SudokuSolver Forum

I am hopelessly stuck trying to solve puzzlemadness.co.uk Daily Hard Killer Sudoku Puzzle dated 18 July 2023. After failing the puzzle several times, I carefully went through and wrote down my steps - and failed yet again. Here is what I did most recently:

You appear to have done Prelims so best to state them (although some don't) as it makes things easier to follow
22 cage no 1,2,3,4
11 cages no 9
21 cage no 1,2,3
24 cages only 7,8,9
15(5) cage only 1,2,3,4,5
20 cage no 1,2
19 cage no 1
8(2) cage no 4,8,9
9(2) cage no 9

1. clean up N4 and n9 - remove [789]
2. 45 rule N9 - remove [6] from r7c9, r8c9 Because no 1,2 in r7c7
3. 45 rule N7 - remove [1] from r8c3 and [2] from r9c2 and r9c3 (three squares = 19) Because no 8,9 in r8c3
4. clean up N6cage 13 - remove [1-5] from r6c9
5. isolated quintuple - remove [1-5] from r5c8 and r5c9 At this stage 6 must be in r5c8 or r5c9
6. clean up N6cage 16 - remove [4-9] from r6c8
7. clean up N8cage 20 - remove [34] from r7c5 and r7c6
8. 45 rule N6 - remove [89] from r6c6
9. inverse 45 rule N8 -> three sqaures = 29-19 - remove [89] from r9c4 Don't know what you mean by Inverse 45 rule. However 45 rule on N7 is simpler r8c3 = r9c4 so remove 8,9 from r9c4
10. cleanup N6 [6 only in row 5] - remove [6] from r4c7-9, r6c7, and r6c9
11. inverse 45 rule N1-3 45 rule on r123 or n123 (not inverse) -> r4c1+r4c6=9 - remove [15] from r4c1 and [12] from r4c6 Maybe you're using 45 rule to mean when there are extra cell(s) within the 45 and inverse 45 rule for cell(s) which protrude from the 45. They're what are usually referred to on this forum as innie(s) and outie(s). Each of these cases are both referred to as 45 rule. The 45 rule can also be used when there are both innie(s) and outie(s), which can also be useful at times.
12. cleanup N2cage 8 - remove [67] from r3c6
13. 45 rule row 4 - remove [7] from r4c6 This is really 45 rule on r1234 as suggested by Ed. Place 7 in r4c2 and remove from rest of r4
14. cleanup N2cage 8 - remove [1] from r3c6
15. inverse 45 rule N7-9 45 rule on r789 or n789 (not inverse) -> r6c4+r6c9=11 - remove [1,5-8] from r6c4
16. cleanup N5cage9 - remove [1-4,8] from r7c4
17. inverse 45 rule N7-8 Not inverse -> r6c4+r7c7=7 - remove [6] from r7c7
18. clean up N8cage 20 - remove [5] from r7c5 and r7c6
19. 45 rule col 9 - remove [12] from r4c9
20. 45 rule col 1 - remove [1-3] from r1c1 and [1] from r6c1
21. 45 rule N6 - remove [7] from r6c7
22. clean up N5cage 19 - remove [2-5] from r6c5 and r6c6
23. row 6 hidden triple (789) - remove [6] from r6c5 and r6c6
24. clean up N5cage 19 - remove [5] from r6c7
25. clean up N4cage 12 (only [56] in row 6) - remove [234] r6c1, r6c2, and r6c3 Go straight to next step for this reason
26. clean up N4 and row 6 (only [156]) Are you then removing other 1,5,6 from N4 and 1 from R6?
27. clean up row 9 ([6] only in N9) Better written as 6 in N9 only in row 9 - remove [6] from r1-6c9
28. clean up N6cage 16 - remove [9] from r5c8 and r5c9 So 1 has been removed from r6c8. Note that if you had placed 7 in r4c2 earlier, as implied but not stated, then r5c12 would only contain 8 and 9, no other 8,9 in r5
29. clean up N4 ([9] only in row 5) - remove 9 from r4c2
30. clean up N8 N9cage 12 - remove 3 from r9c7-9
31. clean up N7cage 19 - remove [5] from r9c2-4
32. 45 rule on N7 - remove [5] from r8c3 and remove 6
33. 45 rule on N1 and N4 - remove [4-7] from r3c3
34. 45 rule N1 - remove [8] from r2c1 and r3c1 NO! r2c1 + r3c1 + r3c3 = 17 has many valid combinations including {278}, {368} and {458} which can have 8 in any of those 3 cells.
35. clean up col 3(one of r4c1 and r4c4 must be [4]) - remove [4] from r1-2,7-9c3 This step doesn't make sense. N4 has 4 in r4c1, r4c3 and r5c3.
    I'll stop here. But when you re-work, remember to use 45 rule on r6789 r6c8 = 3 and, as mentioned earlier, 45 rule on r1234 r4c2 = 7. You've done the other two 45s which Ed mentioned.
36. clean up N6cage 10 - remove [4] from r8c4 and r8c5
37. 45 rule row 1 - remove [1-3] from r1c9
38. 45 rule col 1 - remove [7-9] from r1c1 and [7] from r5c1
39. clean up col 2 ([7] only in N4) - remove [7] from r1-3,6-9c2
40. clean up N1cage 12 - remove [89] from r1c2 and r1c3
41. inverse 45 rule N1-3 -> r4c1+r4c6=9 - remove [2] from r4c1 and [3] from r4c6
42. clean up N2cage 8 - remove [5] from r3c6
43. clean up N1cage11 - remove [34] from r2c1 and r3c1
44. rule 45 on N1 - remove [5] from r2c1 and r3c1
45. 45 rule on N6 and N9 - remove [4] from r5c7 and r7c7
46. inverse 45 rule N7-8 -> r6c4+r7c7=7 - remove [3] from r6c4
47. clean up N6cage 9 - remove [6] from r7c4
48. rule 45 col 1 - remove [6] from r2-3,8-9c1
49. clean up N1cage11 - remove [2] from r2-3c1 and [4] from r4c1
50. clean up col 3 - remove [2] from r1-2,r7-8c3
51. clean up N1 and col 1 - remove [1] from r-13c1-2 and r7-9c1 [7] from r1-2c3 and r7-9c1
52. clean up N7 (cage 15 must have [2]) - remove [2] from r7-8c2
53. clean up N1cage 12 - remove [6] from r1c2-3
54. 45 rule N1 - remove [8] from r3c3
55. clean up N1cage 21 - remove [6] from r3c4-5
56. clean up N1cage 16 - remove [4] from r2-3c2
57. clean up row 1 (only [4] in N1) - remove [4] from r1c6-9
58. clean up N1cage 12 - remove [6] from r1c1 and [2] from r1c2
59. clean up N1 and row 1 - remove [3] from r2-3c2-3 and r1c5-8 remove [5] from r2-3c2-3 and r1c5-9
60. clean up N2cage22 - remove [8] from r2c4
61. only number in col1 - r6c1 become [6]
62. clean up N2cage 12 - remove [678] from r1c6-8
63. clean up row 1 - remove [9] from r1c45,9
64. clean up N2cage22 - remove [8] from r1c34 and r2c4 becomes [9]
65. only number in row - r1c9 become [8]
66. clean up N2 - remove [6] from r2c56 and [7] from r2c5-6 and r3c4-5
67. clean up N1cage21 - remove [5] from r3c4-5
68. clean up row 2 - remove [5] from r2c7-9
69. clean up N2 and ro2 3 - remove [4] from r2c5-6 and r3c7-9; remove 8 from r2c5-6 and r3c2
70. clean up N3cage 14 - remove [2367] from r2c9 and [1367] from r3c9
71. clean up N2 cage 15 - remove [12] from r2c5-6 and r2c7 recome [7]
72. clean up N1cage 11 - r2c1 become [1] and r3c1 become [7]
73. clean up N3cage14 - r2c9 becomes [4] and r3c9 becomes [2]

Here's the problem: At this point problem: r1c6 is the only [1] in N2 but also the only [2] in row 1. Two requests:
- Is this a hard puzzle or am I being really stupid?
- Can you offer any suggestions as to where I screwed up?

Thank you.

Hi groston
I don't have time today to go through your steps. Having a quick look through I have a couple of suggestions.

There are some immediate placements available. eg, 45 Rule on r1234

Then do the 2 outies available, your steps 11 and 15 (I do these as 45 Rule of r123, and r789: not exactly sure how you do these with your 'inverse' technique)

I avoid clean-up until I'm completely stuck since its so easy to make a mistake. However, Andrew is genius at clean-up.

It gets a score of 0.85 so an easier one.
Cheers
Ed

Hi groston

As before I've marked up comments in red in your post above until I reached one step which looked wrong and the next step which didn't make sense to me.

Please try again including Ed's suggested 45s which give two immediate placements.

Thanks Ed for that compliment, a practice inherited from a former regular on this forum.

Continuing later, with mental arithmetic, from the step reached above, I think the solution is

So neither of 1,2 in r1c6, they must be elsewhere in r1 and n2.

Cheers,

Andrew