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Afmob
 Post subject: Assassin 179
PostPosted: Thu Oct 29, 2009 11:12 pm 
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Posts: 310
Location: MV, Germany
This one came out a bit easier than I wanted but it's better than not having an Assassin, right? Judging from JSudoku and SudokuSolver the solution path seems to be quite narrow but please feel free to prove me wrong! :cheesey:

Assassin 179

Image
Note: No repeat on the diagonals! (Neither required for uniqueness nor reasonable difficulty)

3x3:d:k:2818:4625:4625:4625:4123:1817:6165:6165:6165:2830:2818:4625:4123:4123:1817:6165:4624:2580:2830:2312:7681:4114:4114:4114:4624:4107:2580:2312:2312:6916:7681:4114:4624:3589:4107:4107:3079:3079:6916:6916:7681:3589:3589:2054:2054:2569:2569:6916:2831:5655:7681:3589:4108:4108:3085:2569:2831:5655:5655:5655:7681:4108:3850:3085:2831:5651:1816:4122:4122:5910:1027:3850:5651:5651:5651:1816:4122:5910:5910:5910:1027:

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

Estimated rating: Hard 1.0.
SS Score: 1.26

Edit: No further versions planned (at least from me).


Last edited by Afmob on Sun Nov 01, 2009 8:04 pm, edited 1 time in total.

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manu
 Post subject: Re: Assassin 179
PostPosted: Fri Oct 30, 2009 6:08 pm 
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You have made a great puzzle, Afmob ! Not so easy, but I might have missed something since this puzzle offers many possibilities. My solving path is quite long and uses many little steps. It was a pleasure to solve it.

Edit : Andrew have pointed out some steps that could be optimized or deleted, and there was a missing step at the end of 5) : thanks a lot.

WT :

Hidden Text:
There is no neat cracking move in this WT.
The hardest steps were : 4)a) and 5)a).
1)a) Outies for n3 : r4c689=h23(3)={689} locked for r4
b) Max r4c8+r4c9=15
=> Min r4c6 = 8 : r4c6<>6, and 6 is locked for n6 at r4c89
=> r3c8=(12) (cage sum for 16(3))
=> 8(2)n6={17/35}

2)a) 12(2)n4+27(4)n4 = 39(6)={456789} since cells of 12(2) and 27(4) see each over.
=> 12(2)n4={48/57}
b) 12(2)n4 <> {57}, blocked by combinations of 8(2)n6 ( step 1)b) ), so 12(2)n4={48}, locked for n4 and r5.
c) From steps a)+b), 27(4)={5679}.
d) 9 locked for n4 and c3 at r456c3 since cages 10(3) and 9(3) cannot contain digit 9
=> CPE : r5c4 <> 9
e) 14(4)n6+8(2)n6 = 22(6)={123457} since cells of 14(4) and 8(2) see each over.
=> 4 locked for c7 and n6 at r46c7.

3)a) Innies-outies for n2 : r1c4 = 6 + r4c5
=> r1c4=(789), r4c5=(123).
b) Innies-outies for n1 : r3c2+r3c3= 5 + r1c4 = 12/13/14
=> r3c23 = [48/57/58/67/68] since r3c3 <> 9 ( step 2)d) ) and r3c2 < 7.
c) Combinations of 9(3)n1 : [4{23}/ 5{13}/6{12}]
=> Naked triple {123} locked for r4 at r4c125.
d) Innies-outies for n12 : r3c3 = 2+r4c1+r4c2+r4c5 =2+6=8.
e) Innies-outies for n8 : r6c5=r9c6
f) Innies-outies for n7 : r6c4=r7c2 : no 8.

4)a) 8 locked for n5 at r4c6+r6c5 => (step 3)e) ) 8 locked for c6 at r49c6
=> CPE : r9c1 <> 8.
b) 12(2)n7 = {39/57} ({48} blocked by r5c1=(48)) : no 8.
c) Hidden single for c1 : r5c1=8 => r5c2=4
Clean up : r1c4<>7 (step 3)b) ), r4c5<> 1 (step 3)a) ) and r6c4(=r7c2) <> 4 (step 3)f))
d) 4(2)n9={13} locked for D\ and n9
e) Innies-outies for n9 : r7c78=3+r9c6. Since r7c78<>3, r9c6<>r7c7 and r9c6<>r7c8, so
digit at r9c6 is locked for n9 at 4(3)+15(2) : r9c6 = (136789) : no 4 (nor 2,5)
=> (step 3) e) ) : r6c5<>4

5)a) 4 locked for D\ at r4c4+r6c6
=> 30(5) at D\ contains digit 4.
b) 11(2) at D\ <>{56} blocked by r3c2=(56) => 11(2)D\ = {29} locked for n1 and D\.
c) 30(5)D\ = {45678}.
d) deleted
e) 11(2) at r2c1 = {47} locked for c1 and n1 ({56} blocked by r3c2=(56)).
f) 12(2)n7 = {39} locked for c1 and n7
g) r1c1=2, r2c2=9, r4c1=1.
h) deleted
i) Combination for 10(3)n4 : [5{23}] blocked by r4c2=(23)
=> no 5 at r6c1 => r69c1=[65]
j) Innies for D/ : r1c9+r5c5+r9c1=h16(3).
Combinations with r9c1=5 and r5c5=(67) : [475].

The puzzle is now cracked


6)a) r67c2=[31] (last combination for 10(3))
b) r34c2=[62] (last combination for 9(3)), and r6c4=1 (cloned with r7c2)
c) 11(3) at D/ = [128]
d) 8(2)n6={35} locked for n6 and r5
e) 18(3) at D/ = [639]
f) r4c89={68} locked for n6 => r3c8=2
g) 10(2)n3=[19], 15(2)n9=[87]


the rest is straightforward


Last edited by manu on Tue Nov 03, 2009 5:08 pm, edited 1 time in total.

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Andrew
 Post subject: Re: Assassin 179
PostPosted: Sun Nov 01, 2009 7:42 pm 
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Thanks Afmob for another nice Assassin!

manu wrote:
There is no neat cracking move in this WT.
Maybe not but there were still some neat moves in it. I liked the "see each other" moves in steps 2a and 2e, which would become even more important if there was a V1.5 or V2 with the same cage pattern, and also the "must be equal to one of" move in step 4e.

Rating Comment:
I'll rate my A179 walkthrough at Easy 1.25. I used two killer quads and two 3(2+1) outies.

Here is my walkthrough for A179. I hope I got all my references to early steps correct; I had to renumber a lot of my steps after I found that I had two step 9s. :oops:

Prelims

a) 11(2) cage at R1C1 = {29/38/47/56}, no 1
b) R12C6 = {16/25/34}, no 7,8,9
c) R23C1 = {29/38/47/56}, no 1
d) R23C9 = {19/28/37/46}, no 5
e) R5C12 = {39/48/57}, no 1,2,6
f) R5C89 = {17/26/35}, no 4,8,9
g) R78C1 = {39/48/57}, no 1,2,6
h) R78C9 = {69/78}
i) R89C4 = {16/25/34}, no 7,8,9
j) 4(2) cage in N9 = {13}
k) 9(3) cage at R3C2 = {126/135/234}, no 7,8,9
l) 10(3) cage at R6C1 = {127/136/145/235}, no 8,9
m) 11(3) cage at R6C4 = {128/137/146/236/245}, no 9
n) 27(4) cage at R4C3 = {3789/4689/5679}, no 1,2
o) 14(4) cage at R4C7 = {1238/1247/1256/1346/2345}, no 9

1. Naked pair {13} in 4(2) cage in N9, locked for N9 and D\, clean-up: no 8 in 11(2) cage at R1C1

2. 45 rule on N3 1 outie R4C6 = 1 innie R3C8 + 7, R3C8 = {12}, R4C6 = {89}
2a. 45 rule on N3 3 outies R4C689 = 23 = {689}, locked for R4, 6 also locked for N6, clean-up: no 2 in R5C89
2b. 45 rule on N3 3 innies R2C8 + R3C78 = 11 = {128/137/146/236/245}, no 9

3. R5C12 = {39/48} (cannot be {57} which clashes with R5C89), no 5,7

4. 45 rule on N7 3 outies R6C124 = 10 = {127/136/145/235}, no 8

5. 45 rule on N2 1 innie R1C4 = 1 outie R4C5 + 6, R1C4 = {789}, R4C5 = {123}

6. Killer quad 6,7,8,9 in R23C9, R4C9 and R78C9, locked for C9, clean-up: no 1 in R5C8
6a. Max R6C9 = 5 -> min R67C8 = 11, no 1 in R6C8

7. 45 rule on N6 3(2+1) outies R3C8 + R5C6 + R7C8 = 9
7a. Min R37C8 = 3 -> max R5C6 = 6
7b. Min R3C8 + R5C6 = 2 -> max R7C8 = 7, clean-up: no 2,3 in R6C8 (max R67C8 = 11, step 6a)

8. 45 rule on N12 1 innie R3C3 = 3 outies R4C125 + 2
8a. Min R4C125 = 6 -> min R3C3 = 8
8b. R3C3 = {89} -> R4C125 = 6,7 = {123/124}, no 5, 1,2 locked for R4

9. 45 rule on N1 2 innies R3C23 = 1 outie R1C4 + 5
9a. Min R1C4 = 7 -> min R3C23 = 12, no 1,2
[I originally saw this before step 8 but it’s simpler this way round.]

10. Killer quad 1,2,3,4 in R4C12, R5C12 and R6C12 (must contain at least one of 1,2,3,4), locked for N4
[There’s a hidden killer quad at this stage but it’s unnecessary after the next 2 steps.]

11. 27(4) cage at R4C3 = {5679} (only remaining combination, cannot be {3789/4689} because R456C3 = {689/789} clash with R3C3), no 3,4,8, CPE no 9 in R5C12, clean-up: no 3 in R5C12
11a. 9 in N4 locked in R56C3, locked for C3 and 27(4) cage (no 9 in R5C4) -> R3C3 = 8, placed for D\, clean-up: no 3 in R23C1, no 2 in R2C9

12. Naked pair {48} in R5C12, locked for R5 and N4
12a. Naked triple {123} in R4C125, locked for R4

13. 45 rule on N1 1 outie R1C4 = 1 remaining innie R3C2 + 3, no 3 in R3C2

14. 45 rule on N9 2 innies R7C78 = 1 outie R9C6 + 3
14a. Min R7C78 = 6 -> min R9C6 = 3
14b. 45 rule on N8 1 outie R6C5 = 1 innie R9C6 -> min R6C5 = 3

15. 45 rule on N4 3(2+1) outies R3C2 + R5C4 + R7C2 = 13
15a. Min R3C2 + R5C4 = 9 -> max R7C2 = 3 (R37C2 cannot be [44]

16. 1,3 in N1 locked in 18(4) cage at R1C2 = {1359/1368}, no 2,4,7, clean-up: no 4 in R3C2 (step 12)
16a. 8,9 must be in R1C4 -> no 9 in R1C2
16b. 9(3) cage at R3C2 = {126/135}, 1 locked for R4 and N4

17. Naked quad {1356} in R1C23 + R2C3 + R3C2, locked for N1
[Alternatively both 11(2) cages in N1 cannot contain {56} which clashes with R3C2.]

18. 4 in C3 locked in R789C3, locked for N7, clean-up: no 8 in R78C1
18a. Killer pair 7,9 in R23C1 and R78C1, locked for C1, clean-up: no 2,4 in R2C2
18b. Killer pair 2,4 in R1C1 and R23C1, locked for C1 -> R5C12 = [84]

19. 45 rule on N7 1 outie R6C4 = 1 innie R7C2 -> R6C4 = {123}

20. Min R4C7 + R5C67 = 7 -> max R6C7 = 7

21. 10(3) cage at R6C1 = {136/235} (cannot be {127} because R6C1 only contains 3,5,6), no 7, CPE no 3 in R4C2
21a. Killer pair 1,2 in R4C2 and R67C2, locked for C2
21b. 1 in N1 locked in R12C3, locked for C3
21c. 7 in N4 locked in R456C3, locked for C3 and 27(4) cage, no 7 in R5C4
21d. R6C124 (step 4) = {136/235}, 3 locked for R6, clean-up: no 3 in R9C6 (step 13b)
[There’s now an interesting “clone” move.
1 in N7 locked in R7C2 + R9C1
45 rule on N7 1 outie R6C4 = 1 innie R7C2 -> 1 locked in R6C4 + R9C1, locked for D/.]

22. 23(4) at R8C7 = {2489/2579/2678/4568}
22a. All combinations must have one of 6,7,8,9 in R9C6 (to avoid clash with R78C9) -> R9C6 = {6789}, clean-up: no 4,5 in R6C5 (step 13b)

23. 11(3) cage at R6C4 = {128/137/146/236/245}
23a. 4 of {245} must be in R7C3 -> no 5 in R7C3

24. Max R89C3 + R9C2 = 20 (well actually less if one takes account of clashes with the 27(4) cage at R4C3) -> no 1 in R9C1
[I ought to have spotted this earlier.]

25. R7C2 = 1 (hidden single in N7) -> R6C12 = {36} (step 21), locked for R6 and N4 -> R4C12 = [12], R3C2 = 6 (step 16b), R5C4 = 6 (step 15), R4C5 = 3, R6C12 = [63], R6C4 = 1 (step 19), placed for D/, R1C2 = 5, R1C4 = 9 (step 13), clean-up: no 2 in R2C6, no 4 in R2C9, no 6 in R9C6 (step 14b)
25a. Naked pair {13} in R12C3, locked for C3

26. R7C7 = 6 (hidden single on D\), clean-up: no 9 in R78C9
26a. 5 on D\ locked in R4C4 + R5C5 + R6C6, locked for N5 -> R5C6 = 2, clean-up: no 5 in R2C6
26b. R1C1 = 2 (hidden single on D\), R2C2 = 9, placed for D\, clean-up: no 1 in R3C9
26c. Naked pair {78} in R78C9, locked for C9 and N9, clean-up: no 2,3 in R23C9

27. R3C8 + R5C6 + R7C8 = 9 (step 7)
27a. R5C6 = 2 -> R37C8 = 7 = [25], R4C6 = 9 (step 2), R4C89 = [86], R2C9 = 1, R3C9 = 9, R12C3 = [13], R9C9 = 3, R8C8 = 1, R1C9 = 4, placed for D/, R9C1 = 5, placed for D/, R5C5 = 7, placed for D/

and the rest is naked singles.
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Børge
PostPosted: Sat Nov 21, 2009 3:45 pm 
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Scribble images:
If you think that the upward main diagonal is not 100% straight a couple of places, you are absolute correct.
This is NOT a bug in my software, but in Excel. The shifts in the diagonal line are always in the middle of a quadratic Excel cell.
I'll write to Microsoft and see what they say.


Image     Image



Image     Image


					
						

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 Post subject: Re: Assassin 179
PostPosted: Thu Nov 26, 2009 5:56 pm 

				

				

					
		


		


			
				

			
				

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To check some further diagonal connecting tubes between remote parts of a cage, a variation of Afmob's A179 seemed the perfect guinea pig.
Here are some of the guinea pigs JSudoku generated. v0.90 and v0.96 is the same puzzle with and without the restriction of no repeat on the main diagonals.  
Without the restriction of no repeat on the main diagonals the SS Score is a bit higher.  Both puzzles have the same solution.

Assassin 179 v0.90
Image     Image
SS Score: 0.90  
3x3:d:k:7452:3857:3857:3857:3611:3353:6421:6421:6421:3854:7452:3857:3611:3611:3353:6421:9245:2068:3854:5128:4097:4626:4626:4626:9245:1803:2068:5128:5128:6148:4097:4626:9245:6149:1803:1803:2823:2823:6148:6148:4097:6149:6149:2054:2054:2313:2313:6148:9245:5143:4097:6149:5644:5644:1293:2313:9245:5143:5143:5143:4097:5644:2314:1293:9245:4371:1560:3610:3610:5142:7452:2314:4371:4371:4371:1560:3610:5142:5142:5142:7452:

Assassin 179 v0.96
Image     Image
SS Score: 0.96         
3x3::k:7452:3857:3857:3857:3611:3353:6421:6421:6421:3854:7452:3857:3611:3611:3353:6421:9245:2068:3854:5128:4097:4626:4626:4626:9245:1803:2068:5128:5128:6148:4097:4626:9245:6149:1803:1803:2823:2823:6148:6148:4097:6149:6149:2054:2054:2313:2313:6148:9245:5143:4097:6149:5644:5644:1293:2313:9245:5143:5143:5143:4097:5644:2314:1293:9245:4371:1560:3610:3610:5142:7452:2314:4371:4371:4371:1560:3610:5142:5142:5142:7452:
Solution to A179 v0.90 and v0.96:  
741826935
652397841
983145627
579682314
834519762
216734598
468971253
197253486
325468179




JSudoku also produced the following ASSASSIN with an SS Score of 12.85  :shock:  :rambo:
I cannot find a list of the killers/assassins with the highest SS Scores.
If such a list exists, perhaps this puzzle will make it into the top 10.  ;) 

Assassin 179 v13
Image     Image
SS Score: 12.85        
3x3:d:k:3356:4625:4625:4625:4635:3097:4117:4117:4117:2318:3356:4625:4635:4635:3097:4117:6685:3348:2318:5384:8193:2834:2834:2834:6685:2315:3348:5384:5384:5636:8193:2834:6685:4613:2315:2315:2567:2567:5636:5636:8193:4613:4613:3334:3334:4105:4105:5636:6685:4887:8193:4613:4364:4364:1805:4105:6685:4887:4887:4887:8193:4364:2570:1805:6685:5907:2072:4378:4378:6934:3356:2570:5907:5907:5907:2072:4378:6934:6934:6934:3356:
Solution:  
326947185
471685239
589213764
768459312
913762458
254138976
692871543
145396827
837524691


EDIT:
Upon request here the SS Score for the various rotations:
090° rotation. SS Score: 6.67
180° rotation. SS Score: Unsolvable.
270° rotation. SS Score: Unsolvable.

Without the restriction of no repeat on the main diagonals A179 v13 has TWO solutions.


					
						

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 Post subject: Re: Assassin 179
PostPosted: Sun Nov 29, 2009 11:37 pm 

				

				

					
		


		


			
				

			
				

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Thanks Børge for the variants.  I did V0.90 and V0.96 to see whether they would be good puzzles for newcomers.  Not quite but ...
They are good practice for:  
... looking to see which cells see which other cells.  In this cage pattern all cells of the 4-cells cages at R4C3 and R4C7 "see" the 2-cell cages at R5C1 and R5C8 (respectively).  This wasn't needed to solve Afmob's A179 but is very helpful for solving V0.90 and V0.96; I don't know whether it's essential but it definitely gives a much quicker solving path.

Rating Comment:  
I'll rate A179 V0.90 at Easy 1.25 because I used a "common peer" clash between a 4-cell cage and a 2-cell cage.  I wasn't sure how to rate that step until I realised that it's about the same difficulty level as an ALS block.  The SS score is significantly lower so either it rated that step a lot lower or it used a lot of simpler steps.  I also used a killer quad, which made the solving path shorter but probably wasn't essential.

Here is my walkthrough for A179 V0.90.

Prelims

a) R12C6 = {49/58/67}, no 1,2,3
b) R23C1 = {69/78}
c) R23C9 = {17/26/35}, no 4,8,9
d) R5C12 = {29/38/47/56}, no 1
e) R5C89 = {17/26/35}, no 4,8,9
f) R78C1 = {14/23}
g) R78C9 = {18/27/36/45}, no 9
h) R89C4 = {15/24}
i) 20(3) cage at R3C2 = {389/479/569/578}, no 1,2
j) 7(3) cage at R3C8 = {124}, CPE no 1,2 in R5C8, clean-up: no 6,7 in R5C9
k) 9(3) cage at R6C1 = {126/135/234}, no 7,8,9
l) 22(3) cage at R6C8 = {589/679}
m) 29(4) disjoint cage at R1C1 = {5789}
n) 16(5) cage at R3C3 = {12346}
o) 36(6) disjoint cage at R2C8 = {156789/246789/345789}

1. 45 rule on D/ 3 innies R1C9 + R5C5 + R9C1 = 9 = {126/135/234}, no 7,8,9

2. 45 rule on N7 3 innies R7C23 + R8C2 = 23 = {689} -> R7C2 = 6, R7C3 + R8C2 = {89}, locked for N7 and 36(6) disjoint cage at R2C8, clean-up: no 5 in R5C1, no 3 in R8C9
2a. R7C2 = 6 -> R6C12 = 3 = {12}, locked for R6 and N4, clean-up: no 9 in R5C12
2b. Killer pair 1,2 in R6C1 and R78C1, locked for C1

3. 45 rule on N8 1 innie R9C6 = 1 outie R6C5 + 5 -> R6C5 = {34}, R9C6 = {89}

4. R1C9 + R5C5 + R9C1 (step 1) = {135/234} (cannot be {126} because R9C1 only contains 3,4,5), no 6, 3 locked for D/

5. 45 rule on N3 3 innies R2C8 + R3C78 = 12 = {147/156/246}
5a. 9 in N3 locked in 25(4) cage = {1789/2689/3589} (cannot be {3679/4579} which clash with R2C8 + R3C78), no 4
5b. 1,2 of {1789/2689} must be in R1C9 -> no 1,2 in R1C78 + R2C7
5c. 4 in N3 locked in R2C8 + R3C78 = {147/246}, no 5

6. 45 rule on N4 2 remaining outies R3C2 + R5C4 = 13 = {49/58}/[76], no 1,2,3, no 7 in R5C4

7. 24(4) cage at R4C3 = {3489/4569} (cannot be {3579/3678/4578} which clash with R5C12 because all cells of the 24(4) cage “see” R5C12), no 7, CPE no 4 in R5C12, clean-up: no 7 in R5C12
7a. R5C89 = [62/71] (cannot be {35} which clashes with R5C12), no 3,5

8. Naked triple {124} in R4C89 + R5C9, locked for N6
8a. 4 in N6 locked in R4C89, locked for R4 and 7(3) cage at R3C8, no 4 in R3C8

9. 4 in N3 locked in R2C8 + R3C7, locked for D/, clean-up: no 2 in R1C9 + R5C5 (step 4)
9a.  Naked triple {135} in R1C9 + R5C5 + R9C1, locked for D/
9b. R2C8 + R3C78 (step 5c) = {147/246}
9c. R3C8 = {12} -> no 2 in R2C8 + R3C7
9d. 25(4) cage in N3 (step 5a) = {1789/3589}, no 6

10. Killer quad 1,2,3,4 in R23C9, R4C9, R5C9 and R78C9, locked for C9 -> R1C9 = 5, R9C1 = 3, R5C5 = 1, R5C9 = 2, R5C8 = 6, R5C1 = 8, R5C2 = 3, clean-up: no 7 in R23C1, no 8 in R2C6, no 3,6 in R23C9, no 2 in R78C1, no 4,7 in R78C9

11. Naked pair {17} in R23C9, locked for C9 and N3 -> R2C8 = 4, R3C7 = 6, R23C1 = [69], R1C1 = 7, R3C8 = 2, R4C89 = [14], R4C1 = 5, R6C4 = 7, R4C6 = 2, clean-up: no 9 in R1C6, no 8 in R78C9
11a. Naked pair {14} in R78C1, locked for C1 and N7 -> R6C12 = [21]
11b. R78C9 = [36]

12. 3,7 in N6 locked in R456C7, locked for C7
12a. Naked pair {89} in R12C7, locked for C7 and N3 -> R1C8 = 3
12b. Naked triple {357} in R456C7, locked for C7 and N6, R5C6 = 9 (cage sum), R9C6 = 8, R6C5 = 3 (step 3), R4C45 = [68], R6C6 = 4, R5C34 = [45], R4C23 = [79], R3C3 = 3, R456C7 = [375], R6C3 = 6, R7C3 = 8, R8C2 = 9, R1C6 = 6, R2C6 = 7, R7C7 = 2, R9C9 = 9, clean-up: no 1 in R89C4

13. R6C89 = [98], R7C8 = 5 (cage sum)

and the rest is naked singles.


					



						

						

							
							
							
						

						

							
				

				

					
		


		


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 Post subject: Re: Assassin 179
PostPosted: Sun Nov 29, 2009 11:45 pm 

				

				

					
		


		


			
				

			
				

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My (hidden) introductory comment for A179 V0.90 also applies to V0.96.

Solving this puzzle as a regular Killer, rather than as a Killer-X, makes quite a lot of difference to the solving path so if you used V0.90 as practice (for the technique in my hidden comment), I can recommend that you also solve V0.96.

Rating Comment:  
I'll rate A179 V0.96 at Easy 1.25 because I used a "common peer" clashes between 4-cell cages and 2-cell cages.  I wasn't sure how to rate those steps until I realised that they are about the same difficulty level as ALS blocks.  The SS score is significantly lower so either it rated those steps a lot lower or it used a lot of simpler steps.

V0.96 felt somewhat harder than V0.90 but, because I used the same techniques, I've given it the same rating.

Here is my walkthrough for A179 V0.96.

Prelims

a) R12C6 = {49/58/67}, no 1,2,3
b) R23C1 = {69/78}
c) R23C9 = {17/26/35}, no 4,8,9
d) R5C12 = {29/38/47/56}, no 1
e) R5C89 = {17/26/35}, no 4,8,9
f) R78C1 = {14/23}
g) R78C9 = {18/27/36/45}, no 9
h) R89C4 = {15/24}
i) 20(3) cage at R3C2 = {389/479/569/578}, no 1,2
j) 7(3) cage at R3C8 = {124}, CPE no 1,2 in R5C8, clean-up: no 6,7 in R5C9
k) 9(3) cage at R6C1 = {126/135/234}, no 7,8,9
l) 22(3) cage at R6C8 = {589/679}
m) 29(4) disjoint cage at R1C1 = {5789}
n) 16(5) cage at R3C3 = {12346}
o) 36(6) disjoint cage at R2C8 = {156789/246789/345789}

1. 45 rule on N7 3 innies R7C23 + R8C2 = 23 = {689} -> R7C2 = 6, R7C3 + R8C2 = {89}, locked for N7 and 36(6) disjoint cage at R2C8, clean-up: no 5 in R5C1, no 3 in R8C9
1a. R7C2 = 6 -> R6C12 = 3 = {12}, locked for R6 and N4, clean-up: no 9 in R5C12
1b. Killer pair 1,2 in R6C1 and R78C1, locked for C1

2. 45 rule on N8 1 innie R9C6 = 1 outie R6C5 + 5 -> R6C5 = {34}, R9C6 = {89}

3. 45 rule on N3 3 innies R2C8 + R3C78 = 12 = {147/156/237/246/345}
3a. 9 in N3 locked in 25(4) cage = {1789/2689/3589} (cannot be {3679/4579} which clash with R2C8 + R3C78), no 4
3b. 4 in N3 locked in R2C8 + R3C78 = {147/246/345}

4. 45 rule on N4 2 remaining outies R3C2 + R5C4 = 13 = {49/58}/[76], no 1,2,3, no 7 in R5C4

5. 24(4) cage at R4C3 = {3489/4569} (cannot be {3579/3678/4578} which clash with R5C12 because all cells of the 24(4) cage “see” R5C12), no 7, CPE no 4 in R5C12, clean-up: no 7 in R5C12
5a. R5C89 = [62/71] (cannot be {35} which clashes with R5C12), no 3,5

6. Naked triple {124} in R4C89 + R5C9, locked for N6
6a. 4 in N6 locked in R4C89, locked for R4 and 7(3) cage at R3C8, no 4 in R3C8

7. 4 in N3 locked in R2C8 + R3C7, locked for 36(6) disjoint cage at R2C8
7a. R2C8 + R3C78 (step 3b) = {147/246} (cannot be {345} because R3C8 only contains 1,2), no 3,5
7b. R3C8 = {12} -> no 1,2 in R2C8 + R3C7

8. 36(6) disjoint cage at R2C8 = {246789/345789}, no 1
8a. 2 of {246789} must be in R4C6, 3,5 of {345789} must be in R4C6 + R6C4 -> no 6,7 in R4C6

9. 22(3) cage at R6C8 = {589} (only remaining combination, cannot be {679} which clashes with R5C8 because all the cells of the 22(3) cage “see” R5C8), no 6,7

10. 45 rule on N6 3(2+1) outies R37C8 + R5C6 = 16
10a. Max R37C8 = 11 -> min R5C6 = 5

11. 24(4) cage at R4C7 = {3579} (cannot be {3678} which clashes with R5C8 because all cells of the 24(4) cage “see” R5C8), no 6,8, 3 locked for C7

12. R5C8 = 6 (hidden single in N6), R5C9 = 2, clean-up: no 6 in R23C9, no 5 in R5C2, no 7 in R78C9
12a. Naked pair {14} in R4C89, locked for R4 and 7(3) cage at R3C8, no 1 in R3C8   -> R3C8 = 2, clean-up: no 6 in 25(4) cage in N3 (step 3a)
12b. 7 in N6 locked in R456C7, locked for C7 and 24(4) cage at R4C7, no 7 in R5C6
12c. 8 in N6 locked in R6C89, locked for R6 and 22(3) cage at R6C8, no 8 in R7C8

13. R3C7 = 6, then R2C8 = 4 (hidden singles in N3), R4C89 = [14], clean-up: no 9 in R1C6, no 9 in R2C1, no 5 in R78C9
13a. 36(6) disjoint cage at R2C8 (step 8) must contain 4,6 = {246789} (only remaining combination) -> R4C6 = 2, R6C4 = 7
13b. R5C5 = 1 (hidden single in R5)

14. Naked pair {38} in R5C12, locked for R5 and N4

15. 7 in N4 locked in R4C12, locked for R4 and 20(3) cage at R3C8, no 7 in R3C8
15a. 20(3) cage at R3C8 = {479/578}, no 6
15b. 4,8 only in R3C8 -> R3C8 = {48}

16. 16(5) cage at R3C3 = {12346} -> R7C7 = 2, 6 locked in R4C4 + R6C6, locked for N5, clean-up: no 3 in R8C1

17. R8C9 = 6 (hidden single in C9), R7C9 = 3, clean-up: no 5 in R23C9, no 2 in R8C1
17a. Naked pair {17} in R23C9, locked for C9 and N3
17b. R1C8 = 3 (hidden single in N3)

18. Naked pair {14} in R78C1, locked for C1 and N7 -> R6C12 = [21]

19. R2C1 = 6 (hidden single in C1), R3C1 = 9, clean-up: no 7 in R1C6

20. 9 in 29(4) disjoint cage at R1C1 locked in R8C8 + R9C9, locked for N9 -> R7C8 = 5
20a. 5 in 29(4) disjoint cage at R1C1 locked in R1C1 + R2C2, locked for N1

21. Naked pair {89} in R6C89, locked for R6 and N6
21a. R456C7 = {357}, locked for C7, R5C6 = 9 (cage sum), R9C6 = 8, R6C5 = 3 (step 2)

and the rest is naked singles.


					



						

						

							
							
							
						

						

							
				

				

					
		


		


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