SudokuSolver Forum

1. n5
Two C triplets and one NC triplet
-> NC triplet must be <159>
C triplets are {678} and {234}

2. D\
Given triplet in n5 is <159> the other NC triplets must be <247> <and <368>
Since 2 already in pink group
-> <368> in n1 and <247> in n9

3. Conclusions from above
In Orange group (368) can only go in n8 - must be <368>
-> Orange/Yellow group in n7 = {159}
-> Yellow group in n4 = <247>
In pink group {247} can only go in n2 - Must be 4 in r1c5 and 7 in r2c6
-> Blue/Pink group in n3 = <159>
-> Blue group in n6 = <368>

4. C /3 @r9c234
Given current placements C 3 cage @r9c234 can only be [345] or [321]
-> r9c2 = 3
-> HS 3 in r7 -> r7c9 = 3
Also HS 8 in r9 -> r9c7 = 8
Also HS 7 in r9 -> r9c9 = 7
-> r7c7 = 2

5. n5 again
4 and 6 in r5c19 and r19c5 -> (r4c6,r6c4) = {46}
3 in r4c6c8 -> 2 not in r5c6
-> 2 in n5 in r46c5
-> HS 2 in c6 -> r9c6 = 2
-> r9c234 = [345]

Also HS 2 in r5 -> r5c8 = 2
-> r5c678 = [312]
-> r4c56 = [24]
-> HS 7 in r5 -> r5c4 = 7
-> r6c45 = [68]

Also r5c23 = {89}
Also r46c8 = [83]
Also r3c9 = 2

etc.

Not quite pure Paper Solvable. Where a cage can only have one combination, and one of the three candidates is placed, the other two candidates will be considered to be a naked pair and remembered for later (locked).

1. R2C4 = 2, placed for upper snake

2. Cages R4C56 + R5C6 and R5C4 + R6C45 each contain three consecutive numbers, while R4C4 + R5C5 + R6C6 must contain three ordered non-consecutive numbers -> R4C4 + R5C5 + R6C6 = <159> -> R5C5 = 5, R4C4 + R6C6 = {19}, locked for N5 and D\

3. There are two cages on D\ which contain three ordered non-consecutive numbers which must be {247} and {368}
3a. 2 on D\ only in cage at R7C7 = <247> -> R8C8 = 4, R7C7 + R9C9 = {27}, locked for N9 and D\
3b. 2,4,7 all locked for right-hand and lower snakes

4. Cage at R1C1 = <368> -> R2C2 = 6, R1C1 + R3C3 = {38}, locked for N1
4a. 3,6,8 all locked for upper and left-hand snakes

5. Cage at R1C9 = <159> -> R2C8 = 5, R1C9 + R3C7 = {19}, locked for N3
5a. 1,5,9 all locked for upper and right-hand snakes

6. Cage at R2C5 = <247> -> R1C5 = 4, R2C6 = 7

7. Naked triple {159} in cage at R7C3, locked for N7
7a. 1,5,9 all locked for left-hand and lower snakes

8. Cage at R4C2 = <247> -> R5C1 = 4, R46C2 = {27}, locked for C2 and N4

9. Cage at R8C4 = <368> -> R9C5 = 6, R8C46 = {38}, locked for R8 and N8

10. Cage at R4C8 = <368> -> R5C9 = 6, R46C8 = {38}, locked for C8 and N6

11. Cage at R9C2 contains three ordered consecutive numbers = <123/345> -> R9C2 = 3
11a. R7C9 = 3 (hidden single in N9)
11b. R4C6 + R6C4 = {46} (hidden pair in N5)

[With hindsight, if I’d been writing an optimised walkthrough, I’d have done step 12 before step 11.]
12. 2 in R5 only in consecutive, not in order cage at R5C6 = {123} -> R5C6 = 3, R5C78 = [12], R3C7 = 9, R1C9 = 1, R8C46 = [38]

13. R5C6 = 3 -> consecutive, not in order cage at R4C5 = {234} -> R4C56 = [24], R46C2 = [72], R4C79 = [59] , R4C4 = 1, R6C6 = 9, R89C7 = [68], R8C9 = 5

14. R5C4 = 7 (hidden single in R5), R6C45 = [68], R46C8 = [83]

15. Cage at R9C2 contains three ordered consecutive numbers = <345> -> R9C34 = [45], R13C4 = [98]

and the rest is naked singles.