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There was a lot of sweat here last week. Half of it came from the heat, the other half from Assassin 113 V1 and V2. And then there was Messy One 4 which almost made me miss the deadline for this post. So I thought this week should be a little easier and not so messy. Almost like a regular sudoku. But only almost.

The simple design gives you an easy start and should get you hooked, but be warned, there are still a few surprises.

Assassin 114
Attention: This is a Killer X (1-9 cannot repeat on the diagonals)




Rating SSolver(3.2.1): 0.84
My personal rating: (easy) 1.0



V2 is already waiting to be posted, as is an Extra Special Version!

Have fun!

Cheers,
Nasenbaer

PS: This seemingly simple design makes it actually very hard to find a unique solution. After about 30 tries I gave up on the regular Killer version and tried it with Killer-X. After another 10 failures I got the first good one and three more with the next 20 tries. So I sticked with Killer-X.

Nasenbaer

Thanks Nasenbaer for a fun and most of the time relaxing Killer!
This puzzle even allowed me to be creative, so I spotted a nice Killer pair (step 2l and 4b) which doesn't seem to be a Killer pair at first sight.

A114 Walkthrough:

1. R123
a) 6(3) = {123} locked for R2+N3
b) 16(3) = {457} locked for R3
c) 19(3) = {289} locked for R3+N1
d) 17(3) = {467} locked for R2+N1
e) R3C5 = 6 -> R12C5 = 15(2) = {78} -> R2C5 = 8, R1C5 = 7
f) 9(3) = {135} locked for R1
g) Innies R1 = 13(3) = {247}

2. C456
a) 17(3) @ R7C5 = {359} locked for C5+N8
b) Innies C4 = 22(3) = 9{58/67} -> 9 locked for C4+N5
c) R2C4 = 5 -> R1C4 = 4 and R3C4 = 3; R1C6 = 2, R2C6 = 9, R3C6 = 1
d) 11(3) = {128} locked for C4+N8
e) Naked triple (467) locked in R789C6 for C6
f) 19(3): R6C6 <> 3,5 because R6C5 <= 4
g) R6C6 = 8 -> R6C45 = 11(2) = [74/92]
h) 14(3) <> 1 because R4C6 = (35)
i) Hidden Single: R4C5 = 1 @ N5
j) 12(3) @ R4C4 = {156} -> R4C4 = 6, R4C6 = 5
k) R5C6 = 3
l) R6C45 = 11(2) -> R5C5+R6C4 cannot be [29/47]

3. R789
a) Innies R8 = 20(3) = [857] -> R8C5 = 5, R8C6 = 7
b) Innies R9 = 11(3) = [236] -> R9C4 = 2, R9C5 = 3, R9C6 = 6
c) R7C4 = 1, R7C5 = 9, R7C6 = 4
d) 12(3) = 2{19/46} -> 2 locked for R8+N7
e) 13(3) = 3{19/46} -> 3 locked for N9

4. C123 + D/ !
a) Killer pair (47) locked in R2C2 + 21(3) for C2
b) ! Killer pair (47) locked in R3C7 + (R5C5+R6C4) for D/ (step 2l)
c) 17(3) @ N7 must have one of (47) -> R9C3 = (47)
d) ! R7C3 <> 8 because it sees all 8 of C9
e) 8 locked in 11(3) @ C3 = {128} locked for C3+N4
f) 21(3) = {579} locked for C2+N4
h) 17(3) @ N7 = {179} -> R9C3 = 7, R9C2 = 1, R9C1 = 9
i) R2C2 = 4, R2C3 = 6, R7C3 = 3

5. C789
a) R9C9 = 5
b) 8(3) = {134} locked for C9+N6
c) R3C9 = 7, R3C7 = 4, R3C8 = 5
d) 21(3) = {678} locked for C8+N6

6. Rest is singles without considering diagonals.

Rating: 1.0. I used Killer pairs and one of them wasn't so obvious.

Thanks for the thanks.

Very clever! I didn't see that one! As always you found a much smoother way through the puzzle than me.

V2 will be posted in the evening to give the others time to catch up.

Cheers,
Nasenbaer

Time for V2 (actually more like V1.5). Usually that would be a slight variation of the design. But not this time. I like the simplicity of the design. So today we have a variation of the solution.

Assassin 114 V2
Attention: This is a Killer X (1-9 cannot repeat on the diagonals)





Rating SSolver(3.2.1): 1.29
My personal rating: (easy) 1.25



I hope Afmob doesn't find another of those cracking moves to shorten the puzzle.

Have fun!

Cheers,
Nasenbaer

I didn't find a shortcut this time and had to use some short chains to crack it. After going through SudokuSolver's log I saw that this Killer allowed some really cool moves along diagonals which I didn't find, so my moves are probably too difficult for this puzzle.

A114 V2 Walkthrough:

1. R789
a) 24(3) = {789} locked for R7+N7
b) 23(3) = {689} -> R7C4 = 6, {89} locked for C4+N8
c) 8(3) = 1{25/34} -> 1 locked for R7+N9
d) Innies R8 = 15(3) <> 7 because R8C4 = (89)
e) 7 locked in Innies R9 @ N8 for R9 = 17(3) = 7{19/28} because R9C4 = (89)
f) 7 locked in 21(3) @ R8 = 7{59/68}
g) 16(3) <> 5 because 5{29/38} blocked by Killer pair (35) of 8(3) and (25) of 12(3) @ N7
h) 5 locked in 12(3) @ R9 for N7 = 5{16/34}
i) 2 locked in R8C123 @ N7 for R8

2. C456
a) 9(3) = 3{15/24} -> 3 locked for C4+N2
b) 7 locked in R456C4 @ C4 for N5
c) 22(3) = 9{58/67} -> 9 locked for C5+N2
d) 9 locked in Innies C6 @ N5 = 19(3) = 9{28/46}
e) 3 locked in Innies C5 @ N5 for C5 = 13(3) = 3{28/46}
f) 1 locked in Innies C4 @ N5 for C4 = 13(3) = {157} locked for C4
g) 9(3) = {234} locked for N2
h) 14(3) = 1{58/67} -> 1 locked for C6
i) 12(3) @ N8 = {237} because R9C6 = (27) -> R8C6 = 3, R7C6 = 2, R9C6 = 7
j) Innies R9 = 17(3) = {179} -> R9C4 = 9, R9C5 = 1
k) R8C4 = 8

3. C456
a) Innie R7 = R7C5 = 5
b) R8C5 = 4
c) 22(3) = {679} locked for C5+N2
d) R5C5 = 8
e) 21(3) = {678} -> R5C4 = 7, R5C6 = 6
f) Innies R2 = 14(3) <> 8 because R2C5 >= 6
g) Innies R3 = 14(3) <> 8 because R3C5 >= 6
h) Hidden Single: R1C6 = 8 @ N2

4. R123
a) 19(3) = 9{37/46} -> 9 locked for R1+N2
b) 5 locked in 9(3) @ R1C1 @ R1 = {135} locked for R1+N1
c) 20(3) = {479} loocked for R3+N1
d) R3C5 = 6, R1C5 = 7, R2C5 = 9
e) 19(3) = {469} locked for R1+N3
f) R1C4 = 2, R3C4 = 3, R2C4 = 4
g) 11(3) = {128} locked for R3+N3
h) R3C6 = 5, R2C6 = 1

5. C123 !
a) 12(3) @ N7 = {345} locked for R9
b) 9(3) @ N7 = {126} locked for R8
c) 12(3) @ N4 <> 6,9 because {129/156/246} blocked by R28C2 = (126)
d) 12(3) @ N4 <> 5 since {345} blocked by R9C2 = (345)
e) 17(3) <> 1,7 because 7{19/46} blocked by R37C3 = (479) and {278}
blocked by Killer pair (78) of 12(3) @ N4
f) Hidden Killer pair (56) in 16(3) @ N4 for N4 since 17(3) can only have one of (56)
-> 16(3) <> {178/349}
g) 16(3) @ N4 <> {268} since R2C1 = (268)
h) 16(3) @ N4 <> {367} since (37) is a Killer pair of 12(3) @ N4
i) Hidden Killer triple (789) in R3C2 for C2 since 12(3) can only have one of (789)
j) ! R9C1 <> 4 because it leaves no 4 in N1:
- R9C1 = 4 -> R3C1 <> 4
- R9C1 = 4 -> R6C6 = 4 (HS @ N5) -> R3C3 <> 4

6. C123
a) 16(3) @ N4 <> 3,8 because {358} blocked by R9C1 = (35)
b) Killer triple (126) locked in R28C2 + 12(3) for C2
c) Killer triple (135) locked in R19C1 + 16(3) @ N4 for C1

7. C789 !
a) ! R3C7 <> 1 because it leaves no 1 in N1:
- R3C7 = 1 -> R4C4 = 1 (HS @ N5) -> R1C1 <> 1
- R3C7 = 1 -> R8C3 = 1 (HS @ N7) -> R1C3 <> 1
b) R3C7 = 2
c) Hidden Single: R9C8 = 2 @ C8
d) R9C9 = 6

8. C123
a) Hidden Single: R8C2 = 6 @ C2
b) R8C1 = 2, R8C3 = 1, R2C2 = 2
c) 2 locked in 17(3) @ C3 = {269} locked for C3+N4
d) Hidden Single: R1C1 = 1 @ N1

9. N4569
a) R4C4 = 5 -> R4C56 = 7(2) = [34] -> R4C5 = 3, R4C6 = 4
b) R6C6 = 9, R8C8 = 7
c) 20(3) = 9{38/56} -> 9 locked for C8+N6
d) 16(3) = {457} -> R4C1 = 7, {45} locked for C1+N4
e) R9C1 = 3, R2C8 = 5
f) 20(3) = {389} locked for N6+C8

10. Rest is singles without considering diagonals.

Rating: (Hard) 1.25 - (Easy) 1.5. I used some chains and Killer triples. Definitely easier than A113.

Here is my walkthrough for v2:


The first 5 steps are probably the standard opening moves until it gets interesting.

My steps 7,8,9 are probably not the most elegant tricks but at least they keep the solving path relatively short.

_________________
ADYFNC HJPLI BVSM GgK Oa m

Thanks for a fun puzzle. I like the simple design. It was so easy to colour the cages.

I would think it ought to be possible to make a regular Killer with this cage pattern since there are half a dozen immediately available 45s making N2 and N8 into 3 cell cages both horizontally and vertically. However such a Killer might have too low a score to be appropriate as an Assassin.

I nearly finished this on Thursday evening but found that I'd reached an impossible position because I'd been careless with my manual eliminations. Then it was too late to rework it before bedtime.

Afmob's steps 2l and 4b were really neat! He could have done step 4b immediately after step 2l but I guess it didn't come under the heading C456.

Afmob got to only remaining combinations in his step 1 more quickly than I did. I wasn’t searching for them, or checking with Ruud’s combination calculator, when there were plenty of naked triples that gave the same result.

I'll rate A114 as Hard 1.0. There was a lot of work to be done on the diagonals including, in my case, finding a hidden pair on one of them and several CPEs using the diagonals.

Here is my walkthrough for A114. It's probably more like the way Nasenbaer was expecting it to be solved.

I've given eliminations on the diagonals; it's so easy for those of us doing manual eliminations to overlook them.

Prelims

a) R1C123 = {126/135/234}, no 7,8,9
b) R123C5 = {489/579/678}, no 1,2,3
c) R1C789 = {689}, locked for R1 and N3
d) R2C789 = {123}, locked for R2 and N3
e) R3C123 = {289/379/469/478/568}, no 1
f) R456C2 = {489/579/678}, no 1,2,3
g) R456C3 = {128/137/146/236/245}, no 9
h) R456C8 = {489/579/678}, no 1,2,3
i) R456C9 = {125/134}, 1 locked for C9 and N6
j) R6C456 = {289/379/469/478/568}, no 1
k) R789C4 = {128/137/146/236/245}, no 9

1. Naked triple {457} in R3C789, locked for R3

2. Killer pair 2,3 in R2C9 and 8(3) cage at R4C9, locked for C9

3. 9(3) cage at R1C1 = {135/234}, 3 locked for R1 and N1
3a. 19(3) cage at R3C1 = {289} (only remaining combination), locked for R3 and N1 -> R3C5 = 6, clean-up: no 4 R1C123 (step 3)
3b. Naked triple {135} in R1C123, locked for R1 and N1
3c. Naked triple {467} in R2C123, locked for R2

4. R123C5 = {678} -> R12C5 = [78]

5. 45 rule on C5 3 innies R456C5 = 7 = {124}, locked for C5 and N5
5a. Naked triple {359} in R789C5, locked for N8

6. R789C4 = {128/146}, no 7, 1 locked for C4 and N8 -> R3C4 = 3, R3C6 = 1
6a. R3C4 = 3 -> R12C4 = 9 = [45], R12C6 = [29], clean-up: no 6 in R789C4 (step 6)
6b. Naked triple {128} in R789C4, locked for C4 and N8
6c. Naked triple {467} in R789C6, locked for C6

7. 45 rule on R9 3 innies R9C456 = 11 = {137/236/245} (cannot be {128} because 1,2,8 only in R9C4, cannot be {146} because 4,6 only in R9C6), no 8,9

8. 45 rule on R8 3 innies R8C456 = 20 = {578} (only remaining combination , cannot be {389} because 3,9 only in R8C5, cannot be {479/569} because R8C4 only contains 1,2,8) -> R8C456 = [857], R79C5 = [93]
8a. R9C456 (step 7) = {236} (only remaining combination) -> R9C46 = [26], R7C46 = [14]

9. R6C456 = {289/478} (cannot be {379/568} because R6C5 only contains 2,4, cannot be {469} because 6,9 only in R6C4) -> R6C6 = 8, locked for D\, R6C45 = [74/92], no 6

10. R4C456 = {156/237} (cannot be {129/147/246} because R4C6 only contains 3,5, cannot be {345} because 3,5 only in R4C6), no 4,9

11. R5C456 = {239/257/347} (cannot be {149/167} because R5C6 only contains 3,5, cannot be {356} because 3,5 only in R5C6), no 1,6

12. R4C45 = [61] (hidden singles in N5), 6 locked for D\, R4C6 = 5 (step 10), locked for D/, R5C6 = 3

13. R456C9 = {125/134}
13a. 2 of {125} must be in R4C9 -> no 2 in R56C9

14. R8C123 = {129/246}, no 3, 2 locked for R8 and N7
14a. R8C789 = {139/346}, 3 locked for N9

15. Killer pair 4,7 in R2C2 and R456C2, locked for C2

16. R1C1 + R8C8 = {13} (hidden pair on D\), CPE no 1 in R8C1

17. 5 on D\ locked in R7C7 + R9C9, locked for N9
17a. 15(3) cage at R7C7 = {258/267}
17b. 8 of {258} must be in R7C9 -> no 8 in R7C8

18. 8 in C9 locked in R17C9, CPE no 8 in R7C3
18a. 9 on D\ locked in R3C3 + R9C9, CPE no 9 in R9C3

19. R8C789 (step 14a) = {139/346}
19a. 9 of {139} must be in R8C9 -> no 9 in R8C7

20. R456C1 = {148/157/238/256/346} (cannot be {139} which clashes with R1C1, cannot be {247} which clashes with R456C2), no 9
20a. 9 in N4 locked in R456C2, locked for C2
20b. R456C2 = {489/579}, no 6

21. R9C123 = {179/458}
21a. 1 of {179} must be in R9C2 -> no 1 in R9C13
21b. 9 of {179} must be in R9C1 -> no 7 in R9C1

22. 1 on D/ locked in R2C8 + R8C2, CPE no 1 in R8C8 -> R8C8 = 3, locked for D\, R1C1 = 1
22a. R7C3 = 3 (hidden single on D/), R1C23 = [35]
22b. R7C3 = 3 -> R7C12 = 13 = [58/76/85], no 6 in R7C1

23. 3 in C1 locked in R456C1 (step 20) = {238/346}, no 5,7
23a. R7C1 = 5 (hidden single in C1), R7C2 = 8 (step 22b), R3C123 = [829], 9 locked for D\, R9C2 = 1, R8C2 = 6, locked for D/, R1C9 = 8, R2C8 = 1 (hidden singles on D/), R9C9 = 5 (hidden single on D\), clean-up: no 2 in R456C1 (step 23), no 4 in R456C2 (step 20b), no 2 in R4C9 (prelim i), no 9 in R8C1 (step 14), no 4 in R8C79 (step 14a), no 4 in R9C13 (step 21)
23b. R8C79 = [19], R9C13 = [97], 9 locked for D/, R6C4 = 7, locked for D/, R3C7 = 4, locked for D/, R5C5 = 2, locked for D\, R7C7 = 7, locked for D\, R9C78 = [84]
[I’ll leave the remaining naked singles for now.]

24. Naked triple {346} in R456C1, locked for C1 and N4

25. Naked triple {134} in R456C9, locked for C9 and N6

26. R456C7 = {259} (only remaining combination), locked for C7 and N6

and the rest is naked singles

Wonderful! So many walkthroughs!


OK, I'll try again. The main problem is to make it unique.

Cheers,
Nasenbaer

While trying to create a decent Assassin with the now familiar design I stumbled upon this one. If you add the diagonals constrain to the left Killer you actually have a Killer-X with a unique solution. But SSolver(3.2.1) rating is 4.13, with extended T&E (several Bowman's Bingo). So I wouldn't advice you to try it, unless you are a complete masochist.

Then I started thinking. What if I would rotate the design? I tried it, but now uniqueness was gone. Then I remembered those wonderful TwinKillers on DJApe's site. That was it! And it was solvable, even without the diagonals constrain! So here it is, the first Assassin TwinKiller! [creativity mode on] (Or should I say TwinAssassin? AssassinTwin? TwAssi? Or maybe ...) [creativity mode off] Ups, sorry about that.

So here is something to do for you on this wonderful Sunday. (Here it's cloudy with random rain showers)

Assassin 114 TwinKiller



Attention: Both killers are NOT unique when solved on their own! But together they have a unique solution.



SSolver(3.2.1) can't rate it. I tried it by adding all cages from the second killer as hidden cages to the first killer and then hit F7 for rating. But that didn't work. (BTW, that's what my question was about in this post, Richard.)

My personal rating: (hard) 1.25



Note: The red frames in r9c9 have absolutely no meaning. It's only the cursor from SudoCue. I moved them to r9c9 so you can see all cage sizes. And yes, I was too lazy to paint over them. If anyone feels offended by these frames he/she has my permission to create a new picture.

Have fun!

Cheers,
Nasenbaer

Do you PrintScreen the pics from SumoCue?? Because if you press Ctrl + F12 in SumoCue, it should just copy the image without the red marker and you can paste it in paint.

Para