(Unofficial) Assassin 97

[Afmob]

Here is the first Killer I've created and published so far (other ones were of rating 0.75 and 3.0) .

Once you get to make the first placement you have probably cracked it but will you reach that point? The lucky number "45" might help you.

(Unofficial) Assassin 97 (UA 97)



3x3::k:38403840:56355125:4614:4614:46145635:5635:56355125:5125:51253593:48832325386356573593:48832325386356575668:488331104905:4905:5657:5932:5668:4883:48832609:4905:5657:5657:5932:5668:5668312833875932:593254404418:4418:441831421599:5440:544034033142:3142

(Estimated) Rating: SudokuSolver rates this one 0.96 but it can be solved in an easier way.

[Andrew]

Congratulations Afmob on posting your first Killer! I guess that makes me the only one of the current regular walkthrough posters who hasn't posted one. It will probably stay that way because I think I'm just a solver.

Let's hope someone posts another puzzle, or variant on Afmob's one, so that Afmob has something to solve. Preferably only about a 1.5. I'm still working on J-C's V2 and only making very slow progress; two steps today so I haven't quite ground to a halt.

[Nasenbaer]

Wow, that was a very interesting puzzle. Thanks, Afmob!

It took me a lot longer than I had thought. Somehow I always got sidetracked. So here is my walkthrough, up to the first placements. The rest was solved so fast that I couldn't remember what was next.

Be warned: it's the way I solved it, with all the the things I might not have needed, so it's not very nice.

Walkthrough UA097

1. Preliminaries
1a. n14: 13(2) = {49|58|67} -> no 1,2,3
1b. n5: 13(2) = {49|58|67} -> no 1,2,3
1c. n25: 9(2) = {18|27|36|45} -> no 9
1d. n25: 15(2) = {69|78} -> no 1,2,3,4,5
1e. n36: 7(2) = {16|25|34} -> no 7,8,9
1f. n58: 10(2) = {19|28|37|46} -> no 5
1g. n7: 6(2) = {15|24} -> no 3,6,7,8,9
1h. n9: 11(2) = {29|38|47|56} -> no 1
1i. n56: 19(3) = {289|379|469|478|568} -> no 1
1j. n7: 21(3) = {489|579|678} -> no 1,2,3

2. 45 on c5: r89c5 = h9(2) = {18|27|36|45} -> no 9

3. 45 on r89: r8c37 = h10(2) = {19|28|37|46} -> no 5

4. 45 on c1234: r89c4 = h15(2) = {69|78} -> no 1,2,3,4,5

5. 45 on c6789: r89c6 = h6(2) = {15|24} -> no 3,6,7,8,9

6. cage placement in n8: 13(3): no 6,7,8 in r9c5
6a. -> (step 2) no 1,2,3 in r8c5
6b. 17(3): no 3 -> {359|368} removed

7. 45 on c1 (1 innie, 1 outie): r1c1 - r7c2 = 3 -> no 1,2,3 in r1c1, no 7,8,9 in r7c2

8. 45 on c9 (1 innie, 1 outie): r7c8 - r1c9 = 3 -> no 1,2,3 in r7c8, no 7,8,9 in r1c9

9. 45 on c9 (3 outies): r1c78 + r7c8 = 21 -> no 1,2,3 in r1c7, no 1,2 in r1c8

10. n14: 14(3): {149|257} removed, blocked by 6(2) in c1

11. n56: 19(3): no 2,3,5 in r5c7, blocked by 15(2) in c6

12. 45 on n8: r7c456 = h15(3) = {159|249|348|357} (other combinations blocked by h15(2) and h6(2) -> no 6
12a. -> no 4 in r6c5
12b. 13(3): {139} removed, blocked by h15(3) -> no 9
12c. -> h15(2): no 6 in r8c4
12d. 17(3): {458} removed, blocked by h15(3) -> no 5 -> no 4 in r8c5
12e. -> h6(2): no 1 in r9c6
12f. -> h9(2): no 4,5 in r9c5
12g. 13(3): {247} removed, blocked by 17(3)
12h. h15(3): {249} removed, blocked by 17(3) -> no 2
12i. -> no 8 in r6c5

13. c5: 13(2): {67} removed, blocked by 13(3), 10(2) and h9(2) -> no 6,7
(explanation: 13(3), 10(2) and h9(2) each need one of {6789} -> only one of {6789} left for 13(2) -> {67} removed)
13a. -> 13(3) @ N2: {148} removed, blocked by 13(2)

14. 45 on r1: r1c456 = h12(3) = {129|138|147|156|237|246|345}

15. no 3 in r7c4, can be seen by all 3's in n7

16. 45 on n8 (3 outies): r7c37 + r6c5 = 10 -> no 9 in r7c37 and r6c5
16a. -> no 1 in r7c5

17. n8: h15(3): no 9 in r7c46

18. 45 on n9 (1 outie, 2 innies): r7c89 - r7c6 = 9 -> no 7,8 in r7c6, no 9 in r7c8, no 1,9 in r7c9
18a. -> (step 8) no 6 in r1c9
18b. -> (step 9) no 3 in r1c8

19. n78: 12(3): {147} removed, blocked by 6(2) and 21(3)
19a. -> no 7 in r78c3
19b. -> no 3 in r8c7

20. n8: 17(3): {269} removed, blocked by h15(2) -> 7 locked in r8c45 for 17(3), r8 and n8
20a. -> h15(2): no 8 in r8c4
20b. -> r8: h10(2): no 3 in r8c3
20c. -> no 3 in r6c5
20d. -> 13(3): {157} removed, {148|346} removed, blocked by 17(3), h9(2) -> 2 locked in r9c56 for 13(3), r9 and n8
20e. -> 17(3): {278} removed -> no 8 in r8c5
20f. -> h15(3): {357} removed
20g. -> no 4 in r8c1
20h. -> no 9 in r8c9, no 4 in r9c9
20i. -> no 1 in r9c5, no 4 in r9c6

21. c5: 10(2): {37} removed, blocked by h9(2)
21a. 8 locked in 13(2) and 10(2) for c5
21b. -> 13(3): {238} removed, {256} removed, blocked by h9(2)

22. n78: 12(3): {237} removed

23. n47: 22(4): {1489|2569|2578|4567} removed, blocked by 6(2)

24. n8: h15(3): no 4 r7c6

25. n89: 13(3): {247} removed
25a. h15(3) and 17(3) restrict placement in 13(3): no 1,5,8 in r7c7, no 6 in r8c7
25b. -> no 4 in r8c3

26. n78: 12(3): {345} removed
26a. h15(3) and 17(3) restrict placement in 12(3): no 1,4,5,8 in r7c3, no 8 in r7c4
26b. -> h15(3): no 4 in r7c5
26c. -> no 6 in r6c5

27. c5: killer pair {89} locked in 13(2) and 10(2) for c5
27a. -> 13(3): {139} removed

28. n7: {138} in 12(3) only possible with r7c4 = 1 -> {579} in 21(3) -> {24} in 6(2) -> can't

place 1 in r7c12 -> {138} removed from 12(3) -> no 8 in r8c3, no 3 in r7c3
28a. -> no 2 in r8c7
28b. -> n89: 13(3): {256} removed

29. n7: killer pair {12} in 6(2) and r78c3 -> no 1,2 in r7c12
29a. 3 locked in r7c12 for 22(4), r7 and n7
29b. -> 22(4): {1579|1678|2479} removed -> no 1

30. single: r9c5 = 3, r9c46 = [82], r8c456 = [764], r67c5 = [19]
...

Solution:
654921873
371548296
928376451
245689317
716253984
893417625
432195768
589764132
167832549

EDIT:Corrections in blue. Thanks to Afmob!
EDIT2: Removed tiny text, added solution. Thanks for the reminder, Andrew!
EDIT3: corrections added, thanks to Andrew

I hope you learned from my mistakes...

Cheers,
Nasenbaer

[sudokuEd]

[edit: forgot to say congratulations to Afmob on your first killer!! ]

(Estimated) Rating: SudokuSolver rates this one 0.96 but it can be solved in an easier way

Not by me! I'd call this one a hard 1.0 rating since it took a long time to find my break-through. Not the type of move I look for very early. But admittedly, not that difficult.

This walk-through gets straight to the break-through first placements and is then basically just a very long clean-up. [edit: simplified the early steps to get to the first placement quicker Edit 2 to get step 7 clearer (thanks Andrew)]

unofficial Assassin 97 (uA97)

Prelims
i. n1
13(2) no 123

ii. n2
9(2) no 9
15(2) = {69/78}

iii. n3
7(2) no 789

iv. n5
13(2) no 123
19(3) no 1
10(2) no 5

v. n7
6(2) = {15/24}
21(3) no 123

vi. n9
11(2) no 1

1. "45" c1234: 2 innies r89c4 = h15(2) = {69/78}

2. "45" c6789: 2 innies r89c6 = h6(2) = {15/24} = [4/5..]

3. "45" c5: 2 innies r89c5 = h9(2) = {18/27/36}(no 459) ({45} clashes with h6(2)r89c6)

steps 4-6 deleted: not needed. Hope i got the clean-up OK later.

7. 17(3)n8 = {179/269/467}(no 3,5,8) ({278}=[872] clashes with r89c4 = [87] in h15(2)r89c4);{359/368} blocked by r8c6;{458} has no {45} in r8c45)
7a. = [971/962]/{67}[4]
7b. no 8 in r8c4 -> no 7 in r9c4 (h15(2))
7c. r8c5 = {67} -> r9c5 = {23}(h9(2))
7d. no 1 in r9c6 (h6(2)r89c6)

8. 13(3)n8 = {238/256}(no 4,9) ({346}=[634] blocked by h9(2)r89c5)
8a. = [832/625]
8b. r9c4 = {68} -> r8c6 = {79} (h15(2)r89c4)
8c. r9c6 = {25} -> r8c6 = {14} (h6(2)r89c6)

9. 13(3)n8 = 2{38/56} -> 2 locked for r9 & n8
9a. no 4 in r8c1
9b. no 9 in r8c9
9c. no 8 in r6c5

10. 17(3)n8 = {179/467} (only valid combos)
10a. = 7{19/46}
10b. 7 locked for n8 & r8
10c. no 4 in r9c9
10d. no 3 in r6c5

11. "45" r89: 2 innies r8c37 = h10(2) = {19/28/46} (no 35)

12. 3 in n7 only in r7: 3 locked for r7

13. r9c5 = 3 (hidden single n8)
13a. no 8 in r8c9
13b. no 7 in r6c5

14. r8c5 = 6 (h9(2)r89c5)
14a. no 4 in r67c5
14b. no 5 in r9c9
14c. no 4 in r8c37 (h10(2)r8c37)
14d. no 7 in 13(2)n5

15. r9c4 = 8 (naked single)
15a. no 3 in r8c9
15b. no 1 in 9(2)n2
15c. no 2 r6c5

16. r8c4 = 7 (h15(2)r89c4
16a. no 2 in 9(2)n2

(note: should have done r89c6 now. Not too long a wait)
16. 10(2)n5 = {19}: both locked for c5

17. 13(2)n5 = {58}: both locked for c5 & n5
17a. no 7 in r3c6
17b. no 4 in r3c4

18. 13(3)n2 = {247}: all locked for n2

19. r9c6 = 2 (hidden single n8)
(2 in c4 is now only in 12(3)n4: but didn't seem to help a great deal so left out)

20. r8c6 = 4 (h6(2)r89c6)
20a. no 7 in r9c9

21. naked triple {159} in r7c456: all locked for r7

22. r8c8 = 3 (hidden single n9)
22a. r9c78 = {45}: both locked for n9 & r9

23. r89c9 = [29] (haven't included all the clean-up as singles coming up shortly do it better)

24. r89c1 = [51]

25. r9c23 = {67}: both locked for n7 & r8c2 = 8 (cage sum)

26. r8c37 = [91] (naked singles)
26a. no 4 in 13(2)n1
26b. no 6 in 7(2)n3

27. 12(3)n7 must have 9 -> r7c34 = [21] (only permutation)

28. r67c5 = [19]

29. r7c6 = 5 -> r7c7 = 7 (cage sum)

30. r7c89 = {68} = 14 -> r56c9 = 9 = {45} ({18} blocked by 8 in r7c89)
30a. {45} locked for c9 & n6
30b. no 23 in r3c7

31. "45" c9: r7c8 - 3 = r1c9
31a. -> r7c8 = 6, r1c9 = 3
31b. r7c9 = 8

32. naked pair {34} in r7c12: locked for 22(4) cage
32a. r56c1 = {69/78}(no 2) = [6/7..]

33. "45" c1: r7c2 + 3 = r1c1
33a. r1c1 = {67}

34. Killer pair {67} in r156c1: both locked for c1

35. 18(3)n3 must have 3 = {69/78}[3](no 1245) = [6/7..]
35a. Killer pair {67} in r1c1 & 18(3)
35b. both locked for r1
35c. Killer pair {67} in 18(3)n3 & r23c1: both locked for n3

36. "45" r1: r1c456 = h12(3)
36a. = [921] (only permutation)

37. 18(3)n3 = [873] (only permutation)

rest is hidden and naked singles & clean-up

Cheers
Ed

[Jean-Christophe]

I usually do not rate puzzles, but I personally did not found it really hard. I would even say it's easy if you're familiar with Kakuro.

1. n8:
a. Innies @ c1234 -> r89c4 = 15 = {69|78}
b. Innies @ c6789 -> r89c6 = 6 = {15|24} = {4|5..}
c. Innies @ c5 -> r89c5 = 9 <> {45} = {18|27|36}
d. 13/3 @ r9c456: Min r9c4 = 6 -> Max r9c56 = 7 -> r9c5 <> {678} = {123}
e. h9/2 @ r89c5 -> r8c5 = {678}
f. 17/3 @ r8c456: Min r8c45 = {67} = 13 -> Max r8c6 = 4, r8c6 = {124}
g. h6/2 @ r89c6 -> r9c6 = {245}
h. 13/3 @ r9c456: r9c6 <> {13} -> r9c4 <> 9 = {678}
i. h15/2 @ r89c4 -> r8c4 = {789}
j. 17/3 @ r8c456 <> [962] because it would conflict with h15/2 @ r89c4 = [96] (two 6)
k. 17/3 @ r8c456 <> {782} because it would conflict with h15/2 @ r89c4 = {78} (two {78})
l. 17/3 @ r8c456 = [971|764] -> 7 locked @ r8c45 for n8, r8
m. hidden cages -> 13/3 @ r9c456 = [625|832] -> 2 locked for n8, r9

2. r89
a. Innies @ r89 -> r8c37 = 10 <> {37} (step 1l)
b. 6/2 & 21/3 @ n7 -> no 3
c. 3 @ r8 locked @ r8c89 for n9
d. r9c5 = 3 (HS @ r9), 13/3 -> r9c46 = [82]
e. 17/3 @ r8c456 = [764]

3. c5
a. 10/2 @ r67c5 = {19} (NP @ c5)
b. 13/2 @ r45c5 = {58} (NP @ n5, c5)
c. 13/3 @ r123c5 = {247} (NT @ n2)

4. r78
a. r7c456 = NT {159} @ r7
b. h10/2 @ r8c37 = {19|28}
c. 13/3 @ r7c67+r8c7 = {148|157|256} (no {39})
d. h10/2 @ r8c37 -> r8c3 <> 1
e. 12/3 @ r7c34+r8c3 = {1(29|38)} (no {4567})
f. -> r7c4 = 1, r7c56 = [95], r6c5 = 1

5. n79, c9
a. 21/3 @ n7 -> no 1
b. 1 @ n7 locked @ 6/2 @ r89c1 = {15} (NP @ n7, c1)
c. 21/3 @ r89c2+r9c3 = {8(49|67)} -> r8c2 = 8
d. 12/3 -> r78c3 = [29], 13/3 & h10/2 @ r8c37 -> r78c7 = [71], r89c1 = [51]
e. 21/3 @ n7 -> r9c23 = {67} (NP @ n7, r9)
f. 11/2 @ r89c9 = [29], r8c8 = 3, r9c78 = {45} (NP @ n9)
g. r7c89 = {68} = 14, 23/4 @ n69 -> r56c9 = 9 = {45} (NP @ n6, c9)
h. Innies @ c9 -> r17c9 = 11 = [38], r7c8 = 6

6. c6, n36
a. 19/3 @ r5c67+r6c6 = {379} -> 7 locked @ r56c6 for n5, c6
b. 15/2 @ c6 = {69} (NP @ c6), r56c6 = {37} (NP @ n5, c6), r5c7 = 9
c. r12c6 = {18} (NP @ 20/4) -> r2c78 <> {18}
d. 7/2 @ c7 -> no 8
e. 8 @ n6 locked @ 22/5 -> r3c8 <> 8
f. -> 8 @ n3 locked @ 18/3 -> r1c78 = [87], r12c6 = [18]
g. r4c9 = 7 (HS), r23c9 = NP {16} @ n3
h. 20/4 -> r2c78 = [29], 7/2 @ r34c7 = [43], r3c8 = 5, r9c78 = [54], r6c7 = 6
i. 9/2 @ r34c4 = [36], 15/2 @ r34c6 = [69], r23c9 = [61]
j. r56c4 = {24} = 6, 12/3 -> r5c3 = 6, r12c4 = [95]
...

[Jean-Christophe]

Let's hope someone posts another puzzle, or variant on Afmob's one, so that Afmob has something to solve. Preferably only about a 1.5.

I joined two cages and here is one rated 1.41 by SS

3x3::k:4096:4096:4096:6915486930784105:6915:6915:69154869:4869:4869:4113:4105:6163:4429:44294940:4940:5401:4113:4105:6163:4429:44294940:4940:5401:4113:5668:6163:4646:464636255401:5676:5668:6163:6163:46463625:5401:5401:5676:5668:5668236033875676:567623685186:5186:518654463135236828915446:5446


If it's too easy, here is one rated 1.88 by SS:

3x3::k:5376:5376:5376:4099:4356:435733343337:4099:4099:4099:4356:4357:4357:4357:43696675:5197:5197:4356:5964:5964:5913:43696675:5197:51975964:5964:5913:4369:4900:6675387826015913:6188:4900:6675:667526095913:5913:6188:4900:490033844411:4411:6188:618844164674:4674:4674:441128874416:441639152630:2630

Edited: removed V3 which was too hard, even for Afmob
Sorry for posting too many killers, I really didn't know if these were "hard enough" for Afmob & other regular members.
Also added picture of the one rated 1.88

[Afmob]

Thanks JC for posting another variant! My wt is for the first one (with the picture). I might tackle V2 (SS Rating 1.88) but I certainly won't battle the V3 since it needs lots of T&E.

But I don't know about posting so many variants. There was a discussion started by Ed about this before in the A53 thread.

UA97 V1.5 Walkthrough:

1. N8
a) Innies C1234 = 10(2) <> 5; R9C4 <> 8
b) Innies C5 = 7(2) = [34/43/52/61]
c) Innies C6789 = 14(2) = [68/86/95]
d) 11(3): R9C4 <> 6,7 because R9C6 >= 5
e) Innies C1234 = 10(2): R8C4 <> 3,4
f) Hidden Killer triple (345) in R8C5 for 20(3) -> R8C5 <> 6
g) Innies C5 = 7(2) <> 1

2. R789 !
a) Innies R89 = 8(2) <> 4,8,9; R8C7 <> 1
b) Innies+Outies N7: -15 = R7C4 - R7C12 -> R7C4 = (12)
-> R7C12 = 9{7/8} -> 9 locked for R7+N7+22(4)
c) 12(2) <> 3
d) Outies N7 = 7(2+1) -> R56C1 <> 6,7,8
e) 15(2): R6C5 <> 6
f) Innies N8 = 14(3): R7C6 <> 1,2,3,8 because 7 <= R7C45 <= 10
g) Innies N8 = 14(3) <> 4 because {248} blocked by Killer pair (24) of 11(3)
h) ! Innies N8 = 7{16/25} because {158} blocked by Killer pair (58) of Innies C6789
-> 7 locked for R7+N8
i) Innies+Outies N7: -15 = R7C4 - R7C12 -> R7C4 = 2
j) Innies N8 = 14(3) = {257} -> R7C5 = 7, R7C6 = 5
k) 11(3) = {146} -> R9C4 = 1, R9C5 = 4, R9C6 = 6

3. R789
a) Innies C1234 = 10(2) = {19} -> R8C4 = 9
b) R8C6 = 8, R8C5 = 3
c) Naked pair {89} locked in R7C12 for R7+N7
d) 12(2) = {57} locked for C1+N7
e) 9(3) @ R8C2 = {234} because R9C23 = (23) -> R8C2 = 4, {23} locked for R9+N7
f) 21(3) = 7{59/68} -> 7 locked for N9
g) 13(3) = {256} -> R7C7 = 6, R8C7 = 2
h) 9(2) = {18} -> R8C9 = 1, R9C9 = 8
i) 22(4) @ N9 = {3469} because R7C89 = (34) -> {69} locked for C9+N6

4. C19
a) Innies+Outies C9: 2 = R7C8 - R1C9 -> R1C9 = 2, R7C8 = 4
b) 12(3) = 2{19/37/46} <> 5,8
b) Innies+Outies C1: 5 = R7C2 - R1C1 -> R1C1 = (34)
c) Killer pair (34) locked in R1C1 + 22(4) for C1
d) 16(3) @ R1 <> 1 because R1C1 = (34)
e) 12(3) <> 3,7 because (37) is a Killer pair 16(3) @ R1
f) 16(3) @ R1 <> 9 because (49) is a Killer pair of 12(3)
g) 16(3) @ R1 must have 3 xor 4 and R1C1 = (34) -> R1C23 <> 3,4

5. N25
a) 15(2) = {78} -> R6C5 = 8
b) 1 locked in R123C5 for N2
c) R8C3 = 6 -> R7C3 = 1
d) 17(4) = 2{348/357/456} <> 9 -> 2 locked for C3
e) R9C3 = 3, R9C2 = 2
f) 18(3): R5C3 <> 4 because R56C4 <= 13

6. R123
a) Innies R1 = 17(3) <> {359} since it's a Killer pair of 16(3)
b) Innies R1 = 17(3): R1C5 <> 9 because 1 only possible there
c) 27(4) = 9{378/468/567} -> 9 locked for R2+N1
d) R2C23 <> 8 because it sees all 8 of R1

7. C1234 !
a) ! Innies+Outies C12: 6 = R16C3 - R2C2
-> R6C3 <> 9 because R1C3 <> 6 since 9 in R6C3 forces 9 in R2C2 (step 6c)
b) Killer pair (89) locked in 24(5) + R7C2 for C2
c) Hidden Single: R2C3 = 9 @ N1
d) Killer pair (36) locked in 18(3) + 17(4) for C4
e) Hidden Killer pair (36) in R2C2 for 27(4) -> R2C2 = (36)
f) 16(3) @ R1 = 5{38/47} since {367} blocked by R2C2 = (36) -> 5 locked for R1+N1
g) ! Innies+Outies N1: -4 = R4C1 - (R23C2+R3C3) -> R4C1 <> 6 since there is no 10(3) combo for R23C2+R3C3
h) 16(3) @ R2C1 = 6{19/28} -> 6 locked for N1
i) R2C2 = 3, R1C1 = 4

8. R123
a) 16(3) @ R1 = {457} -> 7 locked for R1+N1
b) 12(3) @ N3 = {129} -> 1,9 locked for R1+N3
c) R1C5 = 6 -> 12(3) @ N1 = {156} -> {15} locked for C5+N2
d) Hidden Single: R3C6 = 9 @ N2, R2C6 = 2 @ N2
e) R1C6 = 3 -> 19(4) @ R1 = {2368} -> R2C7 = 8, R2C8 = 6
f) 19(4) @ R3 = {1459} -> 1 locked R4, 5 locked for C7
g) 27(4) = {3789} -> R2C4 = 7, R1C4 = 8

9. N5
a) 14(3) = {347} -> R5C7 = 3, {47} locked
b) 18(3) = 7{38/56} -> R5C3 = 7

10. Rest is singles.

Rating: (Hard?) 1.25. I used Killer pairs and some Innies+Outies analysis.

[gary w]

Re UA97 V1.

I found this one fairly easy.Took me 35 minutes to complete which was OK,long enough for a Saturday evening!!If we rate the Times "deadly" killers as about 0.5 I'ld say this one is about 0.75.



r89c4=15 r89c5=9 r89c6=6 r8c37=10
combo analysis on the two cages in N8 with the above constraintsshow only 2 possibilities for the 17(2) cage and the 13(2) cage viz;
764,832 or 971,625 in either case the 17(2) cage contains a 7.Therefore
r8c3<>3 (because r8c37=10) so in N7 3 is in r7.
Therefore r8c456=764,r9c456=832.
So r8c8=3,r9c78={45} etc etc and it's a mop-up now.



Thanks to Afmob for the puzzle.

Regards

Gary

[gary w]

I enjoyed 97 v1.5 too.



As for v1 it was relatively straightforward to show that in N8 the numbers are;
275
938
146

After this it got tricky.Could place r1c1=3/4 and r1c9=2
In N2 1 is in the 12(3) cage ..nowhere else in c5
The 27(4) cage N12must contain a 9 so in N1 9 is at r2c23
Also in N1 1 is in r2/3
By using x-wings on the 1s in r123 can now show that in N2 9<>12(3) cage.So 11(2) cage N5={29}.
Still some work to do but it's cracked now.Took me some while to see the x-wing

so I'ld rate it about 1.25.

Regards

Gary

[Afmob]

This Killer was truly devilish. It took me really long to find the important moves.

I think that UA97 V2 can be solved in a "normal" 1.75 way but I think my step 6a (the most difficult one) is more a contradiction chain than combo analysis, so I tend to rate this Assassin 2.0.

I'll take a rest (in solving) this week , 3 Killers is more than enough.

UA97 V2 Walkthrough:

1. R789
a) Innies C1234 = 12(2) <> 1,2,6
b) Innies C5 = 6(2) = {15/24}
c) Innies C6789 = 15(2) = {69/78}
d) 15(3) <> 9 because 9{15/24} clashes with Innies C5
e) Innies C1234 = 12(2): R8C4 <> 3
f) Innies C6789 = 15(2): R8C6 <> 6
g) 18(3) = 9{18/27/45} -> 9 locked for R8+N8
h) Innies R89 = 11(2) <> 1,2
i) 11(2): R9C9 <> 2
j) 10(2): R6C5 <> 1

2. C19 + N789
a) Innies+Outies C1: -5 = R7C2 - R1C1 -> R1C1 <> 4,5; R7C2 = (1234)
b) Innies+Outies C9: 7 = R7C8 - R1C9 -> R1C9 = (12), R7C8 = (89)
c) 13(3) @ C9: R1C78 <> 1,2 because R1C9 = (12)
d) Innies+Outies N7: -7 = R7C4 - R7C12
- R7C1 <> 7 and R7C1 <> 1,2,3,4 because R7C2 <= 4
- R7C4 <> 7,8 because R7C12 <= 13
e) Innies+Outies N9: -7 = R7C6 - R7C89
- R7C9 <> 7 and R7C9 <> 8,9 because R7C6 <= 8
- R7C6 <> 1 because R7C89 >= 9
f) 17(3) @ N9 <> 1 because 9 only possible @ R7C7
g) Innies N89 = 19(4): R7C5 <> 8 because R7C8 = (89)
h) 10(2): R6C5 <> 2

3. R1+C45
a) Innies R1 = 11(3) <> 9
b) Innies R1 = 11(3) <> 8 because R1C9 = (12) blocks {128}
c) Innies C5 = 6(2) + 12(2) = h18(4) = {1359/1458/2349/2457}
d) 17(3) <> 5 because 5{39/48} blocked by Killer pairs (35,45) of h18(4)
e) 17(3) <> 1 because (179) is a Killer triple of h18(4)
f) 1 locked in R789C5 for N8
g) 13(3) @ N8 <> 9 because 1 only possible @ R7C3

4. R789 !
a) Hidden Killer pair (36) in Innies N8 + 15(3) for N8 since none of them can have both
-> 15(3) <> {258} and Innies N8 = 12(3) <> {147}
b) ! Innies = 26(5): R7C5 <> 1 because
- <> 17{369/459/468} because 7 only possible @ R7C5
- <> 189{26/35} since they clash with Innies N8 = 12(3) = 1{38/56}
c) 1 locked in Innies C5 = 6(2) = {15} locked for C5+N8
d) 18(3) = 9{18/45}
e) Innies C1234 = 12(2) <> 7
f) Innies C6789 = 15(2): R9C6 <> 8
g) 2 locked in Innies N8 = 2{37/46} -> 2 locked for R7
h) 10(2) <> 9

5. C15
a) 12(2) <> 7
b) 17(3) <> 3 because {368} blocked by Killer pair (38) of 12(2)
c) Innies+Outies C1: -5 = R7C2 - R1C1 -> R1C1 <> 7

6. R789 + C5 !
a) ! Innies R789 = 26(5) <> 2 since
- <> 27{359/368/458} because 7 only possible @ R7C5
- <> {23489} since it clashes with Innies N8 = 2{37/46}
- <> {12689} because it forces Innies N8 = [327] -> Using Innies+Outies N7
Innies R789 = [91286] -> no combo for 17(3) @ N9
- <> {24569} because it forces Innies N8 = [327] -> 17(3) @ N9 = 7{46}
-> Innies R789 not possible since R7C7 would have no 4,6

b) 10(2) <> 8
c) 2 locked in 17(3) @ C5 = 2{69/78} locked for N2
d) ! Innies R789 = 26(5): R7C5 <> 4,6 because
- 7 of 17{369/459/468} must be @ R7C5
- {13589} -> R7C5 can only be 3
- {34568} -> Innies N8 <> {246} because it can't have 4 without 6 and vice versa

7. C5 + R789
a) 10(2) = {37} locked
b) 12(2) = {48} locked for C5+N5
c) 17(3) @ C5 = {269} locked for N2
d) Innies N8 = {237} because R7C5 = (37) -> 3,7 locked for R7+N8
e) Innies C1234 = 12(2) = {48} locked for C4+N8
f) R8C6 = 9, R9C6 = 6
g) 8(2): R8C1 <> 2
h) 11(2): R8C9 <> 5

8. R123 !
a) Innies R1 = 11(3) = [164/524]
-> R1C6 = 4, R1C4 <> 3,7
b) 21(3) = 7{59/68} -> 7 locked for R1+N1
c) 3 locked in 13(3) @ R1 for N3 -> 13(3) = 3{19/28}
d) 17(4): R2C6 <> 8 because 3 only possible there
e) Hidden Single: R3C6 = 8 @ N2
f) ! 16(4): R1C4 <> 5 because
- 5{128/146/236} blocked by Killer pairs (56,58) of 21(3)
- {1357} blocked by R2C6 = (1357)
g) R1C4 = 1, R1C9 = 2, R1C5 = 6
h) 21(3) = {579} -> R1C1 = 9; 5 locked for N1
i) 13(3) @ R1 = {238} -> 8 locked for N3
j) 17(4) = 14{39/57} -> 1 locked for R2+N3

9. R789
a) 2 locked in 10(3) = 2{17/35}
b) 9 locked in 17(3) @ N7 for R9 = 9{17/26/35} <> 4,8
c) Hidden pair (48) in R9C49 for R9 -> R9C9 = (48)
d) 11(2) = [38/74]
e) Killer pair (37) locked in 10(3) + R8C9 for N9
f) Innies R89 = 11(2): R8C3 <> 4,8
g) Hidden pair (48) locked in R8C47 for R8 -> R8C7 <> 5,6
h) Innies R89 = 11(2) = [38/74]
i) Naked pair (48) locked in R8C7+R9C9 for N9
j) R7C8 = 9

10. N9
a) 17(3) <> 5 because (48) only possible @ R7C7
b) R7C7 = 6
c) 17(3) = 6{38/47}
d) 24(4) = 69{18/45} because 39{48/57} blocked by R8C9 = (37) and R9C9 = (48)
-> 6 locked for C9+N6; R56C9 <> 1,5

11. N36
a) 9 locked in 17(3) = 9{17/35} -> R4C9 = (13)
b) Hidden Single: R3C8 = 6 @ N3, R3C7 = 4 @ N3
c) 23(4) = {2489} -> R4C6 = 2, R4C7 = 9
d) 17(4) = {1457} -> {57} locked for R2
e) 10(3) = 2{17/35} -> R5C7 = 2
f) Hidden Killer pair (78) in 24(4) for N6 since 23(5) can't have both
-> 24(4) = {1689} -> R7C9 = 1, 8 locked for R9+N6

12. N79
a) 17(3) @ N9 = {368} -> R7C6 = 3, R8C7 = 8
b) R7C2 = 4
c) 13(3) = {238} -> R7C3 = 8, R7C4 = 2, R8C3 = 3
d) R7C1 = 5
e) 19(4) = 45{28/37}; R6C1 <> 8

13. N14
a) 16(4) = {1348} -> R2C4 = 3, R2C3 = 4, R2C2 = 8
b) 15(3) = {159} -> R5C3 = 1, {59} locked for C4+N5
c) R3C4 = 7

14. Rest is singles.



9 5 7 1 6 4 3 8 2
6 8 4 3 2 5 1 7 9
3 1 2 7 9 8 4 6 5
4 7 5 6 8 2 9 1 3
8 3 1 9 4 7 2 5 6
2 9 6 5 3 1 7 4 8
5 4 8 2 7 3 6 9 1
1 6 3 4 5 9 8 2 7
7 2 9 8 1 6 5 3 4

Rating: (Hard) 1.75 - 2.0. I used some heavy Innies/Outies combo analysis.

Edit: As shown by JC, this Killer can be solved in an easier way, so my rating is way off (though it fits my wt).

[gary w]

Yes,the last version of 97 was horrible!!What surprised me though was that all the variants,including this one,were solvable in roughly the same way.. combo work on r789 and,especially N8,which then leads to restrictions in c5,especially N2

Like Afmob..a rest is called for!

Regards

Gary

[Jean-Christophe]

UA97 V2 is not that hard if you spot the right In/outies:

1. n8
a. Innies @ c5 -> r89c5 = 6 = {15|24}
b. Innies @ c6789 -> r89c6 = 15 = {69|78}
c. Max r8c56 = {59} = 14; 18/3 -> Min r8c4 = 4
d. Innies @ c1234 -> r89c4 = 12 = [93] | {48|57}
e. h6/2 @ r89c5 -> r9c45 <> 6/2 -> r9c6 <> 9 = {678}
f. h15/2 @ r89c6 -> r8c6 = {789}
g. 18/3 @ r8c456 = {9(18|27|45)} -> 9 locked for n8, r8
h. Innies @ r89 -> r8c37 = 11 = {38|47|56}

2. n789: Three In/outies with 7 on r7!
a. In/outies @ n9 -> r7c89-r7c6 = 7
b. r7c6 <> r7c8 -> r7c9 <> 7, r7c6 <> r7c9 -> r7c8 <> 7
Explanation: since all 3 cells are in the same row, neither r7c8 nor r7c9 may hold 7 because it would force the other 2 cells to hold the same value, which is not possible.
c. In/outies @ n7 -> r7c12-r7c4 = 7 -> r7c12 <> 7 (same reason)
d. In/outies @ n8 (using h11/2 @ r8c37) -> r7c37-r7c5 = 7 -> r7c37 <> 7 (same reason again)

3. r7, n8
a. 7 @ r7 locked @ r7c456 -> locked for n8
b. -> h15/2 @ r89c6 = [96]
c. Innies @ n8 -> r7c456 = 12 = {7(14|23)}
d. h6/2 @ r89c5 = {1|4..} -> h12/3 @ r7c456 <> {147} = {237} (NT @ r7, n8)
e. h6/2 @ r89c5 = {15} (NP @ c5, n8)
f. h12/2 @ r89c4 = {48} (NP @ c4)

4. c5
a. 10/2 @ r67c5 = {37} | [82] = {3|8..}
b. 12/2 in r45c5 = {39|48} = {3|8..}
c. 10/2 & 12/2 = Killer NP {38} @ c5
d. 6 @ c5 locked @ r123c5 -> locked for n2, 12/3 = {6(29|47)}
e. 8 @ n2 locked @ r123c6 -> locked for c6

5. c19
In/outies @ c9 -> r7c8-r1c9 = 7 -> r7c8 = {89}, r1c9 = {12}
In/outies @ c1 -> r1c1-r7c2 = 5 -> r7c2 = {14}, r1c1 = {69}

6. Three In/outies with 7 again
a. Since r7c456 = {237} -> r7c12 = 9|10|14
b. Max r7c12 = [94] = 13 -> r7c4 <> 7 = {23}
c. 13/3 @ n78 = {238|247|256|346} (no {19}) -> r7c3 = {4568}, r8c3 = {34567}
d. h11/2 @ r8c37 -> r8c7 = {45678}
e. r7c89 = 9|10|14 = [81|91|95|86] -> r7c9 = {156}
f. Innies @ n9 -> r7c89+r78c7 = 24 = {69(18|45)} ({4578} can't work with r7c89)
g. -> r7c9 = {15}, r8c7 = {468}
h. 9 locked @ r7c78 for n9, r7
i. 6 locked @ r78c7 for n9, c7
j. 11/2 @ r89c9 = {38|47}
k. 2 @ n9 locked @ 10/3 = {2(17|35)}

7a. h11/2 @ r8c37 -> r8c3 = {357}
b. 13/3 @ n78 = {2(38|47|56)} -> r7c4 = 2, r78c3 = [83|47|65]
c. r7c12 = 9/2 = [81|54]
d. Since r7c6 = {37} -> r7c89 = 10|14 = [91|95] -> r7c8 = 9, r7c9 = {15}
e. In/outies @ c9 -> r1c9 = 2

8a. 10/2 @ r67c5 = {37} (NP @ c5)
b. 12/2 @ r45c5 = {48} (NP @ n5, c5)
c. 17/3 @ r123c5 = {269} (NT @ n2)
d. Innies @ r1 -> r1c456 = 11 = [164]
e. r1c1 = 9, 21/3 -> r1c23 = {57} (NP @ r1, n1), r1c78 = NP {38} @ n3
f. In/outies @ c1 -> r7c12 = [54], r7c9 = 1, r7c6 = 3
g. 10/2 @ r67c5 = [37]
h. 13/3 @ n78 -> r78c3 = [83], r78c7 = [68], r89c4 = [48], r89c5 = [51]
i. 11/2 @ r89c9 = [74], r8c8 = 2
j. r1c78 = [38], r9c78 = [53]
k. 24/4 @ c9 -> r56c9 = {68} (NP @ n6, c9), r4c9 = 3 (HS @ c9), r23c9 = {59} (NP @ n3)
l. 17/4 @ n23 = {1457}, r2c6 = 5, r2c78 = NP {17} @ r2, n3, r23c9 = [95], r3c78 = [46], r23c5 = [29]
...

Edit: continued WT

[Afmob]

JC's move step 2d was really neat and helped to make placements quite early. I was surprised that SudokuSolver didn't spot that. Maybe that means more work for Ed and RCB .

Judging from JC's continued wt, UA97 V2 would be of rating (hard) 1.25 like UA97 V1.5 with steps 2d and 6f being the important/cracking moves.

[Andrew]

I also found uA97 hard going (I guess my "killer brain" had partly switched off!) until I realised that hidden cages R89C4 and R89C6 can be used for clashes with R8C456 and R9C456, rather than just for clean-up eliminations. Then I restarted and found it a straightforward puzzle. I've included comments about interesting moves I spotted while I was struggling.

After completing this puzzle I got "sidetracked" into solving J-C's V1.5 and have only gone through the posted walkthroughs for Afmob's puzzle today.

Based on my re-worked solution I'll rate Afmob's uA97 at 1.0.

Here is my walkthrough. Edit: extra CPE added for step 24.

Prelims

a) R34C3 = {49/58/67}, no 1,2,3
b) R34C4 = {18/27/36/45}, no 9
c) R34C6 = {69/78}
d) R34C7 = {16/25/34}, no 7,8,9
e) R45C5 = {49/58/67}, no 1,2,3
f) R67C5 = {19/28/37/46}, no 5
g) R89C1 = {15/24}
h) R89C9 = {29/38/47/56}, no 1
i) 19(3) cage at R5C6 = {289/379/469/478/568}, no 1
j) 21(3) cage in N7 = {489/579/678}, no 1,2,3

1. 45 rule on C1234 2 innies R89C4 = 15 = {69/78}

2. 45 rule on C6789 2 innies R89C6 = 6 = {15/24}

3. 45 rule on C5 2 innies R89C5 = 9 = {18/27/36} (cannot be {45} which clashes with R89C6), no 4,5,9

[Initially I found this puzzle hard because I was using steps 1, 2 and 3 for elimination but not realising that they also cause clashes and force direct one-to-one relationships between combinations in R8C456 and R9C456. I’m not sure whether the direct one-to-one relationships provide any extra clashes; probably not for this puzzle. The remaining steps come from a complete restart.]

4. R9C456 = {139/148/238/256/346} (cannot be {157/247} because R9C56 = {15/24} clash with R89C6 = {15/24}), no 7, clean-up: no 8 in R8C4 (step 1), no 2 in R8C5 (step 3)
4a. R9C4 = {689} -> no 6,8 in R9C5, clean-up: no 1,3 in R8C5 (step 3)

5. 45 rule on N8 3 innies R7C456 = 15 = {159/348/357} (cannot be {168/267} which clash with R89C4, cannot be {249} which clashes with R9C456, cannot be {258/456} which clash with R89C6), no 2,6, clean-up: no 4,8 in R6C5

6. R8C456 = {179/467} (cannot be {269/278} because R8C45 = [78/96] clashes with R89C4 = [78/96], cannot be {458} because 4,5 only in R8C6), no 2,5,8, clean-up: no 1 in R9C5 (step 3), no 1,4 in R9C6 (step 2)
6a. 7 locked in R8C45, locked for R8 and N8, clean-up: no 3 in R6C5, no 4 in R9C9

7. R9C456 (step 4) = {238/256}, no 9, clean-up: no 6 in R8C4 (step 1)
7a. 2 locked in R9C56, locked for R9, clean-up: no 4 in R8C1, no 9 in R8C9

8. 45 rule on R89 2 innies R8C37 = 10 = {19/28/46}, no 3,5

9. 3 in N7 locked in R7C123, locked for R7, clean-up: no 4,8 in R7C456 (step 5), no 2,6,7 in R6C5

10. Naked triple {159} in R7C456, locked for R7 and N8 -> R8C456 = [764], R9C456 = [832], clean-up: no 1,2 in R34C4, no 7 in R45C5, no 3,8 in R8C9, no 5,7 in R9C9

11. Naked pair {19} in R67C5, locked for C5, clean-up: no 4 in R45C5

12. Naked pair {58} in R45C5, locked for C5 and N5, clean-up: no 4 in R3C4, no 7 in R3C6
12a. Naked triple {247} in R123C5, locked for N2

13. R8C8 = 3 (hidden single in R8), R9C78 = 9 = {45} (only remaining combination), locked for R9 and N9 -> R89C9 = [29], R89C1 = [51]

14. Naked pair {67} in R9C23, locked for N7, R8C2 = 8 (cage sum), R8C3 = 9, R8C7 = 1, clean-up: no 4 in R34C3, no 6 in R34C7
14a. R8C3 = 9 -> R7C34 = 3 = [21], R7C56 = [95], R6C5 = 1, R7C7 = 7 (cage sum)

15. Killer pair 4,5 in R34C7 and R9C7, locked for C7

16. 45 rule on C1 1 innie R1C1 = 1 outie R7C2 + 3 -> R1C1 = {67}

17. 45 rule on C9 1 outie R7C8 = 1 innie R1C9 + 3 -> R1C9 = {35}

18. R1C789 = {369/378/459/567} (cannot be {189/279/468} because R1C9 only contains 3,5), no 1,2
18a. R1C9 = {35} -> no 3 in R1C7, no 5 in R1C8

[At this stage I originally had two powerful in-line IOUs from applying the 45 rule on N7 and N9. There was also the use of overlapping split-cage R7C3467 and hidden-cage R7C456. I had also used combined cage R4589C5 for clashes in C5. Unfortunately they were all removed when the earlier steps were simplified.]

19. R7C12 = {34} = 7 -> R56C1 = 15 = {69/78}, no 2,3,4

20. Killer pair 6,7 in R1C1 and R56C1, locked for C1

21. Naked pair {68} in R7C89, locked for 23(4) cage at R5C9 -> no 6,8 in R56C9
21a. R7C89 = 14 -> R56C9 = 9 = {45} (only remaining permutation), locked for C9 and N6 -> R1C9 = 3, R7C8 = 6 (step 17), R7C9 = 8, clean-up: no 2 in R3C7

22. R1C9 = 3 -> R1C78 = 15 = [69/87], no 4, no 9 in R1C7, no 8 in R1C8
22a. Killer pair 6,7 in R1C1 and R1C78, locked for R1

23. Killer pair 6,7 in R1C78 and R23C9, locked for N3
23a. Hidden killer pair 6,7 in R1C78 and R23C9 for N3 -> R23C9 = {16/17}, 1 locked for C9 and N3

24. 19(3) cage at R5C6 = {379} (only remaining combination, cannot be {289} because 2,8 only in R5C7), no 2,6,8, CPE no 3,9 in R5C4
24a. 7 locked in R56C6, locked for C6, clean-up: no 8 in R3C6

25. Naked pair {69} in R34C6, locked for C6
25a. Naked pair {37} in R56C6, locked for C6, N5 and 19(3) cage -> R5C7 = 9, clean-up: no 6 in R3C4, no 6 in R6C1 (step 19)

26. Naked pair {18} in R12C6, locked for 20(4) cage at R1C6 -> R2C7 = 2, R2C8 = 9 (cage sum), R1C8 = 7, R1C7 = 8 (step 22), R1C1 = 6, R12C6 = [18], R4C7 = 3, R3C7 = 4, R3C8 = 5, R6C7 = 6, R4C9 = 7, R9C78 = [54], R3C4 = 3, R4C4 = 6, R12C4 = [95], R34C6 = [69], R23C9 = [61], clean-up: no 7 in R3C3, no 8 in R4C3, no 9 in R6C1 (step 19)
26a. R34C3 = [85], R1C3 = 4, R1C5 = 2, R1C2 = 5, R23C5 = [47], R2C1 = 3, R7C12 = [43], R45C5 = [85], R4C1 = 2, R4C8 = 1, R4C2 = 4, R3C12 = [92], R56C9 = [45], R56C4 = [24], R56C8 = [82], R56C1 = [78], R56C6 = [37], R6C23 = [93]

27. R56C4 = [24] = 6 -> R5C3 = 6

and the rest is naked singles

[azpaull]

Hey, glad to see there's still action here! (Still would love to see Ruud come back, recharged and ready to go.) I'm printing this out and will give it a try. Thanks, Afmob!