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Ed
 Post subject: Assassin 296
PostPosted: Thu Jul 10, 2014 11:25 pm 
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This puzzle started out life on the software forum with a cage pattern generated by (unreleased) version of SudokuSolver. Changed lots of cages then Jsudoku came up with this. Was too easy for an Assassin but turning it into a zero killer fixed that. So, one decent push available from the beginning to make big inroads then after that, technically nothing harder than killer pairs....but, took the third solve to be sure of that. Found it very, very resistant the first two times through. A true Assassin. Am sure Andrew (and of course Afmob!) will find this puzzle a lot easier than I did initially. SudokuSolver score, 1.55

Assassin 296
note: 1-9 cannot repeat on the diagonals. It also has 4 cages that cross over each other.
Image

code: paste into solver:
3x3:d:k:2560:2560:4097:4097:4097:9218:10243:9218:9218:3844:3844:4097:0000:3078:3078:9218:10243:9218:3335:5384:3844:0000:3078:10243:10243:9218:10243:3335:5384:5384:0000:10243:0000:10243:3595:9218:3335:4620:4620:0000:0000:10243:3595:3595:0000:1550:4620:10511:1552:2833:2833:3090:3090:0000:1550:10511:1552:10511:4115:4115:3604:0000:0000:10511:10511:10511:2829:4115:4362:4362:3604:2313:10511:10511:3077:3077:2829:2829:4362:3604:2313:
solution: 
+-------+-------+-------+
| 7 3 1 | 4 5 8 | 2 6 9 |
| 4 2 6 | 7 9 1 | 5 8 3 |
| 8 5 9 | 6 2 3 | 1 4 7 |
+-------+-------+-------+
| 3 9 7 | 8 6 5 | 4 2 1 |
| 2 4 8 | 1 3 9 | 7 5 6 |
| 1 6 5 | 2 7 4 | 9 3 8 |
+-------+-------+-------+
| 5 8 4 | 3 1 7 | 6 9 2 |
| 9 7 2 | 5 8 6 | 3 1 4 |
| 6 1 3 | 9 4 2 | 8 7 5 |
+-------+-------+-------+
Cheers
Ed
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Andrew
 Post subject: Re: Assassin 296
PostPosted: Fri Jul 11, 2014 4:32 am 
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A nice puzzle Ed!

I'm cheating a bit as this post is just the initial way in.

The early key steps:
R7C4 “sees” all cells in N7 except for R9C3 -> R7C4 = R9C3
R6C3 “sees” all cells in N7 except for R7C1 -> R6C3 = R7C1
These steps lead directly to the first two placements.
I hope to finish tomorrow and post my walkthrough then, but I won't be surprised if Afmob finishes before I do.
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Afmob
 Post subject:
PostPosted: Fri Jul 11, 2014 9:45 pm 
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Thanks for this week's Assassin but don't put too much pressure on me, Ed! ;)

You were right that I didn't feel it was particular hard but I still used some technical difficult moves (maybe I was too lazy to look for easier alternatives? :cheesey:).
My main move (step 3d) does not use any Killer properties, so it can also be applied to regular X-Sudoku. Note that I marked step 4e also with "!" even though it is not a difficult move but I felt that the Killer was cracked after this move.

About Andrew's comment
Initial placements:
I didn't need those moves to make the first two placements but I used one of them to make an early third placement.

A296 Walkthrough:
1. R6789
a) 41(8) = {12356789} -> CPE: R7C3 <> 1,2,5
b) R7C3 = 4 -> R6C4 = 2
c) R6C3 sees all of N7 but R7C1 -> R6C3 = R7C1 = (15)
d) 6(2) = {15} locked for C1
e) Naked pair (15) locked in R6C13 for R6+N4
f) 11(2) = {47} locked for R6+N5 since (38) is a Killer pair of 12(2) @ R6
g) 12(2) @ R6 = {39} locked for R6+N6
h) Using R6C13 = (15): Innie N78 = R8C6 = 6

2. C123 !
a) 18(3) <> 2 since R6C2 = (68)
b) 2 locked in 13(3) = 2{38/47} @ N4 for C1
c) 21(3) = 9{48/57} since {678} blocked by R6C2 = (68) -> CPE: R5C2 <> 9
d) Using R6C13 = (15): Outies N4 = 13(2) = [49/85]
e) Using R6C13 = (15): Innies N14 = 7(2) = {16/25}
f) ! Hidden Killer triple (123) in 10(2), 15(3) and Innies N14 for N1 since each can only have one of (123) -> 10(2) <> 4,6; 15(3) <> {456}
g) Innies N14 + Outies N4 = 7(2) + 13(2) = 20(4) = {1469/1568/2459}
h) 10(2) <> 1,9 since it's a Killer pair of Innies N14 + Outies N4

3. C123 + D/ !
a) Using R6C13 = (15): Outies N14 = 9(2) <> 2,7,9 since (27) is a Killer pair of 10(2)
b) 16(4) = 15{28/46} since 3{148/256} blocked by Killer pairs (23,38) of 10(2)
c) Outies N14 = 9(2) <> 6
d) ! Consider placement of 6 in C1 -> R9C1 = 6
- i) R9C1 = 6
- ii) R2C1 = 6 -> 6 locked in R3C45 @ N2 for R3, R5C3 = 6 (HS @ C3) -> R6C9 = 6 (HS @ R6) -> R9C1 = 6 (HS @ D/)
e) Killer pair (15) locked in Innies N14 + R6C3 for C3
f) 13(3) = 2{38/47}: R45C1 <> 4,8 since R3C1 (48)
g) 4 locked in R45C2 @ N4 for C2
h) 15(3): R2C1 <> 9 because R2C2 <> 4 and R3C3 <> 1,4,5
i) Hidden Single: R8C1 = 9 @ C1

4. C123 !
a) Innies C1 = 11(2) = {38}/[74]
b) 15(3) = {168/249/258/357} since R2C1 = (348) and {348} blocked by R3C1 = (48); R2C2+R3C3 <> 3,8
c) 6 locked in 18(3) = 6{39/48} @ N4; R5C3 <> 3 since R56C2 <> 9
d) 18(3) = 6{39/48} -> R5C2 = (34)
e) ! 15(3): R2C2 <> 6 since R2C1+R3C3 <> 1
f) Hidden Single: R6C2 = 6 @ C2, R6C9 = 8
g) 21(3): R4C2 <> 8 since R3C2+R4C3 <> 4
h) 8 locked in R45C3 @ N4 for C3
i) 12(2) = [39/57]
j) R7C4 sees all of N7 but R9C3 -> R9C3 = R7C4 = (37)
k) 3 locked in R89C3 @ C3 for N7

5. N689
a) 11(3) = 2{18/45} -> 2 locked for R9+N8 since {137} blocked by R7C4 = (37)
b) 41(8) = {12356789} -> CPE: R8C5 <> 3
c) 3 locked in R7C456 @ N8 for R7
d) Innies N9 = 11(2) = {29/56}
e) 9(2) = [27]/{45}
f) Killer pair (25) locked in 9(2) + Innies N9 for N9
g) 17(3) = {368} since {467} blocked by Killer pair (47) of 9(2) -> 3,8 locked for C7+N9

6. R123 + D/
a) 2 locked in R2C2+R3C3 @ D\ for N1
b) 10(2) = {37} locked for R1+N1
c) Innies N14 = 7(2) = {16} locked for C3+N1+16(4)
d) R6C3 = 5, R6C7 = 9, R6C8 = 3
e) 16(4) = {1456} -> 4,5 locked for R1+N2
f) 12(3) = {129/138/237} <> 6
g) Hidden Single: R4C5 = 6 @ C5
h) 5,6 locked in 36(7) = 34569{18/27} @ N3 for 36(7) -> R2C9 = 3
i) Hidden pair (35) locked in R4C6+R5C5 @ D/ for N5 -> R4C6+R5C5 = (35)
j) 40(8) = {12346789} -> R3C6 = 3
k) R4C6 = 5, R5C5 = 3, R1C1 = 7, R6C6 = 4

7. Rest is singles without considering diagonals.

Rating:
1.5. I used a Hidden Killer triple and a forcing chain.
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Andrew
 Post subject: Re: Assassin 296
PostPosted: Wed Jul 16, 2014 3:55 am 
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Thanks Ed for another challenging Assassin. After my initial way in, I found this puzzle a lot harder than I'd expected, so definitely an Assassin.

Here is my walkthrough for Assassin 296:
Thanks Afmob and Ed for the corrections.

Prelims

a) R1C12 = {19/28/37/46}, no 5
b) R67C1 = {15/24}
c) 6(2) cage at R6C4 = {15/24}
d) R6C56 = {29/38/47/56}, no 1
e) R6C78 = {39/48/57}, no 1,2,6
f) R89C9 = {18/27/36/45}, no 9
g) R9C34 = {39/48/57}, no 1,2,6
h) 21(3) cage at R3C1 = {489/579/678}, no 1,2,3
i) 11(3) cage at R8C4 = {128/137/146/236/245}, no 9
j) 40(8) cage at R1C7 = {12346789}, no 5
k) 41(8) cage at R6C3 = {12356789}, no 4

1. 5 in N3 only in R1C89 + R2C79 + R3C8, locked for 36(7) cage at R1C6, no 5 in R1C6 + R4C9
1a. Since the 36(7) cage contains 5 it must also contain 4, 40(8) cage at R1C8 contains 4 -> outies of N3 must contain 4, CPE no 4 in R4C6
1b. Similarly 36(7) cage must contain 9, 40(8) cage contains 9 -> outies of N3 must contain 9, CPE no 9 in R4C6

2. 45 rule on C1 4 innies R1289C1 = 26 = {2789/3689/4679/5678} (cannot be {4589} which clashes with R67C1), no 1, clean-up: no 9 in R1C2

3. R7C4 “sees” all cells in N7 except for R9C3 -> R7C4 = R9C3, no 1,2,6 in R7C4, no 4 in R9C3, clean-up: no 8 in R9C4
3a. 4 in N7 only in R7C13, locked for R7
3b. 4 in R7C13 -> either R67C1 = [24] or 6(2) cage at R6C4 = [24] (locking cages) -> 2 in R6C14, locked for R6, clean-up: no 9 in R6C56
3c. 41(8) cage at R6C3 = {12356789}, 2 locked for N7, clean-up: no 4 in R6C1, no 4 in R6C4
3d. 2 in R6C14, CPE no 2 in R9C1 using D/
3e. 6 in N7 only in R7C2 + R8C123 + R9C12, locked for 41(8) cage, no 6 in R6C3

4. R6C3 “sees” all cells in N7 except for R7C1 -> R6C3 = R7C1 = {15}
4a. R7C3 = 4 (hidden single in R7) -> R6C4 = 2, both placed for D/
4b. Naked pair {15} in R67C1, locked for C1
4c. Naked pair {15} in R6C13, locked for R6 and N4, clean-up: no 6 in R6C56, no 7 in R6C78

5. R6C56 = {47} (cannot be {38} which clashes with R6C78), locked for R6 and N5, clean-up: no 8 in R6C78
5a. Naked pair {39} in R6C78, locked for R6 and N6

6. 18(3) cage at R5C2 = {369/378/468} (cannot be {279} because R6C2 only contains 6,8), no 2
6a. 2 in N4 only in R45C1, locked for C1, clean-up: no 8 in R1C2
6b. 13(3) cage at R3C1 contains 2 = {238/247}, no 6,9

7. 21(3) cage at R3C2 = {489/579} (cannot be {678} which clashes with R6C2), no 6
7a. 21(3) cage = {489/579}, CPE no 9 in R5C2

8. 45 rule on N4, using R6C13 = {15} = 6, 2 outies R3C12 = 13 = [49/85]
8a. 13(3) cage at R3C1 (step 6b) = {238/247}
8b. R3C1 = {48} -> no 4,8 in R45C1
8c. 4 in N4 only in R45C2, locked for C2, clean-up: no 6 in R1C1

9. 6 in N4 only in 18(3) cage at R5C2 (step 6) = {369/468}, no 7
9a. 3 of {369} must be in R5C2, 4 of {468} must be in R5C2 -> R5C2 = {34}
9b. R5C2 = {34} -> no 3 in R5C3

10. 21(3) cage at R3C2 = {489/579}
10a. 4 of {489} must be in R4C2 -> no 8 in R4C2

11. 45 rule on N78 2 outies R6C13 = 1 innie R8C6, R6C13 = {15} = 6 -> R8C6 = 6, clean-up: no 3 in R9C9
11a. R8C6 = 6 -> R89C7 = 11 = {29/38/47}, no 1,5

12. 45 rule on N9 2 remaining innies R7C89 = 11 = {29/38/56}, no 1,7

13. 45 rule on N1, using R3C12 = 13, 2 remaining innies R12C3 = 7 = {16/25}, no 3,7,8,9
13a. Killer pair 1,5 in R12C3 and R6C3, locked for C3, clean-up: no 5 in R7C4 (step 3), no 7 in R9C4
13b. R12C3 = 7 -> R1C45 = 9 = {18/36/45}/[72], no 9 in R1C4, no 7,9 in R1C5

14. 15(3) cage at R2C1 = {168/249/258/357} (cannot be {159/267/456} which clash with R12C3, cannot be {348} which clashes with R3C1
14a. 4 of {249} must be in R2C1 -> no 9 in R2C1
14b. 1,5 of {168/258/357} must be in R2C2 -> no 3,6,7,8 in R2C2
14c. 15(3) cage = {168/249/258/357}, R12C3 (step 13) = {16/25} -> combined cage = {168}{25}/{249}{16}/{258}{16}/{357}/{16}, 1,6 locked for N1, clean-up: no 4,9 in R1C1
14d. R1C45 (step 13b) = {18/36/45} (cannot be [72] which clashes with R1C12), no 7 in R1C4, no 2 in R1C5

15. 9 in C1 only in R89C1, locked for N7 and 41(8) cage at R6C3, no 9 in R7C4 (step 3), clean-up: no 3 in R9C4

16. R1289C1 (step 2) = {3689/4679}
16a. 7 of {4679} must be in R1C1 -> no 7 in R289C1

17. 15(3) cage at R2C1 (step 14) = {168/249/258/357}
17a. 3 of {357} must be in R2C1 -> no 3 in R3C3
17b. 3 in C3 only in R89C3, locked for N7
17c. 3 in 41(8) cage at R6C3 only in R7C4 + R8C3, CPE no 3 in R8C45

18. 45 rule on N6 4 innies R4C7 + R456C9 = 19 = {1468/1567/2458/2467}
18a. 5 of {2458} must be in R5C9, 2 of {2467} must be in R4C79 (R4C79 cannot be {47} which clashes with 21(3) cage at R3C2) -> no 2 in R5C9

19. 16(4) cage at R1C3 = {16}{45}/{25}{18} (cannot be {25}{36} which clashes with R1C12), no 3,6 in R1C45

20. 36(7) cage at R1C6 must contain 9 in R1C689 + R2C79 + R3C8, CPE no 9 in R1C7
20a. 9 in R1 only in R1C689, locked for 36(7) cage, no 9 in R2C79 + R3C8

[It took me a long time to find …]
21. 15(3) cage at R2C1 (step 14) = {168/249/258/357}
21a. 6 of {168} must be in R3C3 (15(3) cage cannot be [618] which clashes with 21(3) cage at R3C2 = [948], because 9 in N1 only in R2C2 + R3C23), no 6 in R2C1
21b. 8 of {168/258} must be in R2C1 -> no 8 in R3C3

22. R9C1 = 6 (hidden single in C1), placed for D/, clean-up: no 3 in R8C9
22a. R8C1 = 9 (hidden single in C1), clean-up: no 2 in R9C7 (step 11a)

[Up to this stage I’ve been sticking to Ed’s comment that nothing harder than killer pairs was needed after the initial push. Now I tried some harder steps, but then realised that I’d missed a hidden single, so I’ve re-worked from here.]

23. R6C2 = 6 (hidden single in C2), R6C9 = 8, clean-up: no 3 in R7C8 (step 12), no 1 in R89C9
23a. R89C7 (step 11a) = [29/38/83] (cannot be {47} which clashes with R89C9), no 4,7
23b. Killer pair 3,9 in R6C7 and R89C7, locked for C7
23c. 1 in N9 only in 14(3) cage at R7C7
23d. Hidden killer pair 4,7 in 14(3) cage and R89C9 for N9, R89C9 contains one of 4,7 -> 14(3) cage must contain one of 4,7 = {149/167}, no 2,3,5,8
23e. 9 of {149} must be in R9C8 -> no 4 in R9C8
23f. 6 of {167} must be in R7C7 -> no 7 in R7C7

24. 14(3) cage at R4C8 = {167/257}, no 4, 7 locked for N6

25. 8 in N4 only in R45C3, locked for C3, clean-up: no 8 in R7C4 (step 3), no 4 in R9C4

26. Moved to step 29c. I’d put this step in the wrong place when doing the re-work.

[And now I’ll use one of my harder steps …]
27. Outies of N3 must contain 4 (step 1a) -> 4 in R13C6 + R4C79
27a. Consider placements for 4 in R13C6 + R4C79
4 in R13C6
or 4 in R4C79 => 21(3) cage at R3C2 = 5{79} => R12C3 (step 13) = {16} => R1C45 (step 13b) = {45}
-> 4 in R1C45 + R13C6, locked for N2

28. 12(3) cage at R2C5 = {129/138/237} (cannot be {156} which clashes with R1C45), no 5,6

29. R4C5 = 6 (hidden single in C5)
29a. 6 in N3 only in 36(7) cage at R1C6
29b. Since the 36(7) cage contains 6 it must also contain 3, 40(8) cage at R1C8 contains 3 -> outies of N3 must contain 3, locked for C6
29c. Outies of N3 must contain 9 (step 1b), 9 locked for C6

30. 45 rule on N7, using R6C13 = {15} = 6, 2 remaining outies R79C4 = 12 = [39/75]
30a. 16(3) cage at R7C5 = {178/259/457} (cannot be {349} because 3,9 only in R7C5, cannot be {358} which clashes with R79C4), no 3
30b. R79C4 = [39] (cannot be [75] which clashes with 16(3) cage), R9C3 = 3, R9C7 = 8 -> R8C7 = 3 (cage sum), R6C78 = [93]

31. R4C1 = 3 (hidden single in R4), R5C1 = 2 (hidden single in C1), R3C1 = 8 (cage sum), R5C2 = 4, R5C3 = 8 (cage sum)
31a. Naked pair {79} in R4C23, locked for R4 and 21(3) cage at R3C2 -> R3C2 = 5, clean-up: no 2 in R12C3 (step 13)

32. R1C1 = 7, placed for D\, R6C6 = 4, placed for D\, R8C8 = 1, placed for D\, R7C7 = 6, placed for D\, R9C8 = 7
32a. R8C9 = 4 (hidden single in N9) -> R9C9 = 5, placed for D\

33. R5C5 = 3 (hidden single on D\), placed for D/, R5C6 = 9 (hidden single in R5), R2C8 = 8, placed for D/, R8C2 = 7, placed for D/, R3C7 = 1, placed for D/, R4C6 = 5

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

Rating Comment:
I'll rate my walkthrough for A296 at 1.5. I used "clones" and a short forcing chain. After seeing Afmob's walkthrough, I realise that with a bit more work in N8 I wouldn't have needed the forcing chain, but I'd still have given the same rating.
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Ed
 Post subject: Re: Assassin 296
PostPosted: Thu Jul 17, 2014 10:02 am 
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This ended up a real good one! Glad it gave enough challenge to Afmob and Andrew. Enjoyed both their solutions. I followed Afmob's route most closely but for different reasons. Andrew got what I felt was my key elimination in his 21b but again, for a very different reason ( my step 12). And three different ways to get the big push start into this puzzle!

While step 12 is my big difference to Afmob's WT, the clean-up steps based on permutations in 3-cell cages are the ones that took me the longest to find, not step 12. That's why I thought Andrew would find this puzzle easier than me (and indeed, his WT is much better than my first solve). He is so good at doing those methodically.

Start to A296
25 steps:
Preliminaries
Cage 6(2) n47 - cells only uses 1245
Cage 6(2) n57 - cells only uses 1245
Cage 12(2) n78 - cells do not use 126
Cage 12(2) n6 - cells do not use 126
Cage 9(2) n9 - cells do not use 9
Cage 10(2) n1 - cells do not use 5
Cage 11(2) n5 - cells do not use 1
Cage 21(3) n14 - cells do not use 123
Cage 11(3) n8 - cells do not use 9
Cage 40(8) n2356 - cells ={12346789}
Cage 41(8) n478 - cells ={12356789}

Missing routine clean-up through this WT.
1. "45" on n7: 2 outies r6c3+r7c4 + 4 = 3 innies r7c13 + r9c3 (IOD=+4)
1a. since those two outies see all n7 except for innies, those outies must repeat there -> r6c3=r7c1, r7c4=r9c3
1b. -> IOD of +4 must go in r7c3 (Afmob's way is much simpler though not as obvious to me!!) ->r7c3 = 4: Placed for D/
1c. r6c4 = 2 (cage sum), Placed for D/
1d. r6c3=r7c1 = (15)
1e. ->6(2)r6c1 = {15}: both locked for c1

2. "45" on n78: 2 remaining outies r6c13 = 1 remaining innie r8c6
2a. r6c13 = 6 -> r8c6 = 6
2b. Naked pair {15} in r6c13: both locked for n4 and r6

3. 12(2)r6c7 = {39/48}(no 7) = 3/8
3a. -> {38} blocked from 11(2)r6c5
3b. = {47} only: both locked for r6 and n5
3c. => 12(2)r6c7 = {39} only: both locked for r6 and n6

4. 21(3)r3c2 = {489/579/678}
4a. but the 21(3) sees r6c2 = (68) ->{678} blocked
4b. = {489/579}(no 6)
4c. 21(3) must have 9 and r5c2 sees all of the 21(3) -> no 9 in r5c2

5. 18(3)r5c2 must have 6 or 8 for r6c2 = {369/378/468}(no 2)
5a. 6 in {369} must be in r6c2 and 4 in {468} must be in r5c2 -> no 6 in r5c2

6. 2 in n4 only in 13(3)r3c1 = {238/247}(no 6,9)
6a. 2 locked for c1

7. r6c13 = 6: "45" on n4: 2 outies r3c12 = 13 = [49/85]
7a. 21(3)r3c2 = {489/579}: 4 in {489} must be in r4c2 -> no 8 in r4c2

8. r3c12 = 13: "45" on n1: 2 innies r12c3 = 7 = {16/25}(no 3,7,8,9) = 1/5

9. Killer pair 1,5 in h7(2)r12c3 and r6c3: both locked for c3

10. 13(3)r3c1 = {238/247}: can't have both 4 & 8 -> no 4,8 in r45c1

11. 4 in c1 only in n1: 4 locked for n1
11a. no 6 in r1c1

The key. Very hard to find though simple enough when you see it.
12. "45" on n1 (remembering h7(2)r12c3): 1 innie r3c1 + 8 = 2 outies r4c23
12a. = [4]+[48] or [8]+{79}
12b. must have 8 -> no 8 in common peer r3c3

13. 15(3)r2c1: {159/267/456} all blocked by h7(2)r12c3 = {16/25}
13a. {348} blocked by r3c1 = (48)
13b. = {168/249/258/357}
13c. 6 in {168} must be in r3c3 -> no 6 in r2c12
13d. 4 in {249} must be in r2c1 -> no 9 in r2c1

14. Hidden single 6 in c1 -> r9c1 = 6. Placed for D/

Forgot about this when I wrote the intro to the puzzle about "nothing harder than Killer pairs."
15. h7(2)r12c3 = {16} or Combined cage 7(2)r12c3+h13(2)r3c12 = {25}+[49], ie, must have 4 or 6, 1 or 9
15a. -> [46/91] blocked from 10(2)n1
15b. 10(2)n1 = [82]/{37}(no 1,4,6,9)

16. Hidden single 6 in c2 -> r6c2 = 6 ->r6c9 = 8.
16a. r6c2 = 6 -> r5c23 = 12 = [39/48] only permutations
16b. no 1 in 9(2)n9

17. Hidden single 9 in c1 -> r8c1 = 9

18. 8 in n4 only in c3: locked for c3
18a. 12(2)r9c3 = [39/75]
18b. r9c3 = (37) and 41(8)r6c3 must have both 3 & 7 -> r7c4 = (37)

Finally moving away from c123
19. 11(3)n8: {137} blocked by r7c4 = (37)
19a. = {128/245}(no 3,7) = 5/8
19b. must have 2, 2 locked for n8 and r9

20. 16(3)n8: {358} blocked by 5/8 in 11(3)
20a. = {178/349/457}
20b. 4 in {349} must be in r8c5 -> no 3 in r8c5

21. 3 in n8 only in r7: locked for r7

22. "45" on n9: 2 innies r7c89 = 11 = {29/56}(no 1,7,8)

23. r89c7 = 11 (cage sum) = [29]/{38/47}(no 1,5)

24. 1 in n9 only in 14(3) = {149/158/167}(no 2,3)

25. 2 in D\ only in n1 in 15(3): 2 locked for n1
25a. -> h7(2)r12c3 = {16} only: both locked for n1, c3 and 16(4) -> no 1,6 in r1c56
25b. no 8 r1c1

On from there.
Cheers
Ed
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