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Assassin 124



Hopefully I have fixed the PS code problem.
SSR: 1.40

your PS code doesn't seem to work in SumoCue or Sudoku Solver.
This one is better i think.

I think the problem for Frank's code is just a missing colon at the end.

Anyway nice puzzle. I've solved it but no time to write a walkthrough yet.

_________________
ADYFNC HJPLI BVSM GgK Oa m

Thanks Frank for this fun Killer though I'm a bit puzzled about SudokuSolver's rating.

By the way, the PS Code that Frank gave was correct (though the last : is missing but it's not needed), but he just forgot to reduce the size of the text font, so not all of the code was visible. But when you mark the whole message and copy it to a text file you can see the full code.

A124 Walkthrough:

1. C123
a) Innies C12 = 12(2) = {57} -> R9C2 = 5, R1C2 = 7
b) Cage sum: R1C3 = 1, R9C3 = 2
c) 13(3) <> 9
d) 14(2): R5C1 <> 9
e) Innies+Outies C1: -2 = R5C2 - R46C1 -> R46C1 <> 2 (IOU @ N4)
f) 2 locked in 13(3) @ C1 for N1 -> 13(3) = 2{38/56}
g) 16(3) <> {367} because (36) is a Killer pair of 13(3)
h) Innies C1 = 16(3) <> 9 because R5C1 = (568) and {169} blocked by Killer pair (19) of 16(3)
i) 9 locked in 16(3) @ C1 for N7 -> 16(3) = 9{16/34}
j) 7 locked in Innies C1 = 7{18/45} for N4 since {367} blocked by Killer pair (36) of 16(3)
k) Innies C1 = 16(3): R46C1 <> 5,8

2. C123 !
a) 7 locked in 21(3) @ N7 = {678} because 5,9 only possible @ R8C4
-> R8C4 <> 7 and CPE: R8C12 <> 6,8
b) 14(2): R5C2 <> 8
c) R6C1 <> 1 since it sees all 1 of N7
d) ! Outies N7 = 17(2+1): R6C2 <> 1,8,9 since 10 <= R6C1+R8C4 <= 15
e) 18(4) = 7{128/146/236} because R6C1 = (47) -> R6C1 = 7
f) 1 locked in 17(4) @ N4 for R4 -> 17(4) = 1{268/349}
g) ! Killer pair (69) locked in 17(4) + R5C2 for C2
h) 18(4) = {1278} -> R6C2 = 2, R8C2 = 1, R7C2 = 8
i) 16(3) = {349} locked for C1
j) 13(3) = {256} locked for C1+N1
k) R5C1 = 8 -> R5C2 = 6
l) 21(3) = {678} -> R8C4 = 8

3. R12345
a) Innies R1234 = {89} locked for C5+45(9)
b) 19(3) = 9{37/46}
c) Grouped X-Wing 9 locked in 19(3) + R34C5 for R34
d) Hidden Single: R2C2 = 9 @ C2
e) 8 locked in 18(3) @ C3 = 8{37/46} -> R2C4 = (67)
f) 9 locked in 12(2) @ R5 = {39} locked for R5+N6
g) 9 locked in 11(2) @ N3 = {29} locked for R1+N3
h) 10(3) = 1{36/45} -> 1 locked for C9+N3

4. C789
a) Innies C89 = 15(2) = {69} -> R1C8 = 9, R9C8 = 6
b) Cage sum: R1C7 = 2, R9C7 = 9
c) R5C8 = 3, R5C9 = 9
d) Innies C9 = 12(2) = [48/75/84]
e) 17(4) = {1457} -> 7 locked for C8+N9; CPE: R4C8 <> 4,5
f) 14(3) @ N9 = {248} -> R9C9 = 8; 4 locked for C9+N9
g) 17(3) = {359} since R78C7 = (135) -> R8C6 = 9; {35} locked for C7+N9
h) 22(4) = {2578} -> R4C9 = 7, R4C8 = 2; {58} locked for C8+N3
i) 10(3) = {136} locked for N3
j) 14(3) = {347} because R23C7 = (47) -> R2C6 = 3; 4 locked for C7

5. R6789
a) R5C7 = 1, R6C8 = 4, R6C9 = 5
b) Innies R6789 = 9(2) = {36} locked for C5
c) 15(3) = {168} because R6C67 = (168) -> 1 locked for C6

6. N2
a) 18(4) = {1458} since R1C456 = (4568) -> R2C5 = 1, R1C6 = 8; {45} locked for R1+N2
b) R2C9 = 6, R2C4 = 7
c) 18(3) = {378} -> R2C3 = 8, R3C3 = 3

7. Rest is singles.

Rating: 1.0. I used Killer pairs and some Outies analysis.

Here is my complete walkthrough. I don't use numerical ratings but personally I think it ought to be the simplest solving path possible. One big step followed by 3 short steps.

_________________
ADYFNC HJPLI BVSM GgK Oa m

Thanks Frank for an enjoyable puzzle.

Having gone through the posted walkthroughs I can see that my solving path wasn't the most direct but I'll post it anyway; some of my steps may be of interest.

I'll rate my walkthrough as Hard 1.0 although I'm not really sure how step 10a, my hardest one, should be rated.

I'm also surprised at the SS score of 1.40. I wonder what SS missed. I can't see anything in Afmob's, udosuk's or my walkthrough that would justify anything like that rating.

Here is my walkthrough

Prelims

a) R1C23 = {17/26/35}, no 4,8,9
b) R1C78 = {29/38/47/56}, no 1
c) R5C12 = {59/68}
d) R5C89 = {39/48/57}, no 1,2,6
e) R9C23 = {16/25/34}, no 7,8,9
f) R9C78 = {69/78}
g) R123C9 = {127/136/145/235}, no 8,9
h) 19(3) cage at R3C4 = {289/379/469/478/568}, no 1
i) 21(3) cage at R7C3 = {489/579/678}, no 1,2,3

1. 1,2 in R5 locked in R5C34567 for 45(9) cage -> no 1,2 in R3467C5

2. 45 rule on R1234 2 innies R34C5 = 17 = {89}, locked for C5 and 45(9) cage

3. 45 rule on R6789 2 innies R67C5 = 9 = {36/45}, no 7
3a. 7 in 45(9) cage locked in R5C34567, locked for R5, clean-up: no 5 in R5C89

4. 45 rule on C12 2 outies R19C3 = 3 = {12}, locked for C3, R1C2 = {67}, R9C2 = {56}
4a. 45 rule on C12 2 innies R19C2 = 12 = [75], R19C3 = [12], clean-up: no 4 in R1C78, no 9 in R5C1

5. 45 rule on C89 2 innies R19C8 = 15 = [69/87/96], clean-up: no 6,8,9 in R1C7, no 7 in R9C7

6. R123C9 = {127/136/145} (cannot be {235} which clashes with R1C7), 1 locked for C9 and N3

7. 45 rule on C9 3 innies R456C9 = 21 = {489/579/678}, no 2,3, clean-up: no 9 in R5C8
7a. 9 of {489} must be in R5C9 (R5C9 of {489} cannot be 4 or 8 because R5C89 = {48} clashes with R456C9)
7b. 8,9 of {579/678} must be in R5C9
7c. -> R5C9 = {89}, no 9 in R46C9, clean-up: no 8 in R5C8

8. 45 rule on C1 3 innies R456C1 = 16 = {169/178/358/367/457} (cannot be {259/268} which clash with R5C12 because no 2 in R5C1, cannot be {349} because R5C1 only contains 5,6,8), no 2
8a. 6 of {169/367} must be in R5C1 -> no 6 in R46C1

9. 2 in C1 locked in R123C1, locked for N1
9a. R123C1 = {238/256}, no 4,9
9b. R456C1 (step 8) = {169/178/457} (cannot be {358/367} which clash with R123C1), no 3
9c. 5,8 of {178/457} must be in R5C1 -> no 5,8 in R46C1

10. 2,5 in C1 locked in R123C1 + R5C1 -> either 5 in R5C1 or R123C1 = {256}
10a. R456C1 (step 9b) = {178/457} (cannot be {169} which clashes with R123C1 = {256}), no 6,9, 7 locked for C1 and N4, clean-up: no 8 in R5C2
10b. 9 in C1 locked in R789C1, locked for N7
10c. R789C1 = {169/349}, no 8

11. 7 in C3 locked in R78C3, no 7 in R8C4
11a. 21(3) cage at R7C3 = {678} (cannot be {579} because 5,9 only in R8C4), no 4,5,9, CPE no 6 in R8C1, no 6,8 in R8C2

12. 45 rule on N1 3 outies R2C4 + R4C12 = 11
12a. Min R4C12 = 3 -> max R2C4 = 8

13. 45 rule on N3 3 outies R2C6 + R4C89 = 12
13a. Min R4C9 = 4 -> max R2C6 + R4C8 = 8, no 8,9

14. 45 rule on N7 3 outies R6C12 + R8C4 = 17
14a. R8C4 = {68} -> R6C12 = 9,11 = [18/72/74], no 4 in R6C1, no 1,3,6,9 in R6C2
14b. R78C2 = 7,9 = [34/43/61/63/81], no 1 in R7C2
14c. 18(4) cage at R6C1 = [1278/1368/1467/2367]
14d. 6,8 must be in R7C2 (2,7 of {1278} must be in R6C12 so 8 must be in R7C2) -> R7C2 = {68}

15. Naked triple {678} in R7C23 + R8C3, locked for N7, clean-up: no 1 in R789C1 (step 10c)
15a. Naked triple {349} in R789C1, locked for C1 and N7 -> R8C2 = 1, R46C1 = [17], R5C1 = 8 (step 10a), R5C2 = 6, R5C9 = 9, R5C8 = 3, R7C2 = 8, R6C2 = 2 (step 14c)
15b. Naked pair {67} in R78C3, locked for C3 and 21(3) cage -> R8C4 = 8
15c. Naked triple {256} in R123C1, locked for N1
15d. R456C9 (step 7) = {489/579}, no 6
15e. R46C9 = [48/75/84], no 5 in R4C9

16. 8 in N1 locked in R23C3 -> 18(3) cage at R2C3 = {189/378/468}, no 2,5
16a. 1,6,7 only in R2C4 -> R2C4 = {167}

17. R67C5 = {36} (hidden pair in 45(9) cage at R3C5), locked for C5

18. R789C9 = {248/257/356} (cannot be {347} which clashes with R46C9)
18a. 7 of {257} must be in R9C9 -> no 7 in R78C9
18b. 8 of {248} must be in R9C9 -> no 4 in R9C9
18c. R123C9 (step 6) = {127/136} (cannot be {145} which clashes with R789C9), no 4,5

19. 1 in R9 locked in R9C456, locked for N8
19a. 17(4) cage in N8 = {1349/1457} (cannot be {1259} because 2,5 only in R8C5, cannot be {1367} which clashes with R7C5), no 2,6, 4 locked for N8
19b. 6 in R9 locked in R9C789, locked for N9

20. 45 rule on N9 3 outies R6C89 + R8C6 = 18
20a. Max R6C89 = 14 -> no 2,3 in R8C6
20b. 2 in N8 locked in R7C46, locked for R7
20c. R789C9 (step 18) = {248/257/356}
20d. 2 of {248} must be in R8C9 -> no 4 in R8C9
20e. 6,7,8 only in R9C9 -> R9C9 = {678}

21. 19(3) cage at R3C4 = {379/469}, no 2,5
21a. Grouped X-Wing for 9 in 19(3) cage at R3C4 and R34C5, no other 9 in R34
21b. R2C2 = 9 (hidden single in C2)

22. 45 rule on R9 2 innies R9C19 = 1 outie R8C5 + 6
22a. R9C19 cannot total 13 -> no 7 in R8C5
22b. R8C5 = {45} -> R9C19 = 10,11 = [37/46/38/47], no 9 in R9C1

23. R2C6 + R4C89 = 12 (step 13)
23a. R4C89 cannot total 5,7 or 8 -> no 4,5,7 in R2C6

24. 45 rule on R1 2 innies R1C19 = 1 outie R2C5 + 8
24a. Max R1C19 = 11 -> no 4,5,7 in R2C5
24b. R1C19 cannot total 10 -> R2C5 = 1, R1C19 = 9 = [63], R23C9 = {16} (step 18c) = [61], R2C4 = 7, clean-up: no 5 in R1C7, no 8 in R1C8

26. R1C78 = [29], R9C8 = 6 (step 5), R9C7 = 9

27. R1C6 = 8 (hidden single in R1), R1C45 = {45}, locked for N2, R34C5 = [98]

28. 17(4) cage in N8 (step 19a) = {1457} (only remaining combination) -> R8C5 = 5, R9C456 = {147}, locked for R9 and N8 -> R9C1 = 3, R9C9 = 8, R8C9 = 2, R7C9 = 4 (step 18), R78C1 = [94], R8C78 = [37], R78C3 = [76], R8C6 = 9, R46C9 = [75], R7C8 = 1, R6C8 = 4 (cage sum), R4C78 = [62], R567C7 = [185], R23C7 = [47]

29. R4C6 = 5 (hidden single in R4), R3C6 = 2 (cage sum)

and the rest is naked singles and a cage sum.

Assassin 124 v2



This version is courtesy of JSudoku.
SSR: 2.60

Nice v2 Frank!

No time for a full walkthrough, just a brief walkin including the trickiest steps for me:

[Edited: please refer to the complete walkthrough posted below.]

I'll be quite busy from now on, and will be participating less actively.

_________________
ADYFNC HJPLI BVSM GgK Oa m

That was a hard Killer! If I had spotted udosuk's step 1 then my wt would have been quite shorter and would have had a lower difficulty (around 1.5). Despite the length of my wt it was quite fun and I could make use of some nice Killer subsets.

How did you solve A124 V2, Frank?

A124 V2 Walkthrough:

1. C123
a) 4(2) = {13} locked for R9+N7
b) Innies C12 = 10(2) = [73/91]
c) Outies C12 = 7(2) = [43/61]
d) Outies N7 = 8(2+1) <> 7,8,9; R8C4 <> 6
e) 19(4): R78C2 <> 2 because R6C12 @ Outies N7 <= 7
f) 19(4) <> {1279} since it's blocked by R1C2 = (79)
g) Outies N7 = 8(2+1): R8C4 <> 5 because R6C12 >= 4
h) 12(3) <> 6,7 since 4{17/26} blocked by Killer pairs (46,47) of 13(2)
and {156/237} blocked by Killer pairs (27,56) of 16(3) @ C1
i) Outies N1 = 20(2+1) <> 1; R2C4 <> 2
j) Innies+Outies C1: -8 = R5C2 - R46C1 -> R4C1 <> 8 (IOU @ N4)

2. 45(9) + R5 !
a) Innies R1234 = 6(2) = {15/24}
b) Outies R1234 = 13(2) <> 1,2,3
c) 45(9) must have 3 -> 3 locked for R5
d) 9(2) <> 6
e) 10(2) <> 7
f) Killer triple (456) in each of Innies R1234 and Innies R6789 for 45(9) + C5
-> R5C34567 can only have one of (456)
g) ! Two of (456) in R5 must be in 9(2) and 10(2) -> Either 9(2) = {45} or 10(2) = {46}
-> 4 locked for R5
h) 4 locked in Outies R5 @ 45(9) for C5 = 19(4) = 9(2) + 10(2) = 4{159/258/267}
i) Hidden Killer pair (57) in R5C34567 for 45(9)+R5
j) Hidden Killer pair (57) in 9(2) for R5 -> 9(2) <> 1,8

3. C789
a) Innies C9 = 10(3) <> 8,9
b) 10(2): R5C8 <> 1,2
c) 11(2) <> 8
d) Outies C89 = 11(2) <> 1,3,8; R9C7 <> 2
e) Innies C89 = 9(2) <> 9; R1C8 <> 1,6,8

4. R1234
a) 13(2) + 9(2) = 4{279/369/567} -> 4 locked for R1
b) 14(4) = 12{38/56} -> 1,2 locked for N2
c) Innies R1234 = 6(2): R4C5 <> 4,5

5. C123
a) Innies C1 = 17(3) <> 3,5 since {359} blocked by Killer pair (39) of 12(3)
b) Innies C1 = 17(3): R46C1 <> 2 because R5C1 <> 6,9
c) 9(2): R5C2 <> 4
d) 3 locked in 12(3) @ C1 for N1 -> 12(3) = 3{18/45}
e) Outies N7 = 8(2+1): R6C2 <> 2 because (24) is a Killer pair of 9(2)

6. C123 !
a) 19(4) <> {1369} since (39) is a Killer pair of Innies C12
b) 14(3) <> 5{18/36} because (56,58) are Killer pairs of 16(3) @ N7
c) Killer triple (789) in each of 16(3) and 14(3) for N7
-> 19(4) can only have one of (789)
-> 19(4) = {1459/1468/1567/3457}
d) Outies N7 = 8(2+1): R8C4 <> 4 since R6C12 @ 19(4) >= 5
e) 24(4) <> 58{29/47} because (58) is a Killer pair of 19(4)
f) ! Hidden Killer triple (258) in R5C2 for C2 since each of 24(4) and 19(4)
can only have one of (258) -> R5C2 <> 7
g) 9(2): R5C1 <> 2
h) 2 locked in 16(3) @ C1 for N7 -> 16(3) = 2{59/68}
i) 7 locked in R45C1 @ C1 for N4

7. C123 !
a) ! Killer quad (1235) in 24(4) + R59C2 for C2
-> 19(4) can only have one of (1235) @ C2
-> 19(4) <> {3457} since (35) would be @ C2
b) 19(4) = 1{459/468/567} <> 3 -> 1 locked for R6+N4
c) Killer triple (789) in R1C2 + 19(4) for C2 -> 24(4) can only have one of (789) @ C2
d) ! 24(4): R23C2 <> 2 because only possible placements are {26}[79] / {27}[96] / {29}[76]
- {26}[79] -> 13(2) = [94] -> R1C2 = R4C2 = 9
- {27}[96] -> Innies C1 = [971] -> 9(2) = [72] -> Two 2s in C2
- {29}[76] blocked by Killer pair (69) of 19(4)
e) 2 locked in 16(3) @ N1 for C3 -> 16(3) = 2{59/68}
f) Hidden Single: R9C3 = 1 @ C3
g) Outie C12 = R1C3 = 6
h) Cage sum: R1C2 = 7, R9C2 = 3
i) 24(4) = 69{18/45} because (67) only possible @ R4C12 -> 6 locked for R4+N6

8. 45(9) + R5
a) Hidden Single: R5C1 = 7 @ C1, R5C2 = 2 @ C2
b) 2 in 45(9) locked in Innies R1234 = 6(2) = {24} -> R4C5 = 2, R3C5 = 4
c) 7 in 45(9) locked in Innies R6789 = 13(2) = {67} locked for C5+45(9)
d) 6 in R5 locked in 10(2) = {46} locked for N6

9. C789
a) 9(2) = {45} locked for R1+N3
b) Innies C89 = 9(2) = {45} locked for C2
c) R5C8 = 6, R5C9 = 4
d) 17(4) = 5{129/138/237} -> R6C9 = 5
e) Innie C1 = R4C9 = 1
f) Outies N3 = 10(1+1) = {37}

10. N2+C789
a) 14(4) = {1238} locked for N2 -> 2 also locked for R1
b) R2C6 = 7 -> R23C7 = 3(2) = {12} locked for C7+N3
c) Hidden Single: R1C9 = 9 @ R1
d) 18(3) @ N1 = {369} -> 3,6 locked for C9+N3
e) Hidden Single: R6C8 = 2 @ N6
f) Outie N9 = R8C6 = 8
g) 15(3) = {348} -> 3,4 locked for C7+N9
h) R9C8 = 5 -> R9C7 = 6, R9C5 = 9

11. N578
a) 20(4) = {2459} since (13) only possible @ R8C7 -> R8C7 = 5, {24} locked for R9+N8
b) 14(3) = 4{19/37} -> 4 locked for C3+N7
c) R9C1 = 8 -> R78C1 = 8(2) = {26} locked for C1+N7
d) 19(4) = {1459} -> R8C2 = 9, R7C2 = 5, {14} locked for R6+N4
e) 14(3) = {347} -> R8C4 = 3
f) R4C1 = 9
g) 16(3) = 7{18/36} because R6C3 = (38) -> 7 locked for C4; R6C4 <> 8
h) 19(3) = 6{49/58} -> R3C4 = 6

12. N1
a) 24(4) = {1689} -> R4C2 = 6, {18} locked for C2+N1

13. Rest is singles.

Rating: 1.75 - (Hard) 1.75. I used Killer triples, Killer quads and a (small?) contradiction move.

I've written a complete walkthrough for A124v2:


Except for the extra-tricky step 1 the rest should be quite short and elegant enough.

_________________
ADYFNC HJPLI BVSM GgK Oa m