SudokuSolver Forum

I messed aound with some cage patterns and noticed that this one messed up SS rating because of its remote cage. I'll post V2 (or more fitting V1.5) on Sunday which has an SS score of 2.0+.

Assassin 112


Note the remote cage 22(4) at R19C19

3x3::k:5632:2561:5378:2563:2563:2563:2310:5383:5632:2561:2561:5378:5378:4621:2310:2310:5383:5383:5138:6163:6163:6163:4621:3351:3351:3351:4634:5138:5138:4893:3358:4621:3358:5409:4634:4634:5138:4893:4893:1831:3358:2345:5409:5409:4634:5165:5165:4893:1831:5169:2345:5409:3380:3380:5165:5165:2104:2104:5169:2875:2875:3380:3380:4927:4927:2625:3138:5169:3138:5445:4166:4166:5632:4927:2625:2625:3138:5445:5445:4166:5632:

Solution:

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

SS Score: 1.33
Estimated rating: (Hard) 0.75

Very enjoyable Afmob. I think (hard) 0.75 is about right.
Clearly there was nothing on TV here in Vancouver this evening

Many thanx.

As Frank said: very enjoyable. Thanks, Afmob!

Took me long enough to be the first for a walkthrough but here it is:

Walkthrough A112



EDIT: correction made in step 7h. Thanks, Andrew.

There is so much going on in so many different places that I think it's hard to keep a clean walkthrough for this one. I hope this one wasn't too messy.

Cheers,
Nasenbaer

Many thanks Afmob for a nice (gentle this time) puzzle.Took me about 25-30 minutes,perfect for a Friday evening.I'ld rate it about the same as The Times "deadly" killers...about 0.5+ ??



In c5 r159={124}
Innies of r1289 -> r28c5=9={36}
r3c159=8 -> r3c5=5 > r2c5=6 -> r4c5=7
And it comes out pretty quickly now.



Regards

Gary

Here is V2 with a SS rating that's totally of the charts.
But don't worry! Take a closer look (and have a calculator nearby ) to spot its weakness.

Assassin 112 V2


Note the remote cage 22(4) at R19C19

3x3::k:5632:2561:5378:2563:2563:2563:2310:5383:5632:2561:2561:5378:5378:4621:2310:2310:5383:5383:5906:5906:6164:6164:4621:2583:2583:5145:5145:5906:4124:6164:3358:4621:3358:2583:5666:5145:5906:4124:4124:1831:3358:2345:5666:5666:5145:5165:5165:4124:1831:5169:2345:5666:3380:3380:5165:5165:2104:2104:5169:2875:2875:3380:3380:4927:4927:2625:3138:5169:3138:5445:4166:4166:5632:4927:2625:2625:3138:5445:5445:4166:5632:

Same solution as V1.

SS Score: 2.49
Estimated rating: (Easy) 1.25 - 1.25

I don't know how easy V2 is supposed to be? But using a very ingenius algebraic trick I'm able to crack it in 4 quick steps:

_________________
ADYFNC HJPLI BVSM GgK Oa m

Indeed it is! Nice way of looking at this move (your step 3), which an automated solver would probably pick up by analyzing all possible permutations.

It would be interesting to know whether this is the move Afmob intended when giving the puzzle a relatively low 1.25. I would personally rate your step 3 as a little harder than this (maybe around the 1.5 level), because it's a non-obvious move of its type. However, Afmob tends to consistently rate puzzles 1 category lower than I do, so I guess your move could be the "weakness" that Afmob was referring to.

I missed udosuk's ingenious step, so had to resort to somewhat more complex moves, otherwise my initial solving path was very similar to his (what else?). Therefore, I've chosen to speed things up and just post a modified copy of his initial steps, with my alternative highlighted in blue:


Last but not least, thanks for the puzzle, Afmob! Hopefully, Richard is listening and will be able to fix the problem with SS not finding that important hidden cage...

_________________
Cheers,
Mike

Congratulations for finding the weakness of V2! Mike is right, this move helps to crack my killer. My initial estimated rating might be a bit low since I also used the same Killer triple as udosuk. The important move (in my case step 2c) can be applied in an easier way which justifies a 1.25 rating, I think:

A112 V2 wt snippet:

1. C456
a) Innies C5 = 7(3) = {124} locked for C5
b) Innies R1289 = 9(2) = {36} locked for C5
c) 20(3) = 9{38/56} because R8C5 = (36) -> 9 locked for C5
d) Innies N5 = 16(2) = {79} -> R4C5 = 7, R6C5 = 9
e) 24(3) = {789} -> 7 locked for R3

2. C123 !
a) ! Killer triple (789) locked in 21(3) + R34C3 for C3
-> 21(3) can only have one of (789) @ R12C3 -> R2C4 <> 4,5,6
b) 7 locked in R123C3 @ C3 for N1
c) ! Innies+Outies N1: 33 = R23C4 + R45C1+R4C3 - R1C1: R1C1 <> 9 because
R23C4 @ N2 <= 17 and R45C1+R4C3 @ N4 <= 24
[alternative: IOD N14: 4 = R23C4 - (R1C1+R6C12) -> R1C1 <> 9 because
R6C12 = 1{2/3} blocked by Killer pairs (12,13) of 16(4)]

By the way, when you score A112 V1 and V2 with the default SS options you get the following results -
V1: 0.92 SudokuSolver spots the hidden cage.
V2: 1.37. SudokuSolver finds udosuk's cracking move.

Those scores are pretty close to our rating, so SudokuSolver's rating is right after all.

Yep, the way Afmob put the cracking move is much more straight forward than mine.

Thanks for the nice puzzle!

_________________
ADYFNC HJPLI BVSM GgK Oa m

I'm still struggling with those "continental" 1s in A111 so after doing SOK1 Variant yesterday I did A112 today.

I'll rate it at 0.75. I note Gary's slightly lower rating and agree that after the simple opening steps it's straightforward but there's still a reasonable amount of work which I feel is probably better done using elimination solving which is why I haven't rated this puzzle lower.

Here is my walkthrough. My solution path is fairly similar to Nasenbaer's but I'll post it anyway.

Prelims

a) R56C4 = {16/25/34}, no 7,8,9
b) R56C6 = {18/27/36/45}, no 9
c) R7C34 = {17/26/35}, no 4,8,9
d) R7C67 = {29/38/47/56}, no 1
e) 10(3) cage in N1 = {127/136/145/235}, no 8,9
f) 21(3) cage at R1C3 = {489/579/678}, no 1,2,3
g) R1C456 = {127/136/145/235}, no 8,9
h) 9(3) cage at R1C7 = {126/135/234}, no 7,8,9
i) 21(3) cage in N3 = {489/579/678}, no 1,2,3
j) R3C234 = {789}, locked for R3
k) R678C5 = {389/479/569/578}, no 1,2
l) 19(3) cage in N7 = {289/379/469/478/568}, no 1
m) 10(3) cage at R8C3 = {127/136/145/235}, no 8,9
n) 21(3) cage at R8C7 = {489/579/678}, no 1,2,3
o) 13(4) cage at R6C8 = {1237/1246/1345}, no 8,9

1. 45 rule on C5 3 innies R159C5 = 7 = {124}, locked for C5

2. R3C678 = {256/346}, no 1, 6 locked for R3
2a. Killer pair 3,5 in R3C5 and R3C678, locked for R3

3. 45 rule on N5 2 innies R46C5 = 16 = {79}, locked for C5 and N5, clean-up: no 2 in R56C6

4. R234C5 = {369/378/567}
4a. 6,8 only in R2C5 -> R2C5 = {68}

5. 45 rule on R1289 2 innies R28C5 = 9 = [63], R3C5 = 5, R4C5 = 7 (step 4), R67C5 = [98], clean-up: no 2 in R3C678 (step 2), no 5 in R7C3, no 3 in R7C7
5a. Naked triple {346} in R3C678, locked for R3

6. R1C456 = {127} (only remaining combination), locked for R1 and N2
6a. Naked pair {34} in R23C6, locked for C6 and N2, clean-up: no 5,6 in R56C6, no 7 in R7C7
6b. Naked pair {89} in R23C4, locked for C4
6c. Naked pair {18} in R56C6, locked for C6 and N5, clean-up: no 6 in R56C4
6d. 7 in R3 locked in R3C23, locked for N1
6e. 6 in N5 locked in R4C46, locked for R4

7. Killer pair 2,4 in R56C4 and R5C5, locked for N5

8. 21(3) cage at R1C3 = {489} (only remaining combination), 4 locked in R12C3, locked for C3 and N1
8a. 10(3) cage in N1 = {136/235}, 3 locked for N1
8b. Naked quad {4789} in R12C3 + R3C23, locked for N1

9. 45 rule on R12 2 remaining innies R1C19 = 13 = [58], no 5,8 in R9C19, clean-up: no 2 in 10(3) cage in N1 (step 8a)
9a. R1C19 = 13 -> R9C19 = 9 = {27/36}, no 1,4,9
9b. 10(3) cage in N1 = {136} -> R1C2 = 6, R2C12 = {13}, locked for R2 and N1 -> R3C1 = 2, R3C9 = 1, R2C6 = 4, R1C7 = 3, R2C7 = 2 (cage sum), R3C6 = 3, clean-up: no 9 in R7C6, no 7 in R9C9 (step 9a)
9c. Naked pair {46} in R3C78, locked for N3 -> R1C8 = 9, R1C3 = 4
[I then spotted that R3C2 cannot be 7 because that would force UR in R23C34 for 8,9 but I don’t use UR]

10. 13(4) cage at R6C8 = {1237/1246/1345}
10a. 1 locked in R67C8, locked for C8
10b. R7C8 = 1 (hidden single in N9), clean-up: no 7 in R7C34

11. 45 rule on N6 1 remaining outie R7C9 = 5, R2C89 = [57], clean-up: no 3 in R7C3, no 6 in R7C67
11a. 13(4) cage at R6C8 = {1345} (only remaining combination) -> R6C89 = {34}, locked for R6 and N6, clean-up: no 3,4 in R5C4

12. Naked pair {25} in R56C4, locked for C4 and N5 -> R7C34 = [26], R4C46 = [36], R5C5 = 4, R7C6 = 7, R7C7 = 4, R1C456 = [712], R3C78 = [64] , R6C89 = [34], R9C5 = 2, clean-up: no 7 in R9C1 (step 9a)

13. Naked pair {39} in R7C12, locked for N7 -> R9C1 = 6, R9C9 = 3

14. 12(3) cage in N8 = {129} (only remaining combination) -> R8C46 = [19], R9C46 = [45]

15. 21(3) cage at R8C7 = {579} (only remaining combination) -> R89C7 = [79], R9C8 = 8, R4C89 = [29], R5C89 = [76], R8C89 = [62], R8C3 = 5, R9C23 = [71], R4C3 = 8, R23C3 = [97], R2C4 = 8, R3C24 = [89], R56C3 = [36], R8C12 = [84],

16. R7C12 = {39} = 12 -> R6C12 = 8 = [71]

and the rest is naked singles