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PostPosted: Sat Apr 21, 2012 1:18 pm 
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Kenyan Killer 3 X - hidden Assassin 237

Ratios apply in either direction.

It is an X.

I used the fact that the red blocks would contain ratios with numbers greater than 5. It is most likely solvable without this.

The Kenyan bit is not too brutal but it is an assassin underneath.

For the assassin SudokuSolver gave it 1.95 using bowmans bingo. JSudoku did better just using two small fishes so I think the score should be lower - see what you think.

Image
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JSudoku code for when you've finished the Kenyan part:
3x3:d:k:4609:3079:3079:3079:3080:3077:3077:3077:4611:3083:4609:21:22:3080:23:24:4611:3078:3083:2065:4609:25:3080:26:4611:27:3078:3083:2065:28:29:30:31:32:33:3078:3854:3854:3854:34:3604:3604:3599:3599:3599:3850:35:36:3604:37:38:1810:1810:3597:3850:39:3844:40:41:42:5378:43:3597:3850:3844:44:45:2320:1811:1811:5378:3597:3844:3849:3849:3849:2320:3596:3596:3596:5378:

Solution:

931852647
648719325
275364981
413295876
852637194
769481253
396548712
587123469
124976538


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PostPosted: Sat Apr 21, 2012 9:41 pm 
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What a great puzzle! I loved it. :bouncy: Two puzzles for the price of one. I especially liked the interactions that the design put on r5, c5, and n5.

For the Kenyan part I used the red squares minimally as follows:
Hidden Text:
I used the ones at r3c23 and r45c9 and just the fact that the adjoining cages were "not equal".

For the assassin part I didn't have any breakthrough moves that opened it up quickly. (Walkthrough would be quite long. Not provided at this time). But the order in which I started to solve it was:
Hidden Text:
Solved most of n5
Solved most of c5
Very few possibilities for innies r1, r9, c1, c9
Solved r9c9

Thanks again HATMAN. Keep 'em coming :)


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PostPosted: Sun Apr 22, 2012 12:42 am 
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I assume that this is also intended to be Assassin 237, so I've used the code string to generate the diagram, for those forum members won't have downloaded JSudoku or SudokuSolver.

I'm unlikely to be doing the Kenyan Killer part, because I can't see a simple way to set up the ratios on an Excel worksheet.

Here is the diagram for A237:
Image


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PostPosted: Sun Apr 22, 2012 8:29 am 
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Andrew

Solution to the Kenyan part attached as a zipped Excel. It is simple algebra and a bit of combination analysis.

I tried to send as a PM but was not allowed to upload a zipped file - strange.


Attachments:
Kenyan Killer X 3.zip [74.86 KiB]
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PostPosted: Sun Apr 22, 2012 8:33 am 
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wellbeback

I used more red than that - I'd like to see your Kenyan solution.

Assassin solution probaly the same - did you avoid the fishes?


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PostPosted: Sun Apr 22, 2012 10:42 pm 
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Here is how I solved the Kenyan part of the puzzle.
Hidden Text:
1. Since /3@r1c1 and /2@r3c2 are not equal - and since they are both ratio 2:3 with /3@r2c1, the ratios of [/3@r1c1:/3@r2c1:/2@r3c2] must be [4:6:9] or [9:6:4].

The only one that works is: [/3@r1c1,/3@r2c1,/2@r3c2] = [+18,+12,+8]

-> /3@r1c2 = /3@r1c5 = /3@r1c6 = +12
-> /3@r1c9 from (+8, +18)
-> Either way /3@r2c9 = +12

Also -> /3@r5c1 = /3@r6c1 = /3@r7c3 = /3@r9c2 = +15
-> /2@r8c5 = +9

2. Consider r5
r5c123 = +15 -> r5c456789 = +30.

-> Max (r5c56789 + r6c4) = (+29 + 9) = +38. -> Max /3@r5c7 = +19.
Also Min (r5c56789 + r6c4) = (+21 + 1) = +22. -> Min /3@r5c7 = +11.

Ratio [/3@r5c7:/2@r6c7] = {1:2} - Must be [2:1]
-> /3@r5c7 from (+12,+14,+16,+18)
-> /2@r6c7 from (+6,+7,+8,+9)

/3@r7c7 is Min +6 and Max +21. (Because of D\)
-> Ratio [/2@r6c7:/3@r7c7] = [1:3]
-> [/2@r6c7,/3@r7c7] = [+6,+18] or [+7:+21]
-> /3@r5c7 from (+12,+14)

But since /3@r5c7 not equal /3@r9c2 (= +12)
-> /3@r5c7 = /3@r5c5 = +14
-> /2@r6c7 = +7
-> /3@r7c7 = +21
-> /2@r8c8 = +7
-> /3@r9c8 = +14

3. Finally
D\ in n5 r4c4,r5c5,r6c6 = +6 = {123}
-> Max D/ in n5 r4c6,r5c5,r6c4 = +20
-> Min /3@r9c1 = +10 (since 15/3@r7c3)
-> /3@r1c9 = +18

By the way, it's my opinion that in a Kenyan Killer puzzle that does not have a ratio shown for adjoining cages - the solver should not be able to assume anything about that ratio. I.e., should not be able to assume that it is a high numbers ratio. The puzzle creator should be free to leave out simple ratios if including them makes the puzzle too easy. What do you think?

I'm not technically knowledgeable about fishes and wings etc. I don't think "Ah - that was a fish" when eliminating a possibility. When solving this Assassin I just went round and round gradually whittling it down. Since a fish is (I think) just a codified short elimination/contradiction chain I probably used lots of them without knowing it :)


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PostPosted: Mon Apr 23, 2012 3:42 pm 
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Nice min-max

I agree about generalising and leaving the creator more choice. We will see how it goes over the next few puzzles.

I have a fourth one ready with an underlying assassin.


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PostPosted: Mon Apr 23, 2012 9:09 pm 
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Thanks to A for the assassin translation.
Thanks to H for the puzzle but - no disrespect - I'm not extending my repertoire beyond regular assassins: got enough to do already.
And my solution seems to have followed the same route as W.

cheers

_________________
Joe


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PostPosted: Wed Apr 25, 2012 2:20 am 
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Just noticed that yesterday was the 4th Anniversary of when I became a member of this forum! :D

I might try the first part of the puzzle, working out the cage totals, but for now I've only solved it as an Assassin.

Thanks HATMAN for a challenging puzzle! I thought that a lot of progress had been made after an early breakthrough but then there was a lot of hard work nibbling away before I found an unusual final breakthrough step.

Here is my walkthrough for Assassin 237:
Prelims

a) R34C2 = {17/26/35}, no 4,8,9
b) R6C78 = {16/25/34}, no 7,8,9
c) R89C5 = {18/27/36/45}, no 9
d) R8C67 = {16/25/34}, no 7,8,9
e) 21(3) cage at R7C7 = {489/579/678}, no 1,2,3

1. 45 rule on D\ 3 innies R4C4 + R5C5 + R6C6 = 6 = {123}, locked for N5 and D\

2. 45 rule on R5 1 innie R5C4 = 1 outie R6C4 + 2, no 4,5 in R5C4, no 8,9 in R6C4

3. 45 rule on D/ 1 outie R5C6 = 1 innie R4C6 + 2, no 8,9 in R4C6, no 4,5 in R5C6

4. 45 rule on R1 3 innies R1C159 = 21 = {489/579/678}, no 1,2,3
4a. Min R1C5 = 4 -> max R23C5 = 8, no 8,9 in R23C5

5. 45 rule on C9 3 innies R159C9 = 19 = {289/379/469/478/568}, no 1

6. 45 rule on R5 3 innies R5C456 = 16 = {169/178/367} (cannot be {268} which clashes with R4C6 + R5C5 + R6C4 = {246} using steps 2 and 3, or alternatively with 3 innies for D/ = 12), no 2 in R5C5
[Alternatively 45 rule on D/ 3 innies R4C6 + R5C5 + R6C4 = 12 = {147/156/246/345}
45 rule on R5 3 innies R5C456 = 16 = {169/178/367} (cannot be {268} which clashes with R4C6 + R5C5 + R6C4 = {246}, no 2 in R5C5]

6a. R5C456 = {169/178/367}, R4C6 + R5C5 + R6C4 = {147/156/345} using steps 2 and 3 -> R456C5 = {158/149/389} = 14,20
6b. 45 rule on C5 4 innies R4567C5 = 24, R456C5 cannot total 14 -> R7C5 = 4, R456C5 = 20 = {389} -> R5C5 = 3, placed for D/, R46C5 = {89}, locked for C5, clean-up: no 1,5,6 in R89C5, no 3 in R8C7

7. Naked pair {67} in R5C46, locked for R5
7a. Naked pair {45} in R4C6 + R6C4, locked for D/

8. Naked pair {27} in R89C5, locked for C5 and N8, clean-up: no 5 in R8C7
8a. Naked triple {156} in 12(3) cage at R1C5, locked for N2

9. 18(3) cage at R1C9 = {189/279}, no 6, 9 locked for N3 and D/

10. 15(3) cage at R7C3 = {168/267}, 6 locked for N7

11. R1C159 (step 4) = {579/678} (cannot be {489} because R1C5 only contains 5,6), no 4
11a. R1C5 = {56} -> no 5,6 in R1C1

12. 18(3) cage at R1C1 = {459/468/567}
12a. R1C1 = {789} -> no 7,8,9 in R2C2 + R3C3

13. 45 rule on R9 3 innies R9C159 = 16 = {178/268} (cannot be {169} because R9C5 only contains 2,7, cannot be {259/457} because 4,5,9 only in R9C9), no 4,5,9, 8 locked for R9
13a. R9C5 = {27} -> no 2,7 in R9C19
13b. R9C159 = {178/268}, CPE no 8 in R1C19 using diagonals

14. Naked pair {79} in R1C19, locked for R1, R1C5 = 5 (step 11)

15. R159C9 (step 5) = {289/469/478} (cannot be {568} because R1C9 only contains 7,9), no 5
15a. 2,4 only in R5C9 -> R5C9 = {24}

16. 14(3) cage at R5C7 = {149/248} (cannot be {158} because R5C9 only contains 2,4), no 5, 4 locked for R5 and N6, clean-up: no 3 in R6C78
16a. Killer pair 1,2 in 14(3) cage and R6C78, locked for N6
16b. Killer pair 1,2 in R6C6 and R6C78, locked for R6

17. 15(3) cage at R5C1 = {159/258}, 5 locked for R5 and N4, clean-up: no 3 in R3C2

18. 18(3) cage at R1C1 = {459/567}, 5 locked for N1 and D\, clean-up: no 3 in R4C2
18a. 21(3) cage at R7C7 = {489/678}, 8 locked for N9
18b. 4 of {489} must be in R8C8 -> no 9 in R8C8
18c. 9 on D\ only in R1C1 + R7C7, CPE no 9 in R7C1

19. 45 rule on C1 3 innies R159C1 = 18 = {189/567} (cannot be {279} because R9C1 only contains 1,6,8), no 2
19a. R1C1 = {79} -> no 9 in R5C1

20. 15(3) cage at R6C1 = {249/267/348/357/456} (cannot be {159/168/258} which clash with R159C1), no 1
20a. 5 in C1 only in R159C1 = {567} or in 15(3) cage -> 15(3) cage = {249/348/357/456} (cannot be {267} which contains 7 but not 5, locking-out cages)

21. 12(3) cage at R2C9 = {138/147/156/237/345} (cannot be {129} which clashes with 18(3) cage at R1C9, cannot be {246} which clashes with R5C9), no 9

22. 14(3) cage at R9C6 = {149/239/356} (cannot be {167/257} which clash with R9C159, cannot be {347} which clashes with 21(3) cage at R7C7), no 7

23. 15(3) cage at R9C2 = {249/357/456} (cannot be {267} which clashes with R9C5, cannot be {159} which clashes with 14(3) cage at R9C6), no 1
23a. 9 of {249} must be in R9C4 -> no 9 in R9C23
23b. 15(3) cage at R7C3 (step 10) = {168/267}
23c. Consider combinations for 15(3) cage at R9C2
15(3) cage at R9C2 = {249/357} => 15(3) cage at R7C3 = {168}
or 15(3) cage at R9C2 = {456}, locked for R9 => R9C9 = 8, R9C1 = 1 => 15(3) cage at R7C3 = {168}
-> 15(3) cage at R7C3 = {168}, locked for N7 and D/

24. Naked triple {279} in 18(3) cage at R1C9, locked for N3

25. 12(3) cage at R1C6 = {138/246}
25a. 2 of {246} must be in R1C6 -> no 4 in R1C6

26. 12(3) cage at R2C9 (step 21) = {138/156/345} (cannot be {147} which clashes with 12(3) cage at R1C6), no 7
26a. 6 of {156} must be in R4C9 (R23C9 cannot be {16} which clashes with 12(3) cage at R1C6), no 6 in R23C9
26b. Killer pair 1,4 in 12(3) cage at R1C6 and 12(3) cage at R2C9, locked for N3

27. 14(3) cage at R6C9 = {167/239/257/347} (cannot be {149/248} which clash with R159C9, cannot be {158/356} which clash with 12(3) cage at R2C9), no 8

28. 12(3) cage at R1C2 = {138/246}
28a. 4 of {246} must be in R1C4 (R1C23 cannot be {46} which clashes with 18(3) cage at R1C1), no 4 in R1C23, no 2 in R1C4

29. 12(3) cage at R2C1 = {129/138/237/246} (cannot be {147} which clashes with R159C1)
29a. 9 of {129} must be in R23C1 (R23C1 cannot be {12} which clashes with 12(3) cage at R1C2), no 9 in R4C1

30. R159C1 (step 9) = {189/567}
30a. 12(3) cage at R2C1 (step 29) = {129/138/237/246}
Consider combinations for 12(3) cage
12(3) cage at R2C1 = {129}, 9 locked for N1
or 12(3) cage at R2C1 = {138} => 12(3) cage at R1C2 = {246} (cannot be {138} which clashes with 12(3) cage at R2C1, ALS block), 6 locked for N1 => R2C2 + R3C3 = {45} => R1C1 = 9 (step 18)
or 12(3) cage at R2C1 = {237/246} => R159C1 = {189} => R1C1 = 9
-> 9 in R1C1 + 12(3) cage at R2C1, locked for C1 and N1
30b. 9 in C1 only in 18(3) cage at R1C1 = {459} or in 12(3) cage at R2C1 -> 12(3) cage cannot be {24}6/{46}2 (locking-out cages), no 4 in R23C1, no 6 in R4C1

31. 15(3) cage at R6C1 (step 20a) = {348/357/456}, no 2
31a. 6 of {456} must be in R6C1 -> no 4 in R6C1
31b. Killer pair 5,8 in R159C1 and 15(3) cage, locked for C1

32. 15(3) cage at R9C2 (step 23) = {249/357} (cannot be {456} which clashes with 15(3) cage at R6C1), no 6
32a. Killer pair 2,7 in 15(3) cage at R9C2 and R9C5, locked for R9

[Just spotted a trickier step which provides the final breakthrough.]
33. Grouped hidden killer pair for 1,2 in 12(3) cage at R1C2, 12(3) cage at R2C1, R34C2 and 15(3) cage at R5C1 for N14, 12(3) cage at R1C2, R34C2 and 15(3) cage at R5C1 each contain one of 1,2, 2 in C1 only in 12(3) cage at R2C1 -> 12(3) cage at R2C1 cannot also contain 1 -> 12(3) cage at R2C1 (step 29a) = {237/246}, no 1,9
[Edit. I've changed Double to Grouped, which seems to be the standard term, even though double feels right to me.]

34. R1C1 = 9 (hidden single in C1), placed for D\, 18(3) cage at R1C1 (step 18) = {459} (only remaining combination), 4 locked for N1 and D\, R1C9 = 7

35. R159C9 (step 15) = {478} (only remaining combination) -> R5C9 = 4, R9C9 = 8

36. R159C1 (step 19) = {189} (only remaining combination) -> R5C1 = 8, R9C1 = 1, R9C5 = 7 (step 13), R8C5 = 2, clean-up: no 5 in R8C6

37. 15(3) cage at R5C1 (step 17) = {258} (only remaining combination), 2 locked for R5 and N4, clean-up: no 6 in R3C2

38. Naked pair {19} in R5C78, locked for N6, clean-up: no 6 in R6C78
38a. Naked pair {25} in R6C78, locked for R6 and N6 -> R6C4 = 4, R4C6 = 5, R5C6 = 7 (cage sum), R5C4 = 6

39. Naked pair {36} in R46C9, locked for C9
39a. Naked pair {15} in R23C9, locked for C9 and N3, R4C9 = 6 (cage sum), 14(3) cage at R6C9 = [329], clean-up: no 2 in R3C2

40. Naked pair {67} in R7C7 + R8C8, locked for N9, clean-up: no 1 in R8C6
40a. 14(3) cage at R9C6 (step 22) = {356} (only remaining combination) -> R9C6 = 6, R9C78 = {35}, locked for R9 and N9, R8C6 = 3, R8C7 = 4

41. 12(3) cage at R1C6 (step 25) = {246} (only remaining combination) = [264]

and the rest is naked singles, without using the diagonals.

Rating Comment:
I'll rate my walkthrough for A237 at least Hard 1.5. After the early breakthrough in C5/N5, which I don't know how to rate but it's not my hardest step, I used a couple of short forcing chains and then a double hidden killer pair.

HATMAN said that SudokuSolver gave a rating of 1.95. I'm still using an older version of SudokuSolver for archive work and posting diagrams. This version gave a score of 3.56!

I'll guess that both versions, and possibly other software solvers, won't be able to do my step 6. That would explain the high scores.


Last edited by Andrew on Thu May 03, 2012 10:53 pm, edited 3 times in total.

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PostPosted: Wed Apr 25, 2012 10:24 pm 
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Location: Sydney, Australia
I haven't worked out how to do Kenyan yet. And this assassin has me beat. Congrats to you guys that solved it! However, I did find a neat way to start which is different to Andrew's start.
Alt start to A237
Hidden Text:

[edit: many thanks to Andrew for some good suggestions to improve clarity]

Alt start
1. "45" on D\: 3 innies r4c4+r5c5+r6c6 = 6 = {123} only: all locked for D\ and n5

A step with no eliminations.
2. "45" on D/: 3 innies r4c6+r5c5+r6c4 = 12
2a. "45" on r5: 3 innies r5c456 = 16
2b. "45" on c5: 4 innies r4567c5 = 24

3. All hidden cages in steps 1&2 cover all of n5, with r5c5 counted an extra 3 times and with 1 outie r7c5
3a. all hidden cages sum to 58 -> 3xr5c5+r7c5 = 13
3b. -> but 3x1+9 doesn't make 13
3c. -> r5c5+r7c5 = [27/34]
3d. ->h24(4)r4567c5 must have {27} or {34} = {2679/3489}(no 5) = [6/8..]
3e. must have 9 -> 9 locked for c5 & n5
3f. has one of 4/7 but not both -> no 4,7 in r46c5

4. h16(3)r5c456: {268} blocked by h24(4) = [6/8..] in n5 (step 3d)
4a. must have 2/3 for r5c5 = {358/367}(no 2,4)
4b. r5c5 = 3, placed for D/
4c. -> r7c5 = 4 (step 3c)
4d. ->from h24(4)r4567c5, r46c5 = 17 = {89} only
4e. 8 locked for c5 & n5

on from there.
Cheerio
Ed


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