 -> 1 locked in r9c89 for r9 -> no 1 in 16(4)n78

32. 25(4)n7={2689}/{4579}/{4678}

[Edit - thanks for the corrections Glyn]

Code: Select all

.-------------------------------.-------------------------------.-------------------------------. 
| 123456    123456    123457    | 123456789 123456789 123456789 | 123456789 123456789 123456789 | 
| 123456    56789     56789     | 123456789 123456789 123456789 | 12345678  1235      123456789 | 
| 4578      56789     12345678  | 356789    123456789 123456789 | 123456789 12346     12345678  | 
:-------------------------------+-------------------------------+-------------------------------: 
| 3456789   123456789 12356789  | 123456789 123456789 1234568   | 12345678  123456789 123456789 | 
| 3456789   123456789 12345679  | 123456789 6789      1234      | 12345678  5678      123456789 | 
| 12345678  123456789 123456789 | 23456789  1234      23456789  | 123456789 123456789 123456789 | 
:-------------------------------+-------------------------------+-------------------------------: 
| 12345678  12345678  123456789 | 123456789 123456789 123456789 | 56789     2456      456789    | 
| 2456789   13        24567     | 2456789   5678      456789    | 13        2456789   2456789   | 
| 2456789   2456789   2456789   | 12345678  12345678  3456789   | 456789    123456789 123456789 | 
'-------------------------------.-------------------------------.-------------------------------'