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Well, we've made it to three years of Assassins (on June 2)! So, in memory of our beginnings, back to a plain cage pattern (the X is only for uniqueness [edit: actually, I did use them, so an almost plain cage pattern). Ruud never experimented with diagonal or remote cages, zero cells etc. However, this puzzle would never have made it as a Ruud Assassin since Jsudoku makes a real hash of it. Here's the end part of the solver log from JS.In fact, it is just normal Assassin difficulty with at least one hard-for-me-to-see-but-no-tricks. Perfect! You might not think so if you can't find the key.

I tried something new to find this particular puzzle. Got sick of finding too-easy-for-an-anniversary possibles with this cage pattern so started just selecting ones that had an SSscore in the target range (1.0-1.50) but JSudoku's "Deduce All Moves" log showed it needed something harder than the "45" techniques. For one such possibility, JS missed a straight line killer quad. Too easy. But this one.....

As an experiment, I had a look at some other recent Assassins and many of them also make JS find interesting stuff (see this post about A150).

Assassin 157



SS(v3.3.0)score: 1.32


Cheers to my fellow assassins
Ed

Thanks for the anniversary Assassin, Ed! This one offered a lot of IOD moves and my first draft was nearly twice as long but after removing all unnecessary steps there was not much left.

A157 Walkthrough:

1. R6789 + D\
a) 3(2) = {12} locked for C1
b) Outies R9 = 4(2) = {13} -> R8C1 = 3, R8C9 = 1
c) R1C1 = 4 -> R1C2 = 1
d) 1 locked in R4C4+R5C5 @ D\ for N5
e) 9(2): R6C5 <> 5, R5C5 <> 8
f) 11(2) @ C6: R5C6 <> 7

2. R456 !
a) 12(3) <> 8,9; R34C2 <> 5,6,7 since R3C1 >= 5
b) Innies+Outies R6789: -8 = R5C5 - R6C46: R6C46 <> 8 (IOU @ N5)
c) Innies+Outies R6789: -6 = R5C4 - R6C56: R6C56 <> 6 (IOU @ N5)
d) Innies+Outies R6789: -6 = R5C6 - R6C45: R6C4 <> 6 (IOU @ N5)
e) Both 11(2): R5C46 <> 3,5
f) 9(2): R5C5 <> 3
g) ! Outies R6789 = 14(3) = {149/167/248} <> 5 because R5C46 <> 1,5 and [752] unplaceable since R6C4 = R6C5 = 4
h) Outies R6789 = 14(3): R5C5 <> 6,7 since 1 only possible there; R5C46 <> 2 since R5C5 = (12)
i) Both 11(2): R6C46 <> 9
j) Innies R6789 = 17(3) = 8{27/45} -> R6C5 = 8
k) Cage sum: R5C5 = 1

3. C123 !
a) Innies+Outies C123: 4 = R127C4 - R9C3 -> R9C3 <> 1
b) Hidden Single: R7C1 = 1
c) ! 12(3) @ N4: R4C2 <> 3 since 4 only possible there and [723] blocked by Killer pair (27) of 24(4)
d) R6C1 = 2, R4C2 = 4
e) Innie N1 = R1C3 = 8
f) 12(3) @ R1 = {138} -> R1C4 = 3, R2C4 = 1

4. R123
a) Outie N25 = R1C7 = 7
b) Outie N1235 = R4C8 = 5
c) Hidden Single: R3C8 = 1 @ R3 -> R3C9 = 8, R2C6 = 8 @ R2 -> R1C6 = 2
d) 11(2) = {56} -> R1C8 = 6, R1C9 = 5

5. R456
a) Innies R6789 = 9(2) = {45} -> R6C4 = 4, R6C6 = 5
b) Cage sum: R5C4 = 7, R5C6 = 6
c) Innies N4 = 8(2) = {17} -> R6C2 = 7, R6C3 = 1
d) 13(3) = {157} -> R7C3 = 7, R7C4 = 5
e) 21(4) = {2478} -> R8C3 = 4; {28} locked for C2+N7

6. N9
a) Hidden Single: R8C8 = 7 @ N9, R7C7 = 8 @ D\
b) 8(3) = {134} -> R9C9 = 3, R9C8 = 4

7. Rest is singles.

Rating: 1.25. I used IOU and small combo analysis.

I was not planning to post a wt for this great puzzle since the way I have solved it was similar to Afmob's wt and does not give something easier. However, Ed has convinced me to post a partial solving path that I send for step 3) that shows a funny aspect of the cage pattern (work on the twin cages 11(2) and some interesting interactions between 14(3) and 15(2) at C89).

Thanks for this nice killer Ed ; I think that others interesting aspects of this Assassin could be exploited by the others solvers (BTW, Ed, why don't you post your solving path ?)

Edit : thanks, Ed, for some corrections.


Partial Walkthrough A157

1)a) {12} locked for c1 at 3(2)
b) Outies for r9 : r8c1+r8c9=4 : r8c1=3, r8c9=1
c) r1c1=4 → r1c2=1
d) 1 locked for D\ and n5 at r4c4+r5c5
e) Outies for n25 : r1c3+r1c7=15 : {69/78}
f) IO for n1 : r4c2=r1c3-4 : r4c2=(2345)
g) Outies for n1235 : r4c2+r4c8=9 : r4c8=(4567)
h) r4c2<>5 since all combos of 12(3) are blocked by 5(2)=[41] → r4c8<>4
i) R5c5<>4 → r6c5<>5

2)a) Innies for r6789 : r6c4+r6c5+r6c6 = h17(3)
b) r6c4<>6 since r6c4=6 would force r6c5 to be equal to r5c6 (cage combinations of h17(3)
and 11(2) at r5c6) (in fact, one can use IOU, but I did not see it before I read Afmob's wt, so I did not
use it here)
c) For the same reason as for step b), r6c6<>6
d) r6c5<>6 since r6c5=6 would force r6c4 to be equal to r5c6 (cage combinations of h17(3)
and 11(2) at r5c6)
e) There is no 1,6 at h17(3) : combinations {278/359/458}
f) h17(3) <> {359} Like this : r6c5 must be 3 (no others candidates) → r5c5=6, and one of
r6c4+r6c6 must be 5 → one of r5c4+r5c6 must be 6 (cage combination for both 11(2))
and digits 6 would clash
→ h17(3) ={27/45}8
g) h17(3) ={27/45}8. But r6c5 and r6c4 (or r6c6) cannot sum to 9 (clash with 9(2)) so 8
of h17(3) must be at r6c5 : 9(2)=[18]

3)a) No 3 for both 11(2) at n5 since r6c5=8 : 3 is locked for r4/n5 at r4c456
→ r4c28=[27/45]
b) Outies for n5 : r3c4+r3c6 = h13(2) : no 1 (2,3, but 1 is the most important for the next steps)
c) Hidden single for r3 : r3c8=1 → (combinations for 14(3)) r3c9=(68))
d) Combinations for 15(2) at c9 = [69/78/96]
e) (i) 15(2)={69} → r3c9=8
(ii) 15(2) = [78] → r4c8=5 → (combination for 14(3)) r3c9=8
We deduce r3c9=8
f) r4c8=5 (14(3) combination) → r4c2=4 (step 1)g))
g) r1c3=8 (step 1)f), and r1c7=7 (step 1)e))
h) At n5 : 11(2)+11(2) must contain 4 and 5 : 11(2)+11(2) = {47} + {56} : No 2,9
→ We deduce from 2)f) that h17(3) = {458}

The puzzle is cracked

Thanks Ed for a challenging Anniversary Assassin!

As you will see from the comments in my walkthrough, I was stuck for a while, partly because I was trying to avoid two directional combination and permutations clashes in N5.

Then I eventually managed to find the key IOUs in N5. It's a neat cage pattern because outies for R6789 and innies for R6789 are obvious but IMHO outies-innies for R6789 are very hard to spot!

Once I'd found the key IOUs the rest was easy.

It should be noted that there is an alternative which gives the same result as the IOUs; CCCs were used in manu's walkthrough.

I'll rate A157 as Easy 1.25 although I was tempted to go higher because of the difficulty of spotting the key IOUs.

Here is my walkthrough. The later stages are possibly more optimised than many of my walkthroughs. That's because several times I had to rework after realising that I'd forgotten to do eliminations on the diagonals or spotted hidden singles that I ought to have been seen earlier.

Prelims

a) R1C12 = {14/23}
b) R1C89 = {29/38/47/56}, no 1
c) R56C4 = {29/38/47/56}, no 1
d) R56C5 = {18/27/36/45}, no 9
e) R56C6 = {29/38/47/56}, no 1
f) R67C1 = {12} locked for C1, clean-up: no 3,4 in R1C2
g) R67C9 = {69/78}
h) 8(3) cage in N9 = {125/134}, 1 locked for N9
i) 31(5) cage in N4 must contain 9, locked for N4

1. 45 rule on R9 2 outies R8C19 = 4 = [31], R1C1 = 4, placed for D\, R1C2 = 1, clean-up: no 7 in R1C89, no 7 in R5C6, no 5 in R6C5
1a. R8C1 = 3 -> R9C12 = 15 = {69/78}
1b. R8C1 = 1 -> R9C89 = 7 = [25/43/52], no 3 in R9C8

2. 45 rule on N5 2 outies R3C46 = 13 = {49/58/67}, no 1,2,3

3. 45 rule on N25 2 outies R1C37 = 15 = {69/78}
3a. 45 rule on N2 4 innies R12C46 = 14 = {1238/1247/1256/1346/2345}, no 9
3b. 1,4 of {1247} must be in R2C46 -> no 7 in R2C46

4. 45 rule on R1 3 remaining innies R1C456 = 14 = {239/257/356}, no 8

5. 45 rule on R1 2 outies R2C46 = 1 innie R1C5
5a. Min R2C46 = 3 -> min R1C5 = 3

6. 45 rule on N1 1 innie R1C3 = 1 outie R4C2 + 4, no 6,7,8 in R4C2

7. 45 rule on N3 1 innie R1C7 = 1 outie R4C8 + 2, R4C8 = {4567}

8. 45 rule on N1235 2 outies R4C28 = 9 = [27/36/45/54]
[No immediate eliminations but used later for clean-up.]

9. Min R1C3 = 6 -> max R12C4 = 6, no 6,7,8, no 5 in R2C4

10. Min R34C2 = 5 -> max R3C1 = 7
10a. Min R3C12 = 7 -> max R4C2 = 4 (because 12(3) cage cannot be {25}5), clean-up: no 9 in R1C3 (step 6), no 6 in R1C7 (step 3), no 4 in R4C8 (step 8)
10b. Min R3C1 + R4C2 = 7 -> no 5,6,7,8,9 in R3C2 (because 12(3) cage cannot be {55}2)
[Afmob’s step 2a gave these eliminations much more directly.]

11. 45 rule on C123 3 outies R127C4 = 1 innie R9C3 + 4
11a. Min R127C4 = 6 -> min R9C3 = 2
11b. 1 in N7 locked in R7C13, locked for R7

12. 1 on D\ locked in R4C4 + R5C5, locked for N5, clean-up: no 8 in R5C5

13. 45 rule on N3 3 innies R1C7 + R3C89 = 16
13a. Min R1C7 + R3C9 = 9 -> max R3C8 = 6 (hidden 16(3) cannot be [772])
13b. Min R1C7 + R3C8 = 8 -> max R3C9 = 8

14. 45 rule on C789 2 innies R19C7 = 1 outie R7C6 + 5
14a. Min R19C7 = 9 -> min R7C6 = 4
14b. Max R7C6 = 9 -> max R19C7 = 14, max R9C7 = 6 (R19C7 cannot be [77])

[I’ve deleted two heavy combination analysis steps and an ALS block step, my original steps 15, 16 and 17, which were unnecessarily complicated.]

15. 45 rule on R6789 2 outies R5C46 = 1 innie R6C5 + 5, IOU no 5 in R5C46, clean-up: no 6 in R6C46
15a. 45 rule on R6789 2 outies R5C45 = 1 innie R6C6 + 3, IOU no 3 in R5C45, clean-up: no 8 in R6C4, no 6 in R6C5
15b. 45 rule on R6789 2 outies R5C56 = 1 innie R6C4 + 3, IOU no 3 in R5C6, clean-up no 8 in R6C6

[Before I found step 15, I’d looked at the combinations for R4C456 and found that I could eliminate a couple of them which clashed with three combinations for the two 11(2) cages in N5. I didn’t use these eliminations because I hoped for something simpler.]

16. 45 rule on R6789 3 innies R6C456 = 17 = {278/359/458}
16a. 8 of {278/458} must be in R6C5 -> no 2,4,7 in R6C5, clean-up: no 2,5,7 in R5C5
16b. 3 of {359} must be in R6C5 -> no 3 in R6C46, clean-up: no 8 in R5C46

17. 45 rule on R6789 3 outies R5C456 = 14 = {149/167} -> R5C5 = 1, placed for D/, R6C5 = 8, R5C46 = [49/76/94], no 2,6 in R5C4, no 2 in R5C6, clean-up: no 5,9 in R6C4, no 9 in R6C6, no 7 in R7C9
17a. 9 in R6 locked in R6C789, locked for N6

18. R7C1 = 1 (hidden single in R7), R6C1 = 2, clean-up: no 6 in R1C3 (step 6), no 9 in R1C7 (step 3), no 7 in R4C8 (step 8), no 9 in R5C46, no 7 in R6C46 (step 16)
18a. R6C4 = 4, placed for D/, R6C6 = 5, placed for D\, R5C46 = [76], clean-up: no 8 in R3C4, no 9 in R3C6 (both step 2), no 2 in R9C8 (step 1b)
18b. Naked pair {78} in R1C37, locked for R1, clean-up: no 3 in R1C89

19. Naked triple {239} in R4C456, locked for R4 and 27(5) cage at R3C4 -> R4C2 = 4, R1C3 = 8 (step 6), R1C7 = 7, R4C8 = 5 (step 8), R9C8 = 4, R9C9 = 3 (step 1b), placed for D\, clean-up: no 6 in R1C9, no 4 in R3C6 (step 2)

20. R1C3 = 8 -> R12C4 = 4 = [31], R1C6 = 2, R2C6 = 8 (step 3a), R3C6 = 7,. R3C4 = 6 (step 2), R3C1 = 5, R3C2 = 3 (cage sum), clean-up: no 9 in R1C89
20a. R1C8 = 6, R1C9 = 5, placed for D/, R123C5 = [954]

21. 45 rule on N4 2 remaining innies R6C23 = 8 = [71], R4C13 = [86], R4C79 = [17], R5C123 = [953], clean-up: no 8 in R7C9, no 6 in R9C2 (step 1a)
21a. Naked pair {69} in R67C9, locked for C9

22. R4C8 = 5 -> R3C89 = 9 = [18]

23. R9C6 = 1 (hidden single in R9), R4C6 = 3 (hidden single in C6), placed for D/, R4C5 = 2, R4C4 = 9, placed for D\, R3C3 = 2, R2C2 = 6, both placed for D\, R2C13 = [79], R2C8 = 2, R3C7 = 9, both placed for D/

and the rest is naked singles