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HATMAN
 Post subject: Assassin 274
PostPosted: Sat Nov 02, 2013 12:00 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 694
Location: Saudi Arabia
Assassin 274

I'm trying to do another Human Solvable however this popped out on the way. SS gives it 1.90 but JS does it with just small fishes - quite a few of them but mostly pretty obvious. I think the SS score is more about the length of the solution not the individual steps.

Note it is X.


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JS Code:
3x3:d:k:2061:22:2053:2053:4113:2305:2305:23:3343:24:2061:2053:25:4113:26:2305:3343:27:2306:2306:6153:6153:4113:5130:5130:2056:2056:2306:28:6153:3861:29:30:5130:31:2056:3092:3092:3092:3861:32:33:4627:4627:4627:2054:34:5131:3861:35:36:5388:37:2308:2054:2054:5131:5131:4626:5388:5388:2308:2308:38:3088:2307:39:4626:40:2055:2062:41:3088:42:2307:2307:4626:2055:2055:43:2062:


Solution:
681394257
924751368
357826914
169472583
435618792
278539641
513947826
746285139
892163475
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Andrew
 Post subject: Re: Assassin 274
PostPosted: Mon Nov 04, 2013 2:46 am 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks HATMAN for a fun puzzle! :D Yes, it could have been posted as a Human Solvable but I'm glad you posted it as an Assassin.

Here is my walkthrough for Assassin 274:
Prelims

a) 8(2) cage at R1C1 = {17/26/35}, no 4,8,9
b) 8(3) cage at R1C3 = {125/134}
c) 9(3) cage at R1C6 = {126/135/234}, no 7,8,9
d) 13(2) cage at R1C9 = {49/58/67}, no 1,2,3
e) 9(3) cage at R3C1 = {126/135/234}, no 7,8,9
f) 24(3) cage at R3C3 = {789}
g) 20(3) cage at R3C6 = {389/479/569/578}, no 1,2
h) 8(3) cage at R3C8 = {125/134}
i) 8(3) cage at R6C1 = {125/134}
j) 20(3) cage at R6C3 = {389/479/569/578}, no 1,2
k) 21(3) cage at R6C7 = {489/579/678}, no 1,2,3
l) 9(3) cage at R6C9 = {126/135/234}, no 7,8,9
m) 12(2) cage at R8C2 = {39/48/57}, no 1,2,6
n) 9(3) cage at R8C3 = {126/135/234}, no 7,8,9
o) 8(3) cage at R8C7 = {125/134}
p) 8(2) cage at R8C8 = {17/26/35}, no 4,8,9

Steps resulting from Prelims
1a. 8(3) cage at R1C3 = {125/134}, CPE no 1 in R1C12, clean-up: no 7 in R2C2
1b. 24(3) cage at R3C3 = {789}, CPE no 7,8,9 in R4C4 using D\
1c. 8(3) cage at R3C8 = {125/134}, CPE no 1 in R2C9
1d. 8(3) cage at R6C1 = {125/134}, CPE no 1 in R8C1
1e. 8(3) cage at R8C7 = {125/134}, CPE no 1 in R9C89, clean-up: no 7 in R8C8

2. 45 rule on N1 3 innies R1C2 + R2C1 + R3C3 = 2(1+1) outies R1C4 + R4C1 + 20
2a. Max R1C2 + R2C1 + R3C3 = 24 -> max R1C4 + R4C1 = 4, max R1C4 = 3, max R4C1 = 3
2b. Min R1C4 + R4C1 = 2 -> min R1C2 + R2C1 + R3C3 = 22, no 1,2,3,4 in R1C2 + R2C1
2c. 4 in N1 only in 8(3) cage at R1C3 = {134} or in 9(3) cage at R3C1 = {234} (locking cages), CPE no 3 in R1C1, clean-up: no 5 in R2C2

3. 45 rule on N9 3 innies R7C7 + R8C9 + R9C8 = 2(1+1) outies R6C9 + R9C6 + 20
3a. Max R7C7 + R8C9 + R9C8 = 24 -> max R6C9 + R9C6 = 4, max R6C9 = 3, max R9C6 = 3
3b. Min R6C9 + R9C6 = 2 -> min R7C7 + R8C9 + R9C8 = 22, no 1,2,3,4 in R7C7 + R8C9 + R9C8
[Ed pointed out that I could also have done the equivalent of step 2c here.]

4. 20(3) cage at R3C6 = {389/479/569/578}
4a. 3,4 of {389/479} must be in R3C67 (R3C67 cannot be {79/89} which clash with 24(3) cage at R3C3, ALS block), no 3,4 in R4C7

5. 20(3) cage at R6C3 = {389/479/569/578}
5a. 3,4 of {389/479} must be in R67C3 (R67C3 cannot be {79/89} which clash with 24(3) cage at R3C3, ALS block), no 3,4 in R7C4

6. 1,2 on D/ only in R4C6 + R5C5 + R6C4, locked for N5

7. 45 rule on C5 3 innies R456C5 = 11 = {137/146/236/245} (cannot be {128} because 1,2 only in R5C5), no 8,9 -> R5C5 = {12}
7a. Killer triple 1,2,3 in 8(2) cage at R1C1, R5C5 and 8(2) cage at R8C8, locked for D\

8. 45 rule on N5 3 remaining innies R456C6 = 19 = {289/379/469/478/568}, no 1

9 3 on D\ only in 8(2) cage at R1C1 = [53] or in 8(2) cage at R8C8 = {35} (locking cages), 5 locked for D\
9a. 8(2) cage at R1C1 = [53] => R12C3 + R1C4 = {14}3 or 8(2) cage at R8C8 = {35} => R89C7 + R9C6 = {14}3 -> 3 in R1C4 + R9C6, CPE no 3 in R1C6 + R9C4
9b. 8(2) cage at R1C1 = [53] => R12C3 + R1C4 = {14}3 => R3C12 = {26} => R4C1 = 1 or 8(2) cage at R8C8 = {35} => R89C7 + R9C6 = {14}3 => R7C89 = {26} => R6C9 = 1 -> 1 in R4C1 + R6C9, CPE no 1 in R4C9 + R6C1
[Note. 3 may be in both of R1C4 + R9C6, 1 may be in both of R4C1 + R6C9.]

10. 8(3) cage at R3C8 = {125/134}, 1 locked for R3 and N3

11. 8(3) cage at R6C1 = {125/134}, 1 locked for R7 and N7

12. Deleted
[Thanks Ed for pointing out that the extra forcing chain I’d inserted here wasn’t necessary. I’d been careless in removing candidates from my Excel worksheet when checking my walkthrough.]

13. 4 on D\ only in R4C4 + R6C6, locked for N5
13a. R456C5 (step 7) = {137/236} => R46C5 = {36/37}, no 5, 3 locked for C5 and N5
[and from step 3 …]
13b. 4 in N9 only in 9(3) cage at R6C9 = {234} or in 8(3) cage at R8C7 = {134} (locking cages), CPE no 3 in R9C9, clean-up: no 5 in R8C8
13c. 5 in R1C1 + R9C9, CPE no 5 in R1C9 + R9C1, clean-up: no 8 in R2C8, no 7 in R8C2

14. R456C6 (step 8) = {289/478/568} (cannot be {469} which clashes with R4C4), 8 locked for C6 and N5
14a. 2 of {289} must be in R4C6 -> no 9 in R4C6

15. 15(3) cage at R4C4 = {249/456} (cannot be {159/258} because R4C4 only contains 4,6, cannot be {168/267} which clash with R456C5) -> R4C4 = 4, R56C4 = [56/65/92]
15a. R5C5 = 1 (hidden single in N5), placed for D\, R46C5 = {37} (step 7), locked for C5 and N5, clean-up: no 7 in R1C1 + R9C9

16. 45 rule on R5 2 remaining innies R5C46 = 14 = [59/68/95], no 6 in R5C6

17. R1C2 + R2C1 + R3C3 = {789} (hidden triple in N1) = 24 -> R1C4 + R4C1 = 4 (step 2) = [13/22/31]

18. R7C7 + R8C9 + R9C8 = {789} (hidden triple in N9) = 24 -> R6C9 + R9C6 = 4 (step 3) = [13/22/31]

19. Naked quad {2356} in 8(2) cage at R1C1 and 8(2) cage at R8C8, locked for D\
19a. 7 on D\ only in R3C3 + R7C7, CPE no 7 in R3C7 + R7C3

20. R456C6 (step 14) = {289/568}
20a. 2,6 only in R4C6 -> R4C6 = {26}

21. 18(3) cage at R7C5 = {459/468}, no 2, 4 locked for C5 and N8
21a. 2 on C5 only in 16(3) cage at R1C5, locked for N2, clean-up: no 2 in R4C1 (step 17)

22. 1 in N1 only in 8(3) cage at R1C3 = {14}3 -> R1C4 = 3, R12C3 = {14}, locked for C3 and N1, R4C1 = 1 (step 17)
22a. R7C2 = 1 (hidden single in R7)

23. 8(3) cage at R8C7 = {125/134}
23a. 1 in N9 only in R89C7, no 1 in R9C6
23b. R9C6 = {23} -> no 2,3 in R89C7
23c. R6C9 + R9C6 (step 18) = [13/22], no 3 in R6C9

24. 7 on D/ only in 13(2) cage at R1C9 = {67} or in 12(2) cage at R8C2 = {57}
24a. Killer pair 5,6 in 13(2) cage, R4C6 + R6C4 and 12(2) cage, locked for D/

25. 9(3) cage at R8C3 = {126/135} -> R9C4 = 1
25a. R8C7 = 1 (hidden single in N9)

26. 9(3) cage at R1C6 = {126/135/234}
26a. 1 of {126/135} must be in R1C6, 4 of {234} must be in R1C6 -> R1C6 = {14}, no 4 in R12C7
26b. 3 of {135} must be in R2C7 -> no 5 in R2C7

27. Naked pair {14} in R1C36, locked for R1, clean-up: no 9 in R2C8

28. 21(3) cage at R6C7 = {579/678} (cannot be {489} which clashes with R6C6 using D/), no 4

29. 12(3) cage at R5C1 = {237/246/345}, no 8,9
29a. 12(3) cage + R6C1 = {2345} must contain 2, locked for N4

30. Killer triple 7,8,9 in 24(3) cage at R3C3 and 20(3) cage at R6C3 (because 8,9 of {569/578} must be in R7C3), locked for C3
30a. 7 of {578} must be in R7C4 (R67C3 cannot be {78} which clashes with 24(3) cage), no 7 in R6C3
30b. 7 in C3 only in R34C3, locked for 24(3) cage, no 7 in R3C4

31. 45 rule on N7 3 innies R7C3 + R8C1 + R9C2 = 1 remaining outie R6C1 + 17
31a. Min R6C1 = 2 -> min R7C3 + R8C1 + R9C2 = 19 but when R6C1 = 2 then R7C1 = 5 => R89C3 = {26} -> R7C3 + R8C1 + R9C2 = 19 cannot be {289} -> no 2 in R8C1 + R9C2

32. 8(3) cage at R6C1 = {25/34}1, 9(3) cage at R8C3 = {26/35}1
32a. Consider placement for 5 on D/
R2C8 = 5 => 13(2) cage at R1C9 = [85], placed for D/ => 12(2) cage at R8C2 = {39}, locked for N7, R89C3 = {26}, locked for N7, no 2 in R7C1 => no 5 in R6C1
or R6C4 = 5, no 5 in R6C1
or R8C2 = 5 => R89C3 = {26}, locked for N7, no 2 in R7C1 => no 5 in R6C1
-> no 5 in R6C1, clean-up: no 2 in R7C1
32b. 2 in N7 only in R89C3 = {26}, locked for C3 and N7

33. 12(3) cage at R5C1 (step 27) = {237/345} (cannot be {246} because R5C3 only contains 3,5), no 6, 3 locked for R5 and N4, clean-up: no 4 in R7C1
33a. Killer pair 2,4 in 12(3) cage and R6C1, locked for N4

34. R67C1 = [25/43]
34a. 9(3) cage at R6C9 = {126} (cannot be {135} which clashes with R7C1, cannot be {234} which clashes with R67C1) -> R6C9 = 1, R7C89 = {26}, locked for R7 and N9 -> R8C8 = 3, R9C9 = 5, both placed for D\, R9C7 = 4, R9C6 = 3 (cage sum), clean-up: no 8,9 in R8C2, no 9 in R9C1
34b. Naked pair {26} in 8(2) cage at R1C1, locked for N1
34c. Naked pair {35} in R3C12, locked for R3
34d. Naked pair {35} in R37C1, locked for C1

35. R3C8 = 1 (hidden single in N3), R34C9 = 7 = [43], R46C5 = [73], clean-up: no 9 in R1C9

36. Naked pair {89} in R3C47, locked for R3 -> R3C3 = 7, placed for D\, R3C56 = [26], R4C6 = 2

37. R7C7 = 3 (hidden single on D/), R7C1 = 5, R6C1 = 2 (cage sum), R8C2 = 4, R9C1 = 8, placed for D/, R3C7 = 9, R4C7 = 5 (cage sum), R3C4 = 8, R4C3 = 9, R6C3 = 8 (hidden single in C3), R7C4 = 9 (cage sum), R7C67 = [78], R6C7 = 6

38. R12C7 = [23], R1C6 = 4 (cage sum)

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

Rating Comment:
I'll rate my walkthrough for A274 at 1.5. I used locking cages and a short forcing chain for the key breakthrough.
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Ed
 Post subject: Re: Assassin 274
PostPosted: Sun Nov 10, 2013 3:30 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Andrew wrote:
Thanks HATMAN for a fun puzzle! :D
Andrew found ways to really get stuck into this puzzle much quicker than I did seeing lots of things I couldn't. :applause: It felt much more of a slog for me which my highly optimised solution doesn't convey. Andrew's early steps are better than my start so have pinched them. I never saw those "45"s and they help a lot to get somewhere quicker. Finally found my step 18 after lots of false burrowing. In the end though, very, very satisfying. As usual, HATMAN makes great zero and x killers. An outstanding assassin.

A274
30 steps:
Preliminaries courtesy of SudokuSolver
Cage 8(2) n9 - cells do not use 489
Cage 8(2) n1 - cells do not use 489
Cage 12(2) n7 - cells do not use 126
Cage 13(2) n3 - cells do not use 123
Cage 24(3) n124 - cells ={789}
Cage 8(3) n36 - cells do not use 6789
Cage 8(3) n12 - cells do not use 6789
Cage 8(3) n89 - cells do not use 6789
Cage 8(3) n47 - cells do not use 6789
Cage 9(3) n78 - cells do not use 789
Cage 9(3) n69 - cells do not use 789
Cage 9(3) n23 - cells do not use 789
Cage 9(3) n14 - cells do not use 789
Cage 21(3) n689 - cells do not use 123
Cage 20(3) n236 - cells do not use 12
Cage 20(3) n478 - cells do not use 12

1. 45 rule on N1 3 innies R1C2 + R2C1 + R3C3 = 2(1+1) outies R1C4 + R4C1 + 20
1a. Max R1C2 + R2C1 + R3C3 = 24 -> max R1C4 + R4C1 = 4, max R1C4 = 3, max R4C1 = 3
1b. Min R1C4 + R4C1 = 2 -> min R1C2 + R2C1 + R3C3 = 22, no 1,2,3,4 in R1C2 + R2C1

2. 45 rule on N9 3 innies R7C7 + R8C9 + R9C8 = 2(1+1) outies R6C9 + R9C6 + 20
2a. Max R7C7 + R8C9 + R9C8 = 24 -> max R6C9 + R9C6 = 4, max R6C9 = 3, max R9C6 = 3
2b. Min R6C9 + R9C6 = 2 -> min R7C7 + R8C9 + R9C8 = 22, no 1,2,3,4 in R7C7 + R8C9 + R9C8

3. 1 & 2 on D/ only in R4C6 + R5C5 + R6C4, locked for N5

4. 4 on D\ only in n5: 4 locked for n5

5. "45" on c5 3 innies r456C5 = 11: but {128/146/245} all blocked since 1,2 & 4 only in r5c5
5a. = {137/236}(no 4,5,8,9) -> R5C5 = {12}
5b. must have 3: 3 locked for c5 and n5

6. 3 on d\ only in one of 8(2) cages at r1c1 and r8c8 -> One of them must be {35} -> 5 locked for D\ (Locking cages)

7. "45" on n5: 3 remaining innies (remembering h11(3)r456c5) r456c6 = 19 (no 1)

8. 24(3)r3c3 = {789}: r4c4 sees all of this cage through D\ -> no 7,8,9 in r4c4 (Common Peer Elimination, CPE)

9. 15(3)r4c4 must have 4 or 6 for r4c4 = {168/249/267/456}
9a. but h11(3)r456c5 = {137/236} = [1/6,2/7..] -> {168/267} blocked from 15(3)
9b. = {249/456}(no 1,7,8)
9c. must have 4 -> r4c4 = 4
9d. -> r56c4 = 11 = {56}/[92](no 9 in r6c4)

10. Hidden single 1 in n5 -> r5c5 = 1; placed for D\
10a. -> r46c5 = 10 = {37} only: 7 locked for c5 and n5
10b. no 7 in 8(2)r1c1 nor 8(2)r8c8

11. 18(3)r7c5 = {459/468}(no 2)
11a. must have 4: 4 locked for c5 and n8

12. 2 in c5 only in 16(3)r1c5 = {259/268}: 2 locked for n2

13. 8(2)r1c1 = {26/35} = [2/5..] -> {25}[1] blocked from 8(3)r1c3
13a. 8(3)r1c3 = {134} only
13b. 4 only in r12c3: 4 locked for n1 and c3
13c. r1c1 sees all of 8(3)r1c3 -> no 3 in r1c1 (CPE)
13d. no 5 in r2c2

14. Naked quad {2356} in r1c1, r2c2, r8c8, r9c9: 6 locked for D\

15. "45" on r5: 2 innies r5c46 = 14 = {59}/[68]: no 6 in r5c6

16. h19(3)r456c6 = {289/568}
16a. 2 and 6 only in r4c6 -> r4c6 = (26)

17. 7 on D\ only in r3c3 & r7c7: r3c7 and r7c3 see both those -> no 7 in either one (CPE: or as udosuk used to call them, Crossover)

This next step is the key one that eluded me for a long time.
18. 4 in r3 only in r3c6789
18a. if 4 in r3c6 -> 20(3) = [497] only
18b. or 4 is in r3c789: ie, 9 in r3c7 or 4 in r3c789 -> {49} blocked from 13(2)r1c9
18b. 13(2) = {58/67}(no 4,9) = [5/6..]

(Andrew did a similar step in an interesting way. See his step 24)
19. 2 in D/ only in r4c6+r6c4 -> exactly one of 5 or 6 in those two cells -> Killer pair 5,6 with 13(2)r1c9: 5 and 6 locked for D/
19a. no 7 in 12(2)r8c2

20. 7 in D/ only in 13(2)r1c9 = {67} only: both locked for n3 and 6 for D/
20a. r4c6 = 2, r6c4 = 5, r5c4 = 6 (cage sum), r5c6 = 8 (1 innie r5), r6c6 = 9 (Placed for D\)

21. 21(3)r6c7 = {678} only: 8 only in c7, locked for c7

22. 20(3)r6c3 = {389} only: 9 only in r7, locked for r7
22a. caged x-wing 8 & 9 with 24(3)r3c3: no other 8 & 9 in c34

23. 6 in c3 only in 9(3)r8c3 = {126} only: 6 locked for n7

24. Naked quad {3789} in r3467c3: 3 and 7 locked for c3
24a. 7 locked for 24(3)r3c3 -> no 7 in r3c4
24b. 3 locked for 20(3)r6c3 -> no 3 in r7c4
[Andrew noticed that an alternative way to 24a and b is R37C4 = {89} (hidden pair in C4)]

25. Naked pair {14} in r12c3: 1 locked for n1 & c3 and no 1 in r1c4
25a. r1c4 = 3

26. Hidden triple 7,8,9 in n1 -> r1c2 + r2c1 from {789}

27. 9(3)r3c1 = {126/135}: Must have 1 -> r4c1 = 1

28. 8(3)r6c1 must have 1 -> r7c2 = 1

29. 8(3)r3c8 = {125/134}: one of 3 or 5 which must be in r4c9 -> no 3,5 in r3c89
29a. must have 1, 1 locked for n3

Cracked.
30. Naked pair {26} in r89c3, 2 locked for c3 and n7 and no 2 in r9c4
30a. r9c4 = 1, r5c3 = 5
30b. r5c3 = 5 -> r5c12 = 7 = {34} only: both locked for r5 and n4

Much easier now with just a few cage sums and lots of naked singles.
Cheerio
Ed
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