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 Post subject: Assassin 340
PostPosted: Sun Oct 09, 2016 9:17 am 
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Assassin 340

(Very) long time no post :oops:

This one is based on a medium killer from my mobile phone which gave me several headaches because of bad math/combination on my side. After combining some cages I got this one, SSolver 3.6.3 gives it a 1.40

Image

Code:
3x3::k:5632:4353:4353:4353:3610:2820:2820:2820:4357:5632:5632:1538:4104:3610:5130:3595:4357:4357:2822:4103:1538:4104:3610:5130:3595:3084:3341:2822:4103:4103:4104:3610:5130:3084:3084:3341:2822:2318:2318:3860:3860:3860:4377:4377:3341:5135:5135:2318:3605:3605:3605:4377:5649:5649:4880:5135:5138:5138:4374:3096:3096:5649:3331:4880:5135:4627:5138:4374:3096:4375:5649:3331:4880:4880:4627:4627:4374:4375:4375:777:777:

Solution:
783615249
961724853
425839671
659187324
132456798
874293165
316542987
248971536
597368412


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 Post subject: Re: Assassin 340
PostPosted: Sun Oct 09, 2016 9:27 am 
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Assassin 340 v0.9

Here is the original version, SSolver gives it a 0.90. Try to do it without writing down any combinations and using a calculator. Then you might see where my headache came from. :lol:

Image

Code:
3x3::k:5632:4353:4353:4353:771:2820:2820:2820:4357:5632:5632:1538:4104:771:5130:3595:4357:4357:2822:4103:1538:4104:2825:5130:3595:3084:3341:2822:4103:4103:4104:2825:5130:3084:3084:3341:2822:2318:2318:3860:3860:3860:4377:4377:3341:5135:5135:2318:3605:3605:3605:4377:5658:5658:1296:5135:5138:5138:4374:3096:3096:5658:3355:1296:5135:4627:5138:4374:3096:4375:5658:3355:3601:3601:4627:4627:4374:4375:4375:796:796:


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 Post subject: Re: Assassin 340
PostPosted: Thu Oct 13, 2016 10:10 am 
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 692
Location: Saudi Arabia
On the easier one, once I eventually identified the hidden pair {12} in r78c6 it flowed reasonably well.


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 Post subject: Re: Assassin 340
PostPosted: Fri Oct 14, 2016 2:25 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
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Location: Saudi Arabia
Solution sketch:

Innies c1234 r56c4 = 6(2) = {15/24}
innies c6789 r56c6 = 9(2) = {18/27/36} <> 45
innies c5 r56c5 = 14(2) = {59/68}
easy combo elimination on r56 r56c5 = [59]
mostly as the easy one from here


Difficulty: say 1.0 but I enjoyed it thanks Nasenbaer


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 Post subject: Re: Assassin 340
PostPosted: Tue Oct 18, 2016 1:59 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Welcome back Nasenbaer! :D

HATMAN wrote "On the easier one, once I eventually identified" I stared at the diagram for a long time until I eventually spotted that there are two 3(2) cages pointing at N8.
Then it was a paper solvable puzzle, although I'll admit that I used the Excel Autosum to calculate totals over multiple columns, rather than adding them by mental arithmetic. It was fortunate that some 3-cell cages had unique permutations.
Here is my walkthrough for Assassin 340 Easier Version:
1. Naked pair {12} in 3(2) cage at R1C5, naked pair {12} in 3(2) cage at R9C8, no 1,2 in 20(3) cage at R7C3 -> R78C6 = {12} (hidden pair in N8) -> R7C7 = 9 (cage sum)

2a. 45 rule on C1234 2 innies R56C4 = 6 = {15/24}
2b. 45 rule on C6789 2 innies R56C6 = 9 = {36} (cannot be {45} which clashes with R56C4)
2c. 45 rule on C5 2 innies R56C5 = 14 = {59} -> R45C4 = {24}
2d. 15(3) cage at R5C4 = [456] -> 14(3) cage at R6C4 = [293]
2e. Naked pair {12} in 3(2) cage at R1C5, naked pair {12} in R78C6 -> R4C4 = 1 (hidden single in N5)

3. 45 rule on R1234 2 outies R5C19 = 9, no 9, 9(3) cage at R5C2 cannot contain 7,8,9 -> R5C8 = 9 (hidden single in R5)
3a. R5C19 must contain one of 7,8 -> R5C7 must contain one of 7,8 -> R56C7 = [71]
3b. R5C19 must contain 8 = [18]
3c. 9(3) cage can only be {234} -> R6C3 = 4
3d. 5(2) cage at R7C1 must be {23}, R5C1 = 1 -> R34C1 = 10 = [46]
3e. R4C56 = {78} -> 11(2) cage at R3C5 = [38], R4C6 = 7
3f. R5C23 = {23}, R6C12 = {78} (hidden pair in R6) -> R4C23 = {59}, R3C2 = 2 (cage sum), R5C23 = [32]

4. 6(2) cage at R3C2 = {15} -> 22(3) cage at R1C1 = {679} -> R2C2 = 6, R12C1 = {79} -> R6C12 = {78} (hidden pair in R6) = [87]
4a. 8 in N1 only in 17(3) cage at R1C2 = [836]
4b. 11(3) cage at R1C6 = {245} -> 3(2) cage at R1C5 = [12]
4c. 14(2) cage at R2C7 = [86]
4d. 16(3) cage at R2C4 = [781]
4e. 22(3) cage at R1C1 = [796] -> 14(2) cage at R9C1 = [59], 16(3) cage at R3C2 = [259]
4f. 20(3) cage at R2C6 = [497]
4g. R9C6 = 8 (hidden single in C6) -> R89C7 = 9 = {45}, 11(3) cage at R1C5 = [524]
4h. R1C9 = 9 -> R2C89 = 8 = {35} -> R2C3 = 1, R3C3 = 5
4i. 12(3) cage at R3C8 = [732] -> 13(3) cage at R3C9 = [148] -> 3(2) cage at R9C8 = [12]

5. R9C12 = [59], R789C4 = [593] -> R7C3 = 6 (cage sum), 13(2) cage at R7C9 = [76]

and the rest is naked singles.

Rating:
0.75, which is the equivalent of a score of 0.5 on Mike's original definitions.


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 Post subject: Re: Assassin 340
PostPosted: Tue Oct 18, 2016 2:38 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
And then I did the Assassin, finding the same way in that HATMAN used.

Here is my walkthrough for Assassin 340:
Prelims

a) R23C2 = {15/24}
b) R23C7 = {59/68}
c) R78C9 = {49/58/67}, no 1,2,3
d) R9C89 = {12}
e) 22(3) cage at R1C1 = {589/679}
f) 11(3) cage at R1C6 = {128/137/146/236/245}, no 9
g) 20(3) cage at R2C6 = {389/479/569/578}, no 1,2
h) 11(3) cage at R3C1 = {128/137/146/236/245}, no 9
i) 9(3) cage at R5C2 = {126/135/234}, no 7,8,9
j) 20(3) cage at R7C3 = {389/479/569/578}, no 1,2
k) 14(4) cage at R1C5 = {1238/1247/1256/1346/2345}, no 9

Steps resulting from Prelims
1a. Naked pair {12} in R9C89, locked for R9 and N9
1b. 22(3) cage at R1C1 = {589/679}, 9 locked for N1

2a. 45 rule on C1234 2 innies R56C4 = 6 = {15/24}
2b. 45 rule on C5 2 innies R56C5 = 14 = {59/68}
2c. 45 rule on C6789 2 innies R56C6 = 9 = {18/27/36} (cannot be {45} which clashes with R56C4), no 4,5,9
2d. 14(3) at R6C4 = {149/167/239} (cannot be {158/248} which clash with R56C4 CCC, cannot be {347} because 3,7 only in R6C6, cannot be {257/356} which clash with R56C6 CCC), no 5,8, clean-up: no 1 in R5C4, no 6,9 in R5C5, no 1 in R5C6
2e. 3,7 of {167/239} must be in R6C6 -> no 2,6 in R6C6, clean-up: no 3,7 in R5C6
2f. 15(3) cage at R5C4 = {258/456}, 5 locked for R5 and N5

3a. 45 rule on R1234 2 outies R5C19 = 9 = {18/27/36}, no 4,9
3b. 45 rule on R6789 2 outies R6C37 = 5 = {14/23}
3c. 9 in R5 only in 17(3) cage at R5C7 = {179/269} -> R5C78 = {69/79}, 9 locked for N6, R6C7 = {12}, clean-up: no 1,2 in R6C3
3d. 9(3) cage at R5C2 = {234} (only remaining combination, cannot be {126} because R6C3 only contains 3,4), locked for N4, 2 also locked for R5, clean-up: no 7 in R5C1, no 6,7 in R5C9
3e. 15(3) cage at R5C4 (step 2f) = {456} = [456] -> 14(3) cage at R6C4 (step 2d) = {239} = [293], R6C37 = [41], R5C19 = [18], clean-up: no 2 in R23C3, no 5 in R78C9
3f. Naked pair {79} in R5C78, locked for N6
3g. Naked pair {56} in R6C89, locked for R6, N6 and 22(4) cage at R6C8
3h. R6C89 = {56} = 11 -> R78C8 = 11 = {38} (cannot be {47} which clashes with R89C9), locked for C8 and N9
3i. 5 in N9 only in R789C7, locked for C7, clean-up: no 9 in R23C7
3j. Naked pair {68} in R23C7, locked for C7 and N3
3k. Naked pair {78} in R6C12, locked for N4 and 20(4) cage at R6C1
3l. R6C12 = {78} = 15 -> R78C2 = 5 = {14} (cannot be {23} which clashes with R5C2), locked for C2 and N7
3m. Naked pair {15} in R23C3, locked for C3 and N1
3n. R5C1 = 1 -> R34C1 = 10 = [46], R4C12 = [59] -> R3C2 = 2 (cage sum), R5C23 = [32]
3o. 22(3) cage at R1C1 = {679} (only remaining combination) -> R2C2 = 6, R1C12 = {79}, locked for C1 and N1, R23C7 = [86], R6C12 = [87]
3p. R1C23 = [83] -> R1C4 = 6 (cage sum), R9C2 = 9

4. 11(3) cage at R1C6 = {245} (only remaining combination), locked for R1
4a. 17(3) cage at R1C9 cannot be 1{79} which clashes with R2C1, no 1 in R1C9
4b. Killer pair 7,9 in R1C9 and R78C9, locked for C9
4c. R5C9 = 8 -> R34C9 = 5 = [14/32]
4d. R4C7 = 3 (hidden single in N6) -> R34C8 = 9 = [54/72]
4e. R1C7 = 2 (hidden single in C7)
4f. 9 in N3 only in N3 = {179/359}, no 4
4g. R1C8 = 4 (hidden single in N3) -> R34C8 = [72], R34C9 = [14], R1C6 = 5, R1C9 = 9, R12C1 = [79], R1C5 = 1
4h. 20(3) cage at R2C6 = {479} (only remaining combination) = [497], 16(3) cage at R2C4 = [781], 14(4) cage at R1C5 = [1238]
4i. R9C6 = 8 -> R89C7 = {45}, locked for N9
4j. R8C4 = 9 (hidden single in R8) -> R7C34 = 11 = [65] (cannot be [83] which clashes with R7C8)

and the rest is naked singles.

Rating Comment:
I agree with HATMAN's rating of 1.0. I don't understand why the SS score is 1.4; surely SS can do the analysis in step 2d, which is the hardest part of my walkthrough.


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