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 Post subject: paper solvable +
PostPosted: Fri Jul 02, 2021 8:07 am 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Paper Solvable 1 +(2021)

SS gives this a 1.8, but JS does it without fishes, a lot of interacting work but no really complex moves.

Your views on difficulty?


Image

JS Code:
3x3::k:7169:7169:7169:2306:1795:1795:3844:4869:4869:7169:7169:4358:2306:5127:5127:3844:4869:4869:7169:4358:4358:3336:5127:3593:3593:2570:2570:2571:2571:3336:3336:7180:3593:3593:4365:3854:3087:3088:3088:7180:7180:7180:4365:4365:3854:3087:3088:6161:6161:7180:3602:3602:787:787:2324:2324:6161:6161:3093:3602:4630:4630:6935:4376:4376:2585:3093:3093:2330:4630:6935:6935:4376:4376:2585:4123:4123:2330:6935:6935:6935:
Solution:
961834725
274156839
358297164
736512498
812469357
495783612
189345276
547621983
623978541


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 Post subject: Re: paper solvable +
PostPosted: Mon Jul 05, 2021 10:34 pm 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
I did this before trying Ed's new Assassin. I'm pretty good at mental arithmetic but I wouldn't call it paper solvable although the first two placements clearly are. As HATMAN said there are lots of interactions. It's more like a moderate Assassin, like some of Ruud's later ones but not his hardest ones.

My hardest step was 6b, then apart from 6f all the other steps were fairly routine ones. I won't rate my walkthrough but definitely nowhere near 1.80.

Here's my walkthrough:
Prelims

a) R12C4 = {18/27/36/45}, no 9
b) R1C56 = {16/25/34}, no 7,8,9
c) R12C7 = {69/78}
d) R3C89 = {19/28/37/46}, no 5
e) R4C12 = {19/28/37/46}, no 5
f) R45C9 = {69/78}
g) R56C1 = {39/48/57}, no 1,2,6
h) R6C89 = {12}
i) R7C12 = {18/27/36/45}, no 9
j) R89C3 = {19/28/37/46}, no 5
k) R89C6 = {18/27/36/45}, no 9
l) R9C45 = {79}
m) 20(3) cage at R2C5 = {389/479/569/578}, no 1,2
n) 14(4) cage at R2C6 = {1238/1247/1256/1346/2345}, no 9

1a. Naked pair {12} in R6C89, locked for R6 and N6
1b. Naked pair {79} in R9C45, locked for R9 and N8, clean-up: no 1,3 in R8C3, no 2 in R89C6
1c. 45 rule on N3 1 innie R3C7 = 1, clean-up: no 9 in R3C89
1d. 45 rule on N7 1 innie R7C3 = 9, clean-up: no 1 in R9C3
1e. 45 rule on N2 2 innies R3C46 = 9 = {27/36/45}, no 8,9
1f. 45 rule on N4 2 innies R46C3 = 11 = {38/47/56}, no 1,2
1g. 45 rule on N6 2 innies R46C7 = 10 = {37/46}
1h. Killer pair 6,7 in R12C7 and R46C7, locked for C7
1i. Killer pair 6,7 in R46C7 and R45C9, locked for N6
1j. 45 rule on N8 2 innies R7C46 = 8 = {26/35}
1k. R7C12 = {18/27/45}, (cannot be {36} which clashes with R7C46), no 3,6
1l. R89C6 = {18/45} (cannot be {36} which clashes with R7C46), no 3,6

2a. 2 in C7 only in R789C7, locked for N9
2b. 18(3) cage at R7C7 = {279/369/378/459/468} (cannot be {189} which clashes with R12C7, cannot be {567} because 6,7 only in R7C8), no 1
2c. 9 of {279/459} must be in R8C7 -> no 2,5 in R8C7
2d. 6,7 of {369/378/468} must be in R7C8 -> no 3,8 in R7C8
2e. Killer pair 8,9 in R12C7 and R78C7, locked for C7

3a. 45 rule on C6789 3 innies R125C6 = 19 = {289/379/469/478/568}, no 1, clean-up: no 6 in R1C5
3b. 1 in C6 only in R89C6 = {18}, locked for N8, 8 locked for C6
3c. R125C6 = {379/469}, no 2,5, 9 locked for C6, clean-up: no 2,5 in R1C5
3d. R12C4 = {18/27/45} (cannot be {36} which clashes with R1C56), no 3,6
3e. R3C46 (step 1e) = {27/45} (cannot be {36} which clashes with R1C56), no 3,6
3f. 9 in N2 only in 20(3) cage at R2C5 = {389/569} (cannot be {479} which clashes with R3C46), no 4,7

4a. 45 rule on C1234 3 innies R589C4 = 19 = {289/379/469/478/568}, no 1
4b. R589C4 = {289/379/469} (cannot be {478} which clashes with R12C4, cannot be {568} because R9C4 only contains 7,9), no 5, 9 locked for C4
4c. 2 of {289/379} must be in R8C4 -> 2,3 in R5C4

5a. 9 in R6 only in R6C125
5b. 45 rule on R6789 3 innies R6C125 = 21 = {489/579}, no 3,6, clean-up: no 9 in R5C1
5c. Min R6C2 = 4 -> max R5C23 = 8, no 8,9

6a. R1C56 = [16]/{34}, R125C6 (step 3c) = {379/469}, R3C7 = 1
6b. 14(4) cage at R2C6 = {1247/1256} (cannot be {1346} = [41]{36} which clashes with R125C6 = [694], combination crossover clash), no 3, 2 locked for C6, clean-up: no 7 in R6C7 (step 1g), no 6 in R7C4 (step 1j)
6c. 6 of {1256} must be in R4C7 -> no 6 in R4C6
6d. 14(3) cage at R6C6 = {356} (only remaining combination, cannot be {347} = [743] which clashes with R6C125), 5 locked for C6, clean-up: no 4 in R3C4 (step 1e)
6e. 14(4) cage at R2C6 = {1247}, no 6
6f. R3C46 (step 1e) = {27} (cannot be [54] because 13(3) cage at R3C4 = [571/562] clashes with 14(4) cage at R3C6 = [4127], locked for R3 and N2, clean-up: no 3,8 in R3C89
[Cracked. The rest is fairly straightforward.]
6g. Naked pair {46} in R3C89, locked for R3 and N3, clean-up: no 9 in R12C7
6h. Naked pair {78} in R12C7, locked for C7 and N3 -> R4C7 = 4, R6C7 = 6 (step 1g), clean-up: no 6 in R4C12, no 5 in R4C3, no 7 in R6C3 (both step 1f), no 9 in R45C9, no 2 in R7C4 (step 1j)
6i. Naked pair {35} in R7C46, locked for R7 and N8, clean-up: no 4 in R7C12
6j. R7C7 = 2, R8C7 = 9 (hidden single in C7) -> R7C8 = 7 (cage sum)
6k. Naked pair {18} in R7C12, locked for R7 and N7, clean-up: no 2 in R89C3
6l. Naked pair {46} in R37C9, locked for C9
6m. Naked pair {78} in R45C9, 8 locked for C9 and N6
6n. Naked quad {2359} in R1245C8, locked for C8 -> R6C89 = [12]
6o. R46C3 (step 1f) = {38/56} (cannot be [74] which clashes with R89C3, no 4,7
6p. Killer pair 3,6 in R46C3 and R89C3, locked for C3
6q. Killer pair 5,8 in R3C3 and R46C3, locked for C3

7a. 13(3) cage at R3C4 = {238/256} (cannot be {157} because 1,5 only in R4C4), no 1,7 -> R3C4 = 2, R4C34 = {38}/[65], R34C6 = [72], clean-up: no 8 in R4C12
7b. R56C1 = {48/57} (cannot be [39] which clashes with R4C12
7c. 1 in C4 only in R12C4 = {18}, locked for N2, 8 locked for C4, clean-up: no 6 in R1C6, no 3 in R4C3, no 8 in R6C3 (step 1f)
7d. Naked pair {35} in R67C6 -> R1C56 = [34]
7e. Naked pair {35} in R47C4, locked for C4
7f. Naked pair {35} in R6C36, locked for R6, clean-up: no 7 in R5C1
7g. R6C3 + R7C4 = {35} = 8, R7C3 = 9 -> R6C4 = 7 (cage sum), R9C45 = [97], clean-up: no 5 in R5C1
7h. Naked pair {48} in R56C1, locked for C1 and N4
7i. R4C3 = 6 -> R4C4 = 5 (cage sum), R6C36 = [53], clean-up: no 4 in R89C3
7j. R6C2 = 9 -> R5C23 = 3 = {12}, 1 locked for R5 and N4
7k. R3C3 = 8 -> R2C3 + R3C2 = 9 = [45]

and the rest is naked singles.


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 Post subject: Re: paper solvable +
PostPosted: Wed Jul 28, 2021 6:04 pm 
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Grand Master
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
This is a reworked WT with the key conclusion in Step 1. It took me way too long to spot it but once I did - it all went pretty smoothly. Definitely 'paper solvable' and I would rate it less than 1.0. Thanks HATMAN!
paper solvable + WT:
1. Innies n3 -> r3c7 = 1
Innies c6789 = r125c6 = +19(3) (No 1)
3(2)n6 = {12}
16(2)n8 = {79}
-> Innies n8 = r7c46 = +8(2) = {26} or {35}
-> 1 in c6 only in r89c6 -> 9(2)n8 = {18}

2. -> Innies c6789 = r125c6 = +19(3) = {469} or {379}
-> Remaining cells c6 = r3467c6 = {25(37|46)}

3. Innies n6 = r46c7 = +10(2) = {37} or {46} (No 589)
Innies n7 -> r7c3 = 9
-> 9 in r6 only in r6c125 (which are the innies r6789)
-> Innies r6789 = r6c125 = +21(3) = {579} or {489}
12(2)n4 means r6c12 cannot = +12.
-> 9 in r6 in r6c12

4. Remaining cells in r6 = r6c3467 = +21(4) and contains (36)
24(4)r6c3 cannot contain all of (369) -> at least one of (36) in r6c67
-> No solution for 14(3)r6c6 with r7c6 = 2
-> 2 in c6 in r34c6

5. Given at least one of (36) in r6c67 and r7c6 only from (356)
-> 14(3)r6c6 = {356} with 5 in r67c6
-> Innies n6 = r46c7 = [46] or [73]
-> 14(4)r3c6 = {1247} with 1 in r3c7 and 2 in r34c6

6. Innies n2 = r3c46 = +9(2) can only be {27} or [54]
But it cannot be [54] since that puts r4c67 = [27] which leaves no solution for 13(3)r3c4
-> r3c46 = {27}

7. -> 10(2)n3 = {46}
-> 15(2)n3 = {78}
-> 19(4)n3 = {2359}
Also -> r46c7 = [46]
-> 15(2)n6 = {78}
-> 17(3)n6 = {359}
Also r67c6 = {35}
-> Innies n8 = r7c46 = {35}
-> 12(3)n8 = {246}

8. Innies n4 = r46c3 = +11(2) (No 1)
6 in r6c7 -> r4c3 cannot be 5
Also 4 in r4c7 -> no solution for 13(3)r3c4 with r3c4 = 7
-> r3c46 = [27]
-> r4c6 = 2

9. 9 in r6c12 and r4c67 = [24] -> 10(2)n4 = {37}
-> 12(2)n4 = {48}
-> 12(3)n4 = [{12}9]
-> r46c3 = [65]
-> r4c4 = 5
-> r67c6 = [35]
-> r67c4 = [73]

10. 1 in r4 only in r4c5
-> 1 in n2 in r12c4 -> 9(2)n2 = {18}
-> 7(2)n2 = [34]
-> 20(3)n2 = {569} with 5 in c5 and 6 in r2

11. 8 in r3 in r3c23
-> (Given previous placements) 17(3)n1 = [458]
-> 20(3)n2 = [569]
-> r5c6 = 9
Also -> r3c1 = 3

12. Also 10(2)n7 = [73]
-> r7c8 = 7
-> 18(3)n9 = [279]
-> (HS 3 on c7) -> 17(3)n6 = [935]
-> r9c7 = 5
-> 19(4)n3 = [2539]
etc.


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 Post subject: Re: paper solvable +
PostPosted: Wed Jul 28, 2021 8:33 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
A lovely start - simple but not obvious.


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