SudokuSolver Forum

My Rating: 1.5

1. n1
6 cage cannot be +6 must be +16
-> Other cages are +10 amd +19 or +20 and +9
But a +10 must be <136> which leaves no solution for +19 (neither <379> or <469>)
-> r123c1 = <135>
-> r123c3 = <479>
-> r123c2 = <268>


2. n123
9 cage at r1c789 cannot be <135> - must be <379> or <469>
-> r123c3 = [479]
-> r1c789 = <379>
-> 9 in n2 in r2 and 7 in n2 in r3
-> 8 in n2 in r1
-> r123c2 = [268]
Also -> 6 in n2 in r1
-> HS 5 in r1 -> r123c1 = [531]
-> r1c456 = <168>
-> 3 in n2 in r3
-> (24) in n2 in r2
-> r2c456 = <249>
-> r3c456 = <357>
-> r2c789 = <158>
-> r3c789 = <246>


3. D\
Since r123c5 = [645] -> ?9 cage in n5 can only be <379>
-> Values not yet placed in D\ are 12348
NC3 cage at r6c6 cannot have both (34) nor both (12)
-> 3 cage at r6c6 is from <138>, <148>, or <248>
-> r7c7 from (34)
Also 3 in D\ in r7c7 or r9c9
Also 8 in D\ in r6c6 or r8c8
Also (r4c4, r9c9) are {24}, [23], [13]


4. n5
All in n5... this is what we know:

5 already in both diagonals
-> 5 in n5 in r5c46

(12) cannot both go in c4 -> at least one of (12) in c6

r1c46 = {18} and r456c5 = <379>
-> one of (18) in each of c46.

r4c4 from (124)
r6c6 from (128)

So these are the possibilities for c46 in n5:

c4 c6
a) [146] [852] (since 6 in r6c4 -> r3c7 = 2 -> r4c6 not 2)
b) [248] [651]
c) [258] [461] or [641]
d) [268] [451]
e) [468] [251] (since 4 in r4c4 -> r7c7 = 3 -> r6c6 not 2)

However:
a) -> r7c7 = 4
-> r9c9 = 3
-> r1c9 = 9
Which leaves NC cage in n7 with {134}
-> a) is eliminated

e) -> r9c9 = 2 which leaves no place for 2 in n3
-> e) is eliminated


5. Conclusions from Step 4
Remaining possibilities above are b), c), d).

-> r4c4 = 2, r6c4 = 8, r6c6 = 1
-> r1c4 = 1 and r1c6 = 8
Also r2c4 = 9 and r2c6 = 2

Also (HS 1 in D/) -> r7c3 = 1 -> 1 in c2 in r45c2.
-> (HS 2 in D/) -> r3c7 = 2
-> r3c9 = 6

Also (r7c7,r9c9) = {34}


6. n7

1 in r7c3 prevents r9c1 from being a 2 or a 4, and [531] in r123c1 prevents 2 or 4 in C cage in r78c1.
-> (24) in c1 in n4. I.e., (24) in r456c1
-> r789c1 all from (6789) with the following restrictions:
r9c1 from (69) (78 already in D/)
r8c1 not 8 (8 already in r8 in r8c8)
r78c1 are consecutive

-> Possibilities for C cage at r6c2 and r9c1 are:

[567][9] - but this leaves the three numbers (179) trying to all go in r45c2.
[789][6] - but this leaves no place for 7 in n7
and
[987][6 or 9] which are the only possibilities left

But putting a 6 in r9c1 leaves no place for 9 in n7

-> r6c2 = 9
r789c1 = [879]
-> r456c1 = {246}
Also r45c2 = [71]
-> r456c3 = {358}
-> r789c2 = {345}
-> r89c3 = {26}


7. Further conclusions from Step 6
r789c5 = [218]
Also r1c9 = 3 and r1c7 = 9
-> r7c7 = 3 and r9c9 = 4

Also r46c5 = [93]
-> 9 in n6 in r5c89. Since that is in a C cage -> 9 cannot be in r5c9
-> C cage at r5c8 = [987]

Also -> r789c2 = [543]
-> r4c6 = 6

Rest is cleanup

This is a KiMo so the 9 cage for example can be 9 or 19.
The dashed cages (coloured cages on my worksheet) are non-consecutive and the red-border cages consecutive; numbers must be in order in each cage.

Prelims
KiMo non-consecutive cages
6 KiMo cage must total 16 (cannot be 6 because 1,2,3 are consecutive) = {169/259/268/358}, no 4,7
9 KiMo cages must total 9 or 19 = {135/379/469}, no 2,8
0 KiMo cage must total 10 or 20 = {136/479}, no 2,5,8

1. 2,8 in N1 only in 6 KiMo cage at R1C2 = <268>, locked for C2 and N1
1a. Candidates must be in ascending or descending order -> R2C2 = 6, placed for D\

2. 5 in N1 only in 9 KiMo cage at R1C1 = <135>, locked for C1 and N1
2a. Candidates must be in ascending or descending order -> R2C1 = 3

3. Naked triple {479} in 0 KiMo cage at R1C3, locked for C3
3a. Candidates must be in ascending or descending order -> R2C3 = 7

4. 9 KiMo cage at R1C7 must total 19 = <379> (only remaining combination, cannot be <135> which clashes with R1C1, cannot be <469> which clashes with R1C3), locked for R1 and N3 -> R1C3 = 4, R3C3 = 9, placed for D\
4a. Candidates must be in ascending or descending order -> R1C8 = 7

5. 9 KiMo cage at R4C5 = <135/379> (cannot be <469> because no 6 in R5C5, the centre cell of this cage), no 4,6, 3 locked for C5 and N5
5a. Candidates must be in ascending or descending order -> R5C5 = {37}
5b. 7 of <379> must be in R5C5 -> no 7 in R46C5

6. 9 in R2 only in non-consecutive cage at R2C4 -> no 8 in this cage

7. 6 in R1 only in non-consecutive cage at R1C4, locked for N2
7a. 6 in R1 only in non-consecutive cage at R1C4 -> no 5 in this cage

8. R1C1 = 5 (hidden single in R1), placed for D\, R3C1 = 1

9. 1 in R1 only in non-consecutive cage at R1C4 = <168> (cannot contain both of 1,2), locked for R1 and N2 -> R13C2 = [28]
9a. Candidates must be in ascending or descending order -> R1C5 = 6

10. 1 in R2 only in non-consecutive cage at R2C7 -> cannot contain 2

11. 3 in R3 only in non-consecutive cage at R3C4 -> cannot contain 2 or 4 = <357>
11a. Candidates must be in ascending or descending order -> R3C5 = 5

12. Naked triple <249> in non-consecutive cage at R2C4
12a. Candidates must be in ascending or descending order -> R2C5 = 4

13. Naked triple <158> in non-consecutive cage at R2C7
13a. Candidates must be in ascending or descending order -> R2C8 = 5, placed for D/
13b. 5 in N5 only in R5C46, locked for R5

14. Naked triple <246> in non-consecutive cage at R3C7
14a. Candidates must be in ascending or descending order -> R3C8 = 4

15. 9 KiMo cage at R4C5 (step 5) = <379> (only remaining combination), locked for C5 and N5
15a. Candidates must be in ascending or descending order -> R5C5 = 7, placed for both diagonals
15b. 3 on D\ only in R7C7 + R8C8 + R9C9, locked for N9

16. Naked triple {128} in R789C5, locked for N8

17. Non-consecutive cage at R6C6 must contain 8 (cannot contain three of 1,2,3,4), locked for D\
17a. Candidates must be in ascending or descending order -> no 1,2,8 in R7C7
17b. R7C7 = {34} -> no 3,4 in R6C6 + R8C8
17c. 8 in R6C6 + R8C8, CPE no 8 in R6C8
17d. 3 in C8 only in R456C8, locked for N6

18. Consecutive cage at R6C2 = <567/789> (cannot be <123/234/345/456/678> because of candidates missing from R6C2 or from R78C1) -> R7C1 = {68}, R6C2 + R8C1 = {57/79}
18a. R6C2 + R8C1 = {57/79}, CPE no 7 in R46C1 + R79C2
18b. R8C1 = 7 (hidden single in C1)
18c. R4C2 = 7 (hidden single in N4)

19. Consecutive cage at R5C8 = <123/345/789> (cannot be <234/456/567/678> because of candidates missing from R5C89 or from R6C9), no 6
19a. 7 of <789> must be in R6C9 with R5C89 = [98] -> no 8 in R5C8, no 9 in R5C9, no 8,9 in R6C9
19b. <123> must be [321] -> no 1 in R5C89, no 2 in R5C8 + R6C9
19c. 4 of <345> must be in R5C9 -> no 4 in R6C9

20. Non-consecutive cage at R4C4 must contain one of 6,8, no 6,8 in R4C4 -> R6C4 = {68}, no 8 in R5C4
20a. Candidates must be in ascending or descending order -> no 1,2 in R5C4

21. Non-consecutive cage at R7C3, candidates must be in ascending or descending order -> no 1,9 in R8C2
21a. R8C2 = {34} -> no 3,4 in R7C3 + R9C1
21b. 4 in C1 only in R456C1, locked for N4
21c. 4 on D/ only in R4C6 + R8C2, CPE no 4 in R8C6

22. Consider placements for 3 on D/
R1C9 = 3 => R9C1 = 9 (hidden single on D/) => no 8 in non-consecutive cage at R7C3
or R8C2 = 3 => R4C6 = 4 (hidden single on D/) => R5C4 = {56} => R6C6 = 8 (because of non-consecutive cage at R4C4), locked for D/
-> no 8 in non-consecutive cage at R7C3
22a. 8 on D/ only in R4C6 + R6C4, locked for N5
22b. R8C8 = 8 (hidden single on D\)

23. Non-consecutive cage at R7C3 = <136/146/149/249> (cannot be <246> which clashes with R3C7)
23a. 1 of <136/146> must be in R7C3 -> no 6 in R7C3
23b. R7C3 = {12} -> no 2 in R9C1
23c. 2 in C1 only in R456C1, locked for N4

24. Consider combinations for consecutive cage at R6C2 = <567/789>
<567> => R7C1 = 6 => no 6 in R9C1
or <789> => R6C2 = 9 => R9C1 = 9 (hidden single in C1)
-> R9C1 = 9, placed for D/, R1C9 = 3, placed for D/, R1C7 = 9, R8C2 = 4, placed for D/

25. R7C7 = 3 (hidden single on D\) => R6C6 = 1 (because of non-consecutive cage at R6C6), placed for D\, R1C46 = [18]
25a. Naked pair {24} in R4C4 + R9C9, CPE no R4C9 + R9C4
25b. Naked pair {26} in R3C7 + R4C6, CPE no 2,6 in R4C7
25c. Naked pair {26} in R3C7 + R4C6, locked for D/ -> R6C4 = 8, R7C3 = 1, R79C2 = [53], R6C2 = 9, R7C1 = 8 (completion of <789> consecutive cage at R6C2), R5C2 = 1, R46C5 = [93]
25d. Naked pair {26} in R89C3, locked for C3 -> R6C3 = 5

26. R6C9 = 7 -> consecutive cage at R5C8 = [987], R2C79 = [81], R45C3 = [83]

27. Naked triple {246} in R4C146, locked for R4 -> R4C789 = [135]
27a. Naked triple {246} in R356C7, locked for C7 -> R89C7 = [57]

[Catching up on naked singles …]
28. R789C5 = [218], R679C8 = [261]

29. R3C7 = 2 (hidden single in C7), placed for D/, R4C6 = 6

30. Non-consecutive cage at R4C4 must be <248/258> (cannot contain both of 4,5) -> R4C4 = 2, placed for D\, R9C9 = 4

and the rest is naked singles, without using the diagonals.

I'll rate my walkthrough at Easy 1.5. I used a couple of short forcing chains after I'd got as much as I could out of the non-consecutive and consecutive cages.