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Ed
 Post subject: Assassin 439
PostPosted: Tue Aug 01, 2023 6:32 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Attachment:
a439.png
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Note: broken 28(5) at r2c9

Assassin 439
Hard time cracking this one. Nothing pretty. Easy starts get me nervous!! It gets 1.95. However, JSudoku finds it pretty easy so perhaps I missed something.

triple click code:
3x3::k:3072:3072:9729:9729:2562:3075:6404:6404:6404:2309:2309:9729:9729:2562:3075:6404:6404:7174:2309:8455:9729:9729:3592:3592:5897:5897:7174:8455:8455:9729:9729:6154:6154:7174:5897:5897:4363:8455:8455:6154:6154:6154:3852:5897:7174:4363:3597:8455:4110:4110:2831:3852:7174:7952:4363:3597:3345:4110:2831:2831:3852:7952:7952:4363:3597:3345:3090:2579:2579:3852:3348:7952:3349:3349:3349:3090:3094:3094:3348:3348:7952:
solution: 
+-------+-------+-------+
| 5 7 9 | 6 3 4 | 8 1 2 |
| 6 2 3 | 1 7 8 | 9 5 4 |
| 1 4 8 | 2 9 5 | 6 3 7 |
+-------+-------+-------+
| 7 6 4 | 5 8 2 | 3 9 1 |
| 3 9 5 | 7 6 1 | 2 4 8 |
| 8 1 2 | 9 4 3 | 7 6 5 |
+-------+-------+-------+
| 4 5 7 | 3 2 6 | 1 8 9 |
| 2 8 6 | 4 1 9 | 5 7 3 |
| 9 3 1 | 8 5 7 | 4 2 6 |
+-------+-------+-------+
Cheers
Ed
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Andrew
 Post subject: Re: Assassin 439
PostPosted: Fri Aug 04, 2023 4:59 am 
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Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1895
Location: Lethbridge, Alberta, Canada
Thanks Ed for a challenging Assassin! As you said an easy start, then it gets a lot harder on the right-hand side of the grid. It took me a while to spot the forcing chains which I used to crack it. Fortunately I compiled a WORD file of cage combinations a long time ago; very helpful for those 5 and 6 cell cages, which one can't remember.

Here's how I solved Assassin 439:
Prelims

a) R1C12 = {39/48/57}, no 1,2,6
b) R12C5 = {19/28/37/46}, no 5
c) R12C6 = {39/48/57}, no 1,2,6
d) R3C56 = {59/68}
e) R78C3 = {49/58/67}, no 1,2,3
e) R89C4 = {39/48/57}, no 1,2,6
f) R8C56 = {19/28/37/46}, no 5
g) R9C56 = {39/48/57}, no 1,2,6
h) 9(3) cage at R2C1 = {126/135/234}, no 7,8,9
i) 11(3) cage at R6C6 = {128/137/146/236/245}, no 9
j) 38(8) cage at R1C3 = {12345689}, no 7

1a. 45 rule on N58 1 innie R4C4 = 5, clean-up: no 7 in R89C4
1b. 45 rule on C12 3 outies R569C3 = 8 = {125/134}, 1 locked for C3
1c. 7 in C3 only in R78C3 = {67}, locked for N7, 6 locked for C3
1d. 5 in C3 only in R569C3 = {125}, 2 locked for C3
1e. 38(8) cage at R1C3 = {12345689} -> R123C4 = {126}, locked for C4 and N2
1f. R12C5 = {37} (only remaining combination), locked for C5 and N2, clean-up: no 3,7 in R8C6, no 5,9 in R9C6
1g. 4 in N2 only in R12C6 = {48}, locked for C6, 8 locked for N2, clean-up: no 2,6 in R8C5, no 4,8 in R9C5
1h. Naked pair {59} in R3C56, locked for R3
1i. 45 rule on N8 1 outie R6C6 = 1 innie R7C4 = {37}
1j. Naked pair {37} in R69C6, locked for C6
1k. 11(3) cage at R6C6 = {236} (only remaining combination, cannot be {128/146//245} because R6C6 only contains 3,7, cannot be {137} because 3,7 only in R6C6) -> R6C6 = 3, R7C56 = {26}, locked for R7 and N8, R78C3 = [76], R7C4 = 3, clean-up: no 9 in R89C4
1l. Naked pair {48} in R89C4, locked for C4 and N8
1m. R9C6 = 7 -> R9C5 = 5, R3C56 = [95], R8C56 = [19]
1n. R7C4 = 3 -> R6C45 = 13 = [76/94]
1o. 5 in C3 only in R56C3, locked for N4
1p. 13(3) cage at R9C1 = {139/238} (cannot be {148} which clashes with R9C4), no 4, 3 locked for R9 and N7
1q. R9C3 = {12} -> no 1,2 in R9C12
1r. R1C12 = {57} (cannot be {39/48} which clash with R123C3 = {3489}, ALS block), locked for R1 and N1 -> R12C5 = [37]
1s. 9(3) cage at R2C1 = {126} (cannot be {234} which clashes with R123C3 = {3489}, ALS block), locked for N1
1t. Naked triple {126} in R2C124, locked for R2
1u. 9 in N1 only in R12C3, locked for C3
1v. Hidden killer triple 1,2,6 in R1C4 and R1C789 for R1, R1C4 = {126} -> R1C789 must contain two of 1,2,6
1w. 25(5) cage at R1C7 = {12589/14569/23569/24568} (cannot be {13489} which only contains one of 1,2,6), 5 locked for N3
1x. 7 in R3 only in R3C789, CPE no 7 in R4C9

2a. 33(6) cage at R3C2 contains 5 for C3 = {135789/145689/235689/245679} (cannot be {345678} because R56C3 only contain 1,2,5), 9 locked for N4
2b. R56C3 = {125} -> no 1,2 in R4C12 + R5C2
2c. 14(3) cage at R6C2 = {149/158/248} (cannot be {167} because 6,7 only in R6C2, cannot be {257} which clashes with R1C2), no 6,7
2d. 17(4) cage at R5C1 = {1349/1358/2348} (cannot be {1259/1268/1367/2456} which clash with R23C1, ALS block, cannot be {1457/2357} which clash with R1C1), no 6,7
2e. Killer triple 1,2,6 in R23C1 and 17(4) cage, locked for C1
2f. 17(4) cage = {1349/1358/2348} -> R5C1 = 3
2g. 45 rule on N7 3 outies R56C1 + R6C2 = 12, R5C1 = 3 -> R6C12 = 9 = {18}, locked for R6 and N4 -> R4C3 = 4, R3C2 = 4 (hidden single in N1)
2h. R9C3 = 1 (hidden single in C3) -> R9C12 = 12 = [93], R4C1 = 7, R1C12 = [57]
2i. 17(4) cage = {2348} (only remaining combination) -> R678C1 = [842]
2j. R2C2 = 2 (hidden single in N1)
2k. 3 in R4 only in R4C789, CPE no 3 in R3C7

3a. 13(3) cage at R8C8 = {238/247/256/346}
3b. 3,5,7 only in R8C8 -> R8C8 = {357}
3c. 45 rule on N9 2 innies R78C7 = 1 outie R6C9 + 1
3d. R78C7 cannot total 3,7,10 (because no 2 in R78C7, 3,4 only in R8C7, 1,9 only in R7C7, 3,7 only in R8C7) -> R6C9 = {457}, R78C7 = 5,6,8 = [14/15/17/53], no 8,9
3e. 15(4) cage at R5C7 = {1248/1257/1356} (cannot be {1239/2346} which don’t fit with R78C7, cannot be {1347} = {34}[17] because no 3 in R56C7), no 9, 1 locked for C7
3f. 4 of {1248} must be in R8C7 -> no 4 in R56C7
3g. {1356} = [1653] -> no 6 in R5C7
3h. 9 in C7 only in R124C7, CPE no 9 in R2C9
3i. Consider placement for 7 in N9
R8C7 = 7 => 15(4) cage = {1257}
or R8C8 = 7 => R9C78 = {24}, 4 locked for N9
or R8C9 = 7 => R6C9 = {45} => R78C7 = [14/15], R8C8 = 3 (hidden single in N9) => R9C78 = {28/46} => 15(4) cage = {1257/1356} (cannot be {1248} which clashes with R9C7 = {28} or is eliminated by {46}, 4 locked for N9)
-> 15(4) cage = {1257/1356}, no 4,8, 5 locked for C7
3j. R78C7 = [15/17/35] = 6,8 -> R6C9 = {57}
3k. R2C8 = 5 (hidden single in R2)

4a. 45 rule on N9 3 outies R56C7 + R6C9 = 14 = {167/257}
4b. 1 of {167} must be in R5C7, 7 of {257} must be in R6C79 (R6C79 cannot be {25} which clashes with R6C3) -> 7 in R6C79, locked for R6 and N6, R6C4 = 9 -> R6C5 = 4 (cage sum)
4c. 6 in R6 only in R6C78, locked for N6
4d. 28(5) disjoint cage at R2C9 = {14689/23689/24589/34678} (cannot be {13789/34579} because R6C5 only contains 2,6, cannot be {15679} because R2C9 only contains 3,4,8, cannot be {24679/25678} = [47]{269}/[87]{256} which clash with R56C7 + R6C9)
4e. Consider combinations for R56C7 + R6C9 = {167/257}
R56C7 + R6C9 = {167} = [167] => 1 in N9 only in 31(5) cage at R6C9 = {16789} = 7{19}[86], 8 locked for C9 => 28(5) disjoint cage = {14689/23689/34678} (cannot be {24589} = [48952])
or R56C7 + R6C9 = {257}, 5 locked for N6
-> 28(5) disjoint cage = {14689/23689/34678}, no 5
4f. 5 in N6 only in R56C7 + R6C9 = {257}, 2 locked for N6 -> R6C8 = 6
4g. 15(4) cage at R5C7 = {1257} (only remaining combination) -> R7C7 = 1, R568C7 = {257}, 2,7 locked for C7

5a. 9 in N3 only in 25(5) cage at R1C7 (step 1w) = {12589/14569/23569}
5b. 23(5) cage at R3C7 = {12389/13469/13478} (cannot be {12479} because R3C7 only contains 6,8, cannot be {23468} = [62]{38}4 which clashes with 25(5) cage)
5c. R3C7 = {68} -> no 8 in R345C8 + R4C9)
5d. 8 in N6 only in R4C7 + R5C9, locked for 28(5) disjoint cage at R2C9, no 8 in R23C9
5e. 28(5) disjoint cage at R2C9 (step 4e) = {14689/23689/34678}
5f. 1 of {14689} must be in R3C9 -> no 1 in R5C9
5g. 1 in N6 only in R4C78 + R5C8, locked for 23(5) cage, no 1 in R3C8
5h. Consider placement for 7 in C8
R3C8 = 7 => 23(5) cage = {13478}
or R8C8 = 7, R9C78 = 6 = [42] => 23(5) cage = {13469/13478}
-> 23(5) cage = {13469/13478}, no 2
5i. 23(5) cage = {13469/13478} -> R5C8 = 4
5j. Naked pair {37} in R38C8, locked for C8
5k. 13(3) cage at R8C8 (step 3a) = {238/247} (cannot be {346} because 4,6 only in R9C7) -> R9C8 = 2, R9C7 = {48}
5l. R9C9 = 6 (hidden single in R9)
5m. Hidden killer pair 3,4 in 13(3) cage and R8C9 for N9, 13(3) cage contains one of 3,4 -> R8C9 = {34}
5n. Naked pair {34} in R28C9, locked for C9
5o. Naked pair {19} in R4C78, locked for R4 and N6
5p. R4C7 + R5C9 = [38], R6C8 = 6, R2C9 = 4 -> R3C9 = 7 (cage sum)

and the rest is naked singles.
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wellbeback
 Post subject: Re: Assassin 439
PostPosted: Sun Aug 06, 2023 8:05 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 282
Location: California, out of London
I echo both of your comments. Tough to finish with a lot of steps! Thanks Ed!

Assassin 439 WT:
1. Start is straightforward and leads to this position.
Attachment:
a439.jpeg
a439.jpeg [ 77.09 KiB | Viewed 13078 times ]

(Note that Innies n3 = +20(4) and contains a 7 in r3. Since at least one of (26) in n3 is in r1 -> Innies n3 cannot also contain a 5.)

2. Since (2346) already on r7 -> 15(4)r5c7 cannot be {2346}
-> 15(4)r5c7 must have a 1 in r5c7 or r7c7.
Innies n36 = r56c7 + r6c9 = +14(3)
-> Min r56c7 = +5
Also Min r8c7 = 3
-> Max r7c7 = 7
Since (23467) already on r7 -> r7c7 from (15)
-> 9 in r7c89
-> Max r6c9 = 7 (Cannot be 8 or 9)
-> Min r56c7 = +7(2)

3. 15(4)r5c7 has a 1 in r5c7 or r7c7
Note that if 1 in r7c7 this puts (IOD n9) r6c9 = r8c7
15(4) must also have at least one of (23)
If it has a 2 that must go in n6 r56c7 in which case 1 must be in r7c7. (Since Min r56c7 = +7(2))
If it has a 3 that must go in r8c7 in which case 1 must be in r5c7. (1 in r7c7 would put a 3 in r6c9)
-> 15(4) cannot contain both (23). I.e., it is not {1239}

4. Either 2 in 15(4) in n6 in r56c7 ...
which puts remaining Innies n36 = +12(2) which cannot be (39) - must be (48) or (57)
Since 8 already on r6, if Innies n36 were {248} this puts 15(4) = [8214].
But that fails since it puts r9c789 = [6{28}] and r8c89 = {37} which leaves no solution for 13(3)n9
-> if 2 in 15(4) that puts innies n36 = {257}, and since r56c3 = {25} - this puts 7 in r6c79
-> also that puts 15(4) = {1257} with 2 in r56c7 and 1 in r7c7

5. ... or 3 in 15(4) in n9 in r8c7 ...
which puts r5c7 = 1 and r7c7 = 5. I.e., 15(4) = [1653] and (Innies n36) r6c9 = 7
-> In all cases 7 in r6c79
-> r6c45 = [94] and r5c4 = 7

6. All solutions of 15(4) contain a 5
-> (HS 5 in n3) r2c8 = 5

7. 9 in c7 in r1234c7
-> 9 not in r2c9
-> 9 in 25(4)n3

8. For the case 15(4) = [1653] and r6c9 = 7, this puts r6c38 = [52] and 31(5) = [7{19}86]
This leaves no solution for 28(5)n36 since r23c9 can be at most [43]
-> 15(4) = {1257} with 2 in r56c7 and 1 in r7c7. Innies n36 = {257}.
-> (HS in r6) r6c8 = 6

9. Since r2c9 cannot be any of (1257) this -> whatever is in r2c9 goes in n6 in r45c8 and in n9 in r9c7
This can only be 4 or 8.
-> r9c47 = {48}
-> (NP in r9) r9c89 = [26]
13(3)n9 from [382] or [742]

10. Trying r2c9 = 8 puts 13(3)n9 = [382] and r3c789 = [372] (Innies n3)
But this leaves no place for 3 in n6
-> r2c9 = 4
-> 13(3)n9 = [742]
-> 15(4) = [2715]
-> 31(5) = [5{89)36]
Also -> r3c9 = 7
-> 28(5)n36 = [47386]
-> r7c89 = [89]
-> 23(5)n36 = [63914]
etc. (Phew!)
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