Killer-X

[Para]

Hi all

This is a Killer-X i created this weekend. So digits 1-9 repeat on the diagonals as well.
I think it worked out nicely. Hope you like it.
Could you guys tell me what you think of it?

PS:
3x3:d:k:486420496404:5381:5381:53814864:48642571:640418063848:4626:4626:4626:4373:6404:463130964635:4373:4373:4373:6404:4631:4631:4631:4899:4635:4635:7462:7462:7462:7462:7462:4899:4899:4635:6702:6702:670236343634:4899363867023634:4924:4924:4924:4159:4159339328842886415936573889:4173:4173:4173:2886:



greetings

Para

[rcbroughton]

Hi all
This is a Killer-X i created this weekend. So digits 1-9 repeat on the diagonals as well.
I think it worked out nicely. Hope you like it.
Could you guys tell me what you think of it?

Nice!!

I haven't seen a good Killer X for a while and this one was fun.

Thought I had it a couple of times when a quick series of moves fell into place but it kept it's secrets!! (And a nice piece of deception to give us the centre number "for free" to lull us into a false sense of security!)

It took another 50+ moves for me to get the next number, but it fell quickly after that.

I'll post a walkthrough when I tidy it up. It has one very unusual move in it where I do a 45 rule on N16 - first time I've found a puzzle where I've resorted to disjoint nonets for the 45-rule.

A good puzzle Para!

Rgds
Richard

[Para]

Thanks.

Glad you enjoyed it. If i make another nice one, i'll try and post it again.

greetings

Para

[rcbroughton]

Ok, this is my solution path,

after revisiting, realised I didn't need the n16 test


Preliminaries:
0. Cage 19(3) at r1c1={289} {379} {469} {478} {568} - no 1
0a. Cage 8(3) at r1c2={125} {134} - no 6789
0b. Cage 21(3) at r1c6={489} {579} {678} - no 123
0c. Cage 10(2) at r2c3={19} {28} {37} {46} - no 5
0d. Cage 7(2) at r2c6={16} {25} {34} - no 789
0e. Cage 26(4) at r6c2={2789} {3689} {4589} {4679} {5678} - no 1
0f. Cage 14(4) at r6c6={1238} {1247} {1256} {1346} {2345} - no 9
0g. Cage 19(3) at r7c7={289} {379} {469} {478} {568} - no 1
0h. Cage 13(2) at r8c3={49} {58} {67} - no 123
0i. Cage 11(2) at r8c6={29} {38} {47} {56} - no 1
0j. Cage 11(3) at r8c8={128} {137} {146} {236} {245} - no 9

First the easy one ...
1. 45 rule on column 5 found single cell at r5c5 value 5
1a. 29(5)n456=5{1689}/{2679}/{3489}/{3678}

2. 18(3)n1 - no {189} as it breaks the 19(3)n1 - no 1 in 18(3)n1

3. 45 on n1 - r2c3 equals r1c4
3a. max r2c3 is 4
3b. 10(2)n12=[19] [28] [37 [46]
3c max r1c4 is 4

4. 45 on N3 r12c6 equal 10 = {46} {37} {28} {19} - no 5 (call this h10(2)r12c6)
4a.7(2)n23 no 2 in r2c7

5. 5 locked in row 3 of n2

6. 45 rule on n7. r8c3 = r9c4 + 1
6a.min val in r9c4 is 3
6b Max val in r9c4 is 8

7. 45 rule on N7. r89c4 total 12 = {48]/{57}/{39} - no 6 (call this h12(2)r89c4)
7a.13(2)n78 - no 7 at r8c3

8. 45 rule on N9. r8c7 = r9c6 -1
8a Min r9c6 is 3
8b Max r8c7 is 8
8c. 11(2)n78 no 2 at r8c6

9. 45 rule on N9. r89c6 total 12={39} {48} {57} - no 6 (call this h12(2)r89c6)
9a. 11(2)n78 no 5 at r8c7

10. 45 rule on r12. r12c5=10, r34c5=15(2)={69}/{78}

11. 45 rule on r34. r4c19 equal 10 - no 5 (call this h10(2)r4c19)

12. 45 rule on r89. r67c5=6={24} locked for c5, r89c5=9={18}/{36}

13. 2 locked in row 7 of N8

14. 45 rule on r67. r6c19 equal 11 - no 1

15. 45 rule on c1234. r5c34=7={16}/{25}/{34}, r5c67=17={89} - locked for r5

16. Must use 1 in 8(3) n12 - no 1 at r1c59

17. r12c5=10={37}/[91] - no 8 at r2c5

18. 1 locked for row 6 in cage 14(4)n568 - no 1 at r7c6, must use 1 in 14(4)

19. 1 locked in c5 of N8 in 15(4)n58 - {2346} not allowed - no {36} at r89c5

20. Only combination {3679} allowed in cage 25(4)n25 - no 8

21. 6 locked in row 7 of N8

22 19(3)n9={379} as {478} blocked by 14(3)n7
22a. {379} locked for r7 and n9

23. 14(3)n7={158} locked for r7, n7
23a. 16(3)n7={349}/{367} - no 2
23b. 13(2)n78 no 5 at r8c4

24. Naked pair {18} at r89c5
24a. 13(2)n78 no 5 at r8c3
24b 16(3) n89 no 4,5 at r9c6
24c. 11(2)n89 no 4 at r8c6
24d. 26(4) n458 only combo with 2 is {2789} - 2 must be in r7c4 - no 2 elsewhere in 26(4)

25. 2 locked in r9c23 in n7 locked for r9 and 14(3)n78
25a. 14(3)n78={27}5 or {29}3

26 16(3)n89 - [358] blocked by 14(3)n78 - no 3 at r9c6

27. hidden pair {35} at r8c6 r9c4 for n8
27a. 11(2)n89=[38]/[56]

28. hidden pair {79} at r8c4 r9c6 for n8
28a. 13(2)n78=[49]/[67]

29. naked triple {279} at r9c236 for r9

30 3 locked in n2 for c5
30a. 7(2)n23 - no 4 at r2c7

31. (from step 3) no 3 at r2c3 -> no 7 at r2c4

32. 45 on n3. r1c6-r2c7=3. No 7 at r1c6

33. 16(3)n89 can't be {178} bacause r9c5=1/8 - no combo with 8 in 16(3)n89

34. (from 10) r12c5={37} locked for n2, r34c5={69}

35. h10(2)r12c4 and h10(2)r12c6 - must be [19],[28],[46] and [82],[91],{64}
35a. but can't have 19 and 64 because of r3c5 - so one or other must be {28} - no 2,8 elsehwere in n2

36. 19(3)n1.
36a. Cant have {478} because need 4 or 7 in 18(3)n1 - only other option with 8 is {568} and 5 must be in r2c1 - no 8 at r2c1
36b. Can't have {289} because need 7 or 8 in 18(3)n1 - no 2 in 19(3)

37. 11(3)n9, only options remaining are {128}/{245} - no 6
37a. {245} can only be [254] - no 4 at r8c89

38. 4 now locked in r9 or n9

39. 45 on n2. r3c456 total 15={1[9]5} or {4[6]5} - no 6,9 at r3c46

40. 45 on r1 - r1c159 total 16={367}/{349} - no 2, 8
40a. must use 3, so no 3 in 8(3)n12
40b. 18(3)n12={125} locked for r1

41. 5 locked in row2 or n3
41a. (from 36a) 19(3)n1={379}/{469} - no 8

42. 8 locked in r3 of n1 in 18(3)
42a. 18(3)n1 - no 2, 9

43. hidden triple {125} at r1c23 r2c3 in n1
43a. 10(2)n12 = [19]/[28]

44. 2 locked in n3 for r3

45. 15(3)n3={348}/{357}/{456}/{168}/{159}
45a. {159} must have 9 at r1c9 - no other place for 9
45b. {456} must have 5 at r2c9, {168} must have {18} r2c89 - no 6 at r2c9
45c. {357} must have 5 at r2c9 - no 7 at r2c9

46. 2 locked in n4 for c1

47. 45 on c1234 - r12c4=10=[19]/[28], r89c4=12=[75]/[93] so r34567c4=23
47a. only options are {13469}/{14567}/{23468}
47b. {23468} - must have 4 at r3c4 - 8 cannot be at r4c4 because can't have {48xx} in 17(4)n254

48. 45 on r2, r2c12589=28 - can't have {12},{18},{29} or {89} because of 10(2)n12
48a. can only have {34579}, {15679} or {34678}
48b. {15679} must have [15] at r2c89 - no 1 at r2c9
48c. {34678} must have {38) at r2c89
48d. {34579} must have [?5] at r2c89 - no 6 at r2c8, no 4 at r2c9

49. 45 n6 r34567c6 equal 23 - r89c6=12(2) blocks any combo with {59} or {37}
49a. can have {12389}, {12578}, {13469} or {23568} - only option with 4 is {13469}
49b. {13469} forces r12c6=10(2)=[82] which forces r12c4=10(2)][19], so 4 must be at r3c6. no 4 at r467c6

50. 4 now locked in n2 for c6

51. revisit step 47, {23468} can't now be placed. so no 2,8 in r34567c4

52. hidden single 2 at r1c4
52a. r12c4=10(2)=[28]
52b. 10(2)n12=[28]

53. 14(3)n78=[275]/[293]

54. 15(3)n3=[357]/[456]/[159]

55. 11(3)n9={128} - no 4

56. hidden singl 5 at r8c6 for r8
56a. 11(2)n89][56]

Rest is singles and simple cage combos . . .

[sudokuEd]

It's a real goodun Para. Have finally been able to get to this spot. To my surprise, the marks pasted into SudoCue (with File-Variant-Diagonals selected) give a unique solution - with a real nice hard rating too.

Any X-tremists want to give me a hand? emm? Let's try it as a vanilla X from here . [edit: if the marks pic looks weird: paste into notepad then paste from there into SudoCue]

Code: Select all

.------------------------------.------------------------------.------------------------------.
| 34679     125       125      | 12        37        4689     | 46789     46789     34679    |
| 34679     34679     12       | 89        37        1246     | 1356      1346789   458      |
| 34678     34678     34678    | 145       69        145      | 1234679   1234679   1234679  |
:------------------------------+------------------------------+------------------------------:
| 12346789  13456789  13456789 | 12346789  69        12346789 | 123456789 123456789 12346789 |
| 123467    13467     1346     | 1346      5         89       | 89        123467    123467   |
| 23456789  3456789   3456789  | 2346789   24        1234678  | 12345678  12345678  23456789 |
:------------------------------+------------------------------+------------------------------:
| 158       158       18       | 246       24        246      | 379       379       379      |
| 3479      3479      46       | 79        18        35       | 68        128       1258     |
| 36        279       279      | 35        18        79       | 1456      1456      48       |
'------------------------------'------------------------------'------------------------------'

[rcbroughton]

Ok Ed,

I like a challenge.

Here's half a dozen moves to get you going. Have the feeling this is going to be a toughone.

1. Either r8c3 or r9c9 is 4 - so no 4 at r3c3
1a r8c3=4/6
1b. r8c3<>4 -> r8c3=6 -> r8c7<>6 -> r8c7=8 -> r8c5<>8 -> r8c5=1 -> r9c5<>1 -> r9c5=8- > r9c9<>8 -> r9c9=4

2. r6c4 can't be 3 - because:
2a. r6c4=3 -> r9c1<>3 -> r9c4=3 -> r6c4<>3 contradiction

3. r3c7 can't be 9 because:
3a. r3c7=9 -> r3c5<>9 -> r4c5=9 -> r5c6<>9 -> r5c7=9 -> r3c7<>9 contradiction

4. Almost Locked Sets [r3c5 r1c5 r2c4 r2c5]=6=[r4c5 r5c6] both share 8 that eliminates 8 from r1c6 r46c4

5. Hidden single 8 at r2c4 for c4

7. r4c3 can't be 8:
7a. r4c3=8 -> r4c6<>8 => r7c3=8 -> r4c3<>8 contradiction

Richard

[Para]

It's a real goodun Para. Have finally been able to get to this spot. To my surprise, the marks pasted into SudoCue (with File-Variant-Diagonals selected) give a unique solution - with a real nice hard rating too.

Maybe that is what you get when you use a sudoku-X puzzle as the basis for you Killer-X puzzle.

Para

[Para]

Ok Ed,

I like a challenge.

Here's half a dozen moves to get you going. Have the feeling this is going to be a toughone.

1. Either r8c3 or r9c9 is 4 - so no 4 at r3c3
1a r8c3=4/6
1b. r8c3<>4 -> r8c3=6 -> r8c7<>6 -> r8c7=8 -> r8c5<>8 -> r8c5=1 -> r9c5<>1 -> r9c5=8- > r9c9<>8 -> r9c9=4

2. r6c4 can't be 3 - because:
2a. r6c4=3 -> r9c1<>3 -> r9c4=3 -> r6c4<>3 contradiction

3. r3c7 can't be 9 because:
3a. r3c7=9 -> r3c5<>9 -> r4c5=9 -> r5c6<>9 -> r5c7=9 -> r3c7<>9 contradiction

4. Almost Locked Sets [r3c5 r1c5 r2c4 r2c5]=6=[r4c5 r5c6] both share 8 that eliminates 8 from r1c6 r46c4

5. Hidden single 8 at r2c4 for c4

7. r4c3 can't be 8:
7a. r4c3=8 -> r4c6<>8 => r7c3=8 -> r4c3<>8 contradiction

Richard

I always wonder how you work these puzzles Richard. You do notice ALS-xz techniques. But then describe other techniques fairly difficult.

Step 1 is basically an xy-wing in R8C3, R8C7 and R9C9.
Step 2 is a simple colouring step. R6C4 sees all 3's on R9.
Step 3 is basically a 2-String Kite(i think this is the proper term)
Step 7 is a similar colouring move as in step 2 only for 8's on D/

Step 4 is nice. But you don't really need R12C5 for the ALS right?
It is also an example of a technique i've been discussing on the sudoku.com forum about distant pair exclusions.
R2C4 and R5C6 together see all 9's in C5. So they can't both be 9. Thus any 8 that sees both cells can be excluded.

Yesterdays One-trick Pony and X-file both had a similar move in them that cracked the puzzle.

greetings

Para

[sudokuEd]

It is also an example of a technique i've been discussing on the sudoku.com forum about distant pair exclusions.

Have missed that. Will go lurking - and spy on emm too.

Thanks for getting this one started Richard - especially the ALS. Very productive. Found some more good stuff - but still plenty more work to do.

8. no 6 in r8c3. Here's how.
8a. r9c14 = {36/35} = [5/6] -> r8c79 must be 5 or 6 (since both 5 and 6 can't be in r9c78)
8b. -> if r8c3 = 6, r8c9 = 5 and r8c7 = 8
8c. r8c9 = 5 -> r2c9 = 4 -> r9c9 = 8
8d. but this means 2 8's in n9
8e. -> no 6 r8c3

9. r9c1 = 6 (hidden single n7)

10. r8c7 = 6 (hidden single r8)

11. r3c2 != 6. Here's how.
11a. r3c2 = 6 -> r12c6 = 6 -> r7c4 = 6.
11b. but this leaves no 6 for D\

12. 6 in n1 only on D\: Locked for D\

13. 3 in n7 in r8:Locked for r8
13a. r9c4 = 3

14. r8c6 = 5
14a. r3c4 = 5 (hidden single n2)

15. no 2 in r3c8: forces 2 in both D\ and D/ into n5

16. 4 in n2 in c6:4 Locked c6

Should be here [edit: if the marks pic looks weird:paste into notepad, then paste from their into SudoCue]

Code: Select all

.------------------------------.------------------------------.------------------------------.
| 3479      125       125      | 12        37        469      | 4789      46789     3479     |
| 3479      34679     12       | 8         37        1246     | 135       13479     45       |
| 3478      3478      3678     | 5         69        14       | 12347     134679    1234679  |
:------------------------------+------------------------------+------------------------------:
| 1234789   13456789  135679   | 12479     69        123789   | 12345789  123456789 12346789 |
| 12347     13467     136      | 146       5         89       | 89        123467    123467   |
| 2345789   3456789   356789   | 2479      24        12378    | 1234578   12345678  23456789 |
:------------------------------+------------------------------+------------------------------:
| 158       158       18       | 246       24        26       | 379       379       379      |
| 379       379       4        | 79        18        5        | 6         128       128      |
| 6         279       279      | 3         18        79       | 145       145       48       |
'------------------------------'------------------------------'------------------------------'

[emm]

Call me a dummy, Ed but how do you get this into Sudocue?

Hey, why not write some poetry while you're over there?

[rcbroughton]

I always wonder how you work these puzzles Richard. You do notice ALS-xz techniques. But then describe other techniques fairly difficult.

I guess you find what you look for. There are some techniques I feel comfortable with and some I'm not. Move 1 for instance, I'll always look at cells with pairs of values to see what I can do with them. I also look for conjugate pairs that I can use to quickly follow implications.

I'm also ashamed to say I've never taken the time to learn colouring, so I don't spot them or call them as such. Maybe "difficult" is the wrong word. It's down to what I know what to look for. Just being lazy not learning different techniques!!

Anyway - couple more moves stemming from looking at conjugate pairs:

17. No 3 at r16c1.
17a. r16c1=3 -> r6c6<>3 -> r4c6=3 -> r8c2<>3 -> r8c1=3 contradicting start point

18. No 6 at r4c2.
18a. r4c2=6 -> r4c5<>6 -> r3c4=6 ->r2c6<>6 -> r2c2=6 contradicts r4c2

19. No 6 at r4c8
19a r4c8=6 -> r4c5<>6 -> r3c4=6 ->r1c6<>6 -> r1c8=6 contradicats r4c8

Rgds

[Para]

Call me a dummy, Ed but how do you get this into Sudocue?

You can just copy and paste it. That simple

[Para]

20. R4C12 no 3, because of 3's on C6.
20a. R4C6 = 3 : R4C12 <> 3
20b. R6C6 = 3 -->> R4/5C3 = 3 : R4C12 <> 3

21. R5C1 no 3, because of 3's on C6
21a. R4C6 = 3 -->> R8C1 = 6: R5C1 <> 3
21b. R6C6 = 3 -->> R4/5C3 = 3 : R5C1 <> 3

Para

[Para]

Here's a few more

22. R6C9: no 2 because of 2's in N5
22a. R6C3/4/5 = 2 : R6C9 <>2
22b. R4C4 = 2 -->> R8C9 = 2: R6C9 <>2
22c. R4C6 = 2 -->> R3C9 = 2: R6C9 <>2

23. R3C7: no 3 because of 3's in N1.
23a. R3C1/2/3 = 3: R3C7 <> 3
23b. R2C1 = 3 -->> R8C2 = 3: R3C7 <> 3
23c. R2C2 = 3 -->> R4C6 = 3: R3C7 <> 3

24. R7C7: no 3 because of 3's in N1
24a. R2C2/R3C3 = 3: R3C7 <> 3
24b. R2/3C1 = 3 -->> R8C2 = 3 -->> R6C6 = 3: R7C7 <> 3
24c. R3C2 = 3 -->> R2C7 = 3: R7C7 <> 3
24d. R3C2 = 3 -->> R1C9/R2C8 = 3 -->> R6C6 = 3: R7C7 <> 3

25. R6C6: no 7
25a. R7C7 and R9C6 both {79}. Together they see all 9's on R5. So they can't both be 9. So any cell that sees both can't contain a 7.

26. R4C1: no 7 because of 7's on R8
26a. R8C1 = 7: R4C1 <> 7
26b. R8C2 = 7 -->> R4C4 = 7: R4C1 <> 7
26c. R8C4 = 7 -->> R4C6 = 7: R4C1 <> 7

27. R1C9 and R2C8: no 7 because of 7's in N5.
27a. R4C6/R6C4 = 7: R1C9/R2C8 <> 7
27b. R4C4 = 7 -->> R9C6 = 7 -->> R6C3 = 7 -->> R1C7/R3C7 = 7: R1C9/R2C8 <> 7

Para

[Para]

Two more eliminations.

28. R1C7: no 9 because of 9's in R5
28a. R5C7 = 9: R1C7 <> 9
28b. R5C6 = 9 -->> R8C4 = 9 -->> R1C9/R2C8 = 9: R1C7 <> 9

29. R3C7: no 7 because of 7's in N5
29a. R4C6/R6C4 = 7: R3C7 <> 7
29b. R4C4 = 7 -->> R9C6 = 7 -->> R3C7/R8C2 = 7: R3C2: no 7 -->> R23C1 = 7 -->> R8C2 = 7: R3C7 <> 7

Para