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 Post subject: Human Solvable 26
PostPosted: Tue Mar 28, 2017 12:46 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 692
Location: Saudi Arabia
Human Solvable 26

I was trying for an assassin but by accident got an HS one.

Neither JS or SS solves it, but after you solve the HS bit it is about hard paper solvable.


Image

JS Code:
3x3:d:k:26:27:3585:3586:3587:3588:4360:5129:5642:28:3585:3586:3587:3588:4360:5129:5642:29:3585:3586:3587:3588:4360:5129:5642:30:31:32:3585:3586:3587:3588:4360:5129:5642:33:2578:2578:2578:34:35:36:4633:4633:4633:37:4632:7191:6934:4373:5396:5651:2577:38:39:40:4632:7191:6934:4373:5396:5651:2577:41:4632:7191:6934:4373:5396:5651:2577:42:4632:7191:6934:4373:43:5396:5651:2577:44:

Solution:
894637125
725418369
316259487
952143678
163872594
478965231
631784952
589321746
247596813


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 Post subject: Re: Human Solvable 26
PostPosted: Tue May 16, 2017 9:19 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
Thanks HATMAN - Here's how I did it...

Human Solvable 26 WT:
1. Innies r1234 (uncaged cells) = +65(8)
-> Uncaged cells in both n1 and n3 = {789}
and r4c19 = {89}

2. -> 22(4)n36 = [{456}7]
-> 20(4)n326 = [{23}96]
-> r1c7 = 1
Also -> r2c9 = 9, r3c89 = [87]
-> r4c19 = [98]
-> r1c2 = 9, r12c1 = {78}

Also
-> 18(3)n6 = {459}
-> r6c789 = {123}

Also 10(3)n4 = {136} or {127} (1 in r5 in n4)
and r5c456 = {278} or {368} (8 in r5 in n5)

3.HS 9 in D\ -> r7c7 = 9
-> HS 9 in D/ -> r6c4 = 9
Also r5c8 = 9
Also -> HP (78) in c7 -> r89c7 = {78}
Since Min r6c7 = 2 and Min r7c8 is 5
-> 22(4)n69 = [25{78}]
-> r1c8 = 2, r2c7 = 3
-> Since 10(4) = {1234} -> r7c9 = 2
-> r89c89 = {1346} with 4 in c8 and 6 in c9

4. 1 in D/ only in n7
Since r5c456 from {278} or {368} -> At least one of (27) in D/ in n7
Since 18(4)n47 contains a 1, does not contain a 9, and at least one of (27) -> 18(4)n47 = {1278} with (12) in n7
-> NS r4c6 = 3
-> 10(3)n4 = {136}
-> r5c456 = {278}

5. HS 9 in 28(4)n487 -> r8c3 = 9
-> r9c5 = 9

6. HP r6c23 = {78}
Whichever of (78) is in r6c2 goes in n7 in r9c3
Whichever of (78) is in r6c3 goes in n7 in r8c2
-> HS 2 in 18(4) -> r9c1 = 2
-> r7c3 = 1

7. Also -> (78) in n8 in r7c456
-> 21(4)r6c6 does not contain 7 or 8
Also 1 in c6 in r89c6
-> 21(4)r6c6 = [59{16}] or [69{15}]
-> HS 2 in n8 -> r8c5 = 2
-> 2 in D\ in r2c2 or r3c3
-> HS 2 in n2 -> r3c4 = 2
-> r2c2 = 2
Also r5c6 = 2

8. 14(4)r1c5 does not contain a 2 -> must be {1346}
-> {1346} locked in D\ in r3489
-> 21(4)r6c6 = [59{16}]
-> HS 6 in r6 -> r6c5 = 6
-> 17(4)r6c5 = [6425]
-> r7c45 = {78}
-> r8c4 = 3
Also r8c1 = 5, r9c2 = 4

9. Finally
17(4)r1c7 = [1853]
-> r12c1 = [87]
-> r5c45 = [87]
-> 18(4)r6c2 = [7182]
etc.


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 Post subject: Re: Human Solvable 26
PostPosted: Wed Mar 14, 2018 8:46 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
Thanks HATMAN for this, probably one of your easiest Human Solvables.

After the human solvable step, there seems to be a fairly narrow solving path so my way was very similar to wellbeback's.

Here is my walkthrough for Human Solvable 26:
Prelims

a) 10(3) cage no 8,9
b) 10(4) cage = {1234}
c) 14(4) cages no 9
d) 27(4) cage no 1,2
e) 28(4) cage no 1,2,3

1. 45 rule on R1234 total of 8 ‘zero’ cells = 65 -> 3 ‘zero’ cells in N1 total 24, 3 ‘zero’ cells in N3 total 24 and 2 ‘zero’ cells in R4 total 17
1a. R1C12 + R2C1 = 24 = {789}, locked for N1
1b. R2C9 + R3C89 = 24 = {789}, locked for N3
1c. R4C19 = 17 = {89}, locked for R4
1d. Naked triple {789} in R123C1, locked for C1, 7 also locked for N1
1e. Naked triple {789} in R234C9, locked for C9, 7 also locked for N3

2. 22(4) cage at R1C9 = {4567} (only remaining combination) -> R4C8 = 7, R1C9 + R2C8 + R3C7 = {456}, locked for N3 and D/
2a. Naked quad {1234} in R1689C8, locked for C8 and 10(4) cage at R6C8, no 4 in R7C9
2b. 20(4) cage at R1C8 = {2369} (only remaining combination) -> R1C8 + R2C7 = {23}, locked for N3, R3C6 + R4C7 = [96], R3C89 = [87], R24C9 = [98], R4C1 = 9, R1C2 = 9 (hidden single in N1)
2c. 18(3) cage at R5C7 = {459} (only remaining combination), locked for R5 and N6
2d. Naked triple {123} in R6C789, locked for R6
2e. 4 in C8 only in R89C8, locked for N9
2f. R1C7 = 1, 17(4) cage at R1C7 = {1268/1358/1367} (cannot be {1457} because R4C6 only contains 2,3) -> R2C6 = {78}, R3C5 = {56}
2g. Naked pair {78} in R2C16, locked for R2
2h. Naked pair {23} in R26C7, locked for C7
2i. 10(3) cage at R5C1 = {127/136}, 1 locked for R5 and N4
2j. 1 in R4 only in R4C45, CPE no 1 in R3C4
2k. 8 in R5 only in R5C456, locked for N5
2l. R7C7 = 9 (hidden single on D\) -> R5C8 = 9 (hidden single in R5)
2m. R89C7 = {78} (hidden pair in C7)
2n. 22(4) cage at R6C7 = {2578} (only remaining combination) -> R6C7 = 2, R7C8 = 5, R1C8 + R2C7 = [23], R2C8 = 6
2o. 10(4) cage at R6C8 = {1234} -> R7C9 = 2
2p. R6C4 = 9 (hidden single on D/)
2q. R8C3 = 9 (hidden single in N7)
2r. 1 on D/ only in R7C3 + R8C2 + R9C1, locked for N7
2s. 18(4) cage at R6C2 = {1278/1368} (cannot be {1458/1467} because 4,5,6 only R6C2), CPE no 8 in R79C2
2t. Killer pair 2,3 in R4C6 and R7C3 + R8C2 + R9C1, locked for D/
2u. Naked pair {78} in R1C1 + R5C1, locked for D\, CPE no 7,8 in R1C5
2v. 45 rule on R5 3 innies R5C456 = 17 = {278/368}
2w. Killer pair 2,3 in R4C4 and R5C46, locked for N5
2x. 2 on D\ only in R2C2 + R3C3, locked for N1
2y. 28(4) cage at R6C3 = {4789/5689}, CPE no 8 in R7C3
2z. 1 in R3 only in R3C123, locked for N1
2aa. 8 in R7 only in R7C456, locked for N8
2ab. R9C5 = 9 (hidden single in C5)
2ac. Min R2C3 + R3C2 + R4C3 = 7 -> max R1C4 = 7
2ad. 8 in N2 only in R12C6, locked for C6
2ae. 1 in C6 only in R789C6, locked for N8

3. 17(4) cage at R6C5 = {1367/1457/2357/2456}
3a. 21(4) cage at R6C6 = {1479/1569/2469/3459} (cannot be {2379} because R6C4 only contains 4,5,6)
3b. Hidden killer pair 1,2 in 17(4) cage and 21(4) cage for N8, 17(4) cage contains one of 1,2 -> 21(4) cage must contain one of 1,2 = {1479/1569/2469}, no 3

4. 18(4) cage at R6C2 (step 2s) = {1278} (cannot be {1368} because R4C6 + R5C5 (hidden pair on D/) clashes with R5C456 (step 2v), no 3,6, 2 locked for N7 and D/, CPE no 7 in R7C2
4a. R4C6 = 3
4b. R5C456 (step 2v) = {278}, locked for R5 and N5
4c. R6C23 = {78} (hidden pair in N6), CPE no 7 in R7C3
4d. R7C3 = 1 -> R9C1 = 2
4e. Naked pair {78} in R68C2, locked for C2
4f. Naked pair {78} in R8C27, locked for R8
4g. 6 in N5 only in R6C56, locked for R6, CPE no 6 in R7C6
4h. 17(4) cage at R6C5 (step 3) = {2357/2456} -> R8C5 = 2

5. 45 rule on R6789 using R689 = {136} = 10, R9C5 = 9 -> remaining cells R6C1 + R7C12 + R8C1 = 18 = 4{36}5/5{346}, 3,6 locked for N7
5a. R8C2 + R9C3 = {78} (hidden pair in N7)
5b. Naked pair {78} in R9C37, locked for R9
5c. 28(4) cage at R6C3 = {4789/4589}, R9C2 = {45} -> no 4 in R7C4

6. 21(4) cage at R6C6 (step 3a) = {1569} (only remaining combination, cannot be {1479} which clashes with R7C6), 1,5,6 locked for C6
6a. 17(4) cage at R6C5 (step 4h) = {2357/2456}
6b. 4 of {2456} must be in R7C6 -> no 4 in R6C5 + R9C4
6c. Naked pair {56} in R6C56, locked for R6 and N5
6d. Naked pair {14} in R4C45, locked for R4, CPE no 4 in R3C4
6e. Naked pair {25} in R4C23, CPE no 5 in R3C2
6f. R6C1 = 4 -> R7C12 = {36}, R8C1 = 5 (step 5), 3,6 locked for R7
6g. Naked triple {478} in R7C456, 4 locked for N8
6h. R9C2 = 4 (hidden single in N7)
6i. R8C8 = 4 (hidden single in N9), placed for D\
6j. R4C4 = 1, placed for D\, R4C5 = 4
6k. R7C6 = 4 (hidden single in R6) -> 17(4) cage = {2456}
6l. R6C4 = 9, R7C5 + R9C3 = {78} -> R8C4 = 3 (cage total)
6m. Naked pair {78} in R12C6, locked for N2 and C6
6n. Naked pair {56} in R36C5, locked for C5 -> R12C5 = [31]
6o. R9C9 = 3 (hidden single on D\) -> R69C8 = [31], R68C9 = [16]
6p. R1C5 + R4C4 = [31] = 4 -> R2C4 + R3C3 = 10 = [46], 6 placed for D\
6q. R1C4 + R2C3 + R4C3 = [652] = 13 -> R3C1 = 1 (cage sum)
6r. R24C5 = [14] = 5 -> R1C6 + R3C4 = 9 = [72]
6s. R1C1 = 8, placed for D\
6t. R5C5 = 7, placed for D/

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

Rating Comment:
I'll rate my WT at not more than 1.25, possibly Easy 1.25. Step 4, which wellbeback saw in a slightly different way, is my technically hardest step.


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