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 Post subject: Assassin350
PostPosted: Tue May 15, 2018 7:09 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1039
Location: Sydney, Australia
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This one keeps on giving. 2-3 times. It wasn't originally going to be a milestone puzzle but it deserves to be I think. Perhaps I missed something. Really enjoyed the challenge. Had to range far and wide to finally crack it. SS gives it 1.55, JSudoku has to use some chains. Took us nearly 4 years to get from 300!

code:
3x3::k:6144:6144:6144:4865:4865:3074:2051:2051:8964:0000:6144:4865:4865:3074:3074:4102:4102:8964:0000:2823:2823:5896:5896:2057:2057:4102:8964:0000:2570:2570:5896:0000:8964:8964:8964:8964:0000:0000:0000:5896:0000:5133:0000:0000:0000:9743:9743:9743:9743:0000:5133:3856:3856:2577:9743:4370:4115:4115:5133:5133:2068:2068:2577:9743:4370:4370:3084:3084:4869:4869:6155:2577:9743:1550:1550:3084:4869:4869:6155:6155:6155:
solution:
Code:
+-------+-------+-------+
| 5 2 9 | 3 8 4 | 1 7 6 |
| 3 8 6 | 2 7 1 | 9 4 5 |
| 1 7 4 | 5 9 6 | 2 3 8 |
+-------+-------+-------+
| 6 9 1 | 8 5 3 | 7 2 4 |
| 7 4 2 | 1 6 9 | 5 8 3 |
| 8 5 3 | 7 4 2 | 6 9 1 |
+-------+-------+-------+
| 4 6 7 | 9 1 8 | 3 5 2 |
| 9 3 8 | 6 2 5 | 4 1 7 |
| 2 1 5 | 4 3 7 | 8 6 9 |
+-------+ -------+-------+
Cheers
Ed


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 Post subject: Re: Assassin350
PostPosted: Sat May 19, 2018 10:09 pm 
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Thanks Ed for this anniversary puzzle. Hope we manage to reach the next anniversary of A400 and that I'll still be an active solver; as you know, from when we met in London in 2014 when we were both on holiday, I'm one of the older members of this forum.

Loved the start to this puzzle. As you said it gives 2-3 times, then it starts resisting. It's hardly surprising one has to move about, with those three large zero areas.

Here is my walkthrough for Assassin 350:
Prelims

a) R1C78 = {17/26/35}, no 4,8,9
b) R3C23 = {29/38/47/56}, no 1
c) R3C67 = {17/26/35}, no 4,8,9
d) R4C23 = {19/28/37/46}, no 5
e) R6C78 = {69/78}
f) R7C34 = {79}
g) R7C78 = {17/26/35}, no 4,8,9
h) R9C23 = {15/24}
i) 10(3) cage at R6C9 = {127/136/145/235}, no 8,9

1. Naked pair {79} in R7C34, locked for R7, clean-up: no 1 in R7C78
1a. 17(3) cage at R7C2 = {269/278/359/368/467} (cannot be {179} which clashes with R7C3, cannot be {458} which clashes with R9C23), no 1
1b. 38(7) cage at R6C1 = {1256789/1346789/2345789} must contain 7,8,9
1c. R6C1234 can only contain one of 7,9 (both would clash with R6C78), R89C1 can only contain one of 7,9 (both would clash with R7C3) -> R6C1234 and R89C1 must each contain one of 7,9
1d. Killer pair 7,9 in R7C3 and R89C1, locked for N7
1d. 17(3) cage = {368} (only remaining combination), locked for N7
1e. 8 in 38(7) cage only in R6C1234, locked for R6, clean-up: no 7 in R6C78
1f. Naked pair {69} in R6C78, locked for R6 and N6
1g. 9 in 38(7) cage only in R89C1, locked for C1 and N7 -> R7C34 = [79], clean-up: no 4 in R3C2, no 3 in R4C2
1h. 38(7) cage at R6C1 = {2345789} (only remaining combination), no 1
1i. 1 in N7 only in R9C23 = {15}, locked for R9 and N7
1j. Naked triple {249} in R789C1, locked for C1 and 38(7) cage
1k. Naked quad {3578} in R6C1234, locked for R6
1l. R4C23 = {19/28/46} (cannot be [73] which clashes with R6C123 which must contain at least one of 3,7), no 7 in R4C2, no 3 in R4C3

2. 45 rule on N9 1 innie R8C7 = 1 outie R6C9 + 3, R6C9 = {124} -> R8C7 = {457}
2a. 10(3) cage at R6C9 = {127/145/235} (cannot be {136} which clashes with R7C78), no 6
2b. 10(3) cage at R6C9 = {127/145} (cannot be {235} = 2{35} which clashes with R6C9 + R8C7 = [25]), no 3, 1 locked for C9
2c. 4 of {145} must be in R6C9 (cannot be 1{45} which clashes with R6C9 + R8C7 = [14]), no 4 in R78C9
2d. 7 of {127} must be in R8C9 -> no 2 in R8C9
2e. 10(3) cage = {12}7
or 10(3) cage = 4{15} => R8C7 = 7
-> 7 in R8C79, locked for R8 and N9
2f. 8,9 in N9 only in 24(4) cage at R8C8 = {1689/3489} (cannot be {2589} which clashes with R7C78), no 2,5
2g. 1 of {1689} must be in R8C8 -> no 6 in R8C8
2h. 2 in N9 only in R7C789, locked for R7 -> R7C1 = 4

3. 45 rule on R6789 1 outie R5C6 = 1 innie R6C5 + 5, R6C5 = {124} -> R5C6 = {679}
3a. 20(4) cage at R5C6 = {1289/1469/1478/1568/2378/2459} (cannot be {3458} because R5C6 only contains 6,7,9, cannot be {1379} because 7,9 only in R5C6, cannot be {2468} because 2,4 only in R6C6, cannot be {2369} = [92]{36} which clashes with R7C78, cannot be {2567} = [72]{56} which clashes with R7C78, cannot be {3467} = [74]{36} which clashes with R7C78)
[Ed pointed out that {2459} should also be eliminated for the same reason as {2468}; having missed that I eliminated it in step 3c for a different reason.]
3b. Hidden killer triple 3,6,8 in R7C2, R7C56 and R7C78 for R7, R7C2 = {368}, R7C78 contains one of 3,6 -> R7C56 must contain ONE of 3,6,8
3c. 20(4) cage = {1289/1469/1478/1568} (cannot be {2378} which contains both of 3,8 in R7C56, cannot be {2459} which doesn’t contain 3,6,8)
3d. 20(4) cage = {1289/1478} (cannot be {1469} = [94]{16} which clashes with R5C6 + R6C5 = [94], cannot be {1568} = [61]{58} which clashes with R5C6 + R6C5 = [61]), no 5,6, clean-up: no 1 in R6C5
3e. 20(4) cage = {1289/1478}, 8 locked for R7 and N8
3f. Killer pair {36} in R7C2 and R7C78, locked for R7
3g. Naked pair {18} in R7C56, locked for R7, N8 and 20(4) cage
3h. Naked pair {24} in R6C56, locked for R6 and N5 -> R6C9 = 1, R8C7 = 4 (step 2), R8C9 = 7 (hidden single in N9), R7C9 = 2 (cage sum), clean-up: no 6 in R7C78
3i. Naked pair {35}, locked for R7 and N9 -> R7C2 = 6, clean-up: no 5 in R3C3, no 4 in R4C3
3j. Naked triple {689} in R9C789, locked for R9 and N9 -> R89C1 = [92], R8C8 = 1, clean-up: no 7 in R1C7, no 5 in R3C3, no 4 in R4C3
3k. Naked pair {37} in R9C56, locked for N8 -> R9C4 = 4
3l. R9C56 = {37} = 10, R8C7 = 4 -> R8C6 = 5 (cage sum), clean-up: no 3 in R3C7
3m. 35(7) cage at R1C9 = {1235789/1245689/1345679/2345678} must contain 5, CPE no 5 in R5C9
3n. 1 of {1235789/1245689/1345679} must be in R4C6, 3 or 8 of {2345678} must be in R4C6 (otherwise 3,4,8 clashes with R5C9, CPE) -> R4C6 = {138}
3o. 6 in C6 only in R123C6, locked for N2

4. 12(3) cage at R1C6 = {129/147/156/237/246/345} (cannot be {138} which clashes with R47C6), no 8
4a. 20(4) cage at R5C6 (step 3e) = {1289/1478} -> R56C6 = [74/92]
4b. 9 in C6 only in 12(3) cage = {129}
or R56C6 = [92]
-> no 2 in R3C6, clean-up: no 6 in R3C7
4c. Hidden killer pair 2,4 in 12(3) cage and R6C6 for C6, R6C6 = {24} -> 12(3) cage must contain one of 2,4 in R12C6 -> 12(3) cage = {129/147/237/246/345} (cannot be {156} which doesn’t contain 2 or 4)
4d. 12(3) cage = {129/147/246/345} (cannot be {237} because R129C6 = {237} clashes with R56C6)
4e. 5 of {345} must be in R2C5 -> no 3 in R2C5
4f. 6 in C6 only in 12(3) cage = {246}, locked for N2
or R3C67 = [62]
-> no 2 in R3C45

5. 23(4) cage at R3C4 = {1589/1679/3569/3578/4568} (cannot be {3479} because 4,9 only in R3C5)
5a. 9 of {1589/1679} must be in R3C5 -> no 1 in R3C5

6. 45 rule on N1 3 innies R2C13 + R3C1 = 10 = {127/136/145/235}, no 8,9
6a. 2,4 of {145/235} must be in R2C3 -> no 5 in R2C3

7. 45 rule on N3 4 innies R123C9 + R3C7 = 21 = {349}5/{469}2/{568}2/{389}1/{569}1 (cannot be {356}7 which clashes with R1C78), no 7 in R3C7, clean-up: no 1 in R3C6
7a. R123C9 + R3C7 = 21 = {469}2/{568}2/{389}1/{569}1 (cannot be {349}5 because 35(7) cage at R1C9 (step 3m) = {1345679} requires 6 in R123C9), no 5 in R3C7, clean-up: no 3 in R3C6
7b. Killer triple 6,8,9 in R123C9 and R9C9, locked for C9
7c. 35(7) cage at R1C9 (step 3m) = {1235789/1245689/2345678} (cannot be {1345679} which clashes with R5C9 using CPE), 2 locked for R4 and N6, clean-up: no 8 in R4C23
7d. 3 of {2345678} must be in R4C6 (otherwise 3,4 clashes with R5C9, CPE) -> no 8 in R4C6
7e. R7C6 = 8 (hidden single in C6) -> R7C5 = 1

8. Max R1C5 + R2C3 = 15 -> min R12C4 = 4 must include at least one of 3,5,7,8
8a. 23(4) cage at R3C4 (step 5) = {1589/1679/3569/4568} (cannot be {3578} which clashes with R12C4, CPE)
8b. 4,9 on 23(4) cage only in R3C5 -> R3C5 = {49}
8c. Killer pair 4,9 in 12(3) cage at R1C6 (step 4d) and R3C5, locked for N2
8d. 19(4) cage at R1C4 = {1378/1567/2368/2458/3457} (cannot be {1468/2467} because 4,6 only in R2C3)
8e. 4,6 of {2368/2458} must be in R2C3 -> no 2 in R2C3
8f. R2C13 + R3C1 (step 6) = {136/145}, no 7, 1 locked for N1
8g. R3C23 = {29/38}/[74] (cannot be [56] which clashes with R2C13 + R3C1), no 5 in R3C2, no 6 in R3C3
8h. Consider placement for 6 in C6
6 in 12(3) cage at R1C6 (4d) = {246}, locked for N2 => R3C5 = 9
or 6 in R3C67 = [62]
-> R3C5 = 9 and/or R3C7 = 2 -> R3C23 = {38}/[74], no 2,9
8i. 2 in R3 only in R3C78, locked for N3, clean-up: no 6 in R1C78
8j. Killer pair 3,4 in R2C13 + R3C1 and R3C23, locked for N1

9. R123C9 (step 7a) = {469}/{568}/{389}/{569}
9a. 16(3) cage at R2C7 = {178/349/358} (cannot be {169//259/268} which clash with R123C9, cannot be {367/457} which clash with R1C78), no 2,6
9b. R3C7 = 2 (hidden single in N3) -> R3C6 = 6
9c. 6 in N3 only in R123C9, locked for C9
9d. R4C8 = 2 (hidden single in R4)

10. 12(3) cage at R1C6 (step 4d) = {129/147/345}, 23(4) cage at R3C4 (step 8a) = {1589/1679/3569/4568}
10a. Consider placement for 1 in C4
1 in R12C4 => 12(3) cage = {345}, locked for N2 => R3C5 = 9
or 1 in 23(4) cage = {1589/1679} => R3C5 = 9
-> R3C5 = 9
[I spent some time trying to find a more routine way to reach the result given by step 10a.
Cracked. The rest is fairly straightforward.]
10b. R5C6 = 9 (hidden single in C6) -> R6C6 = 2 (step 4a), R6C5 = 4
10c. 12(3) cage = {147/345}, no 2
10d. R2C5 = {57} -> no 7 in R12C6
10e. R9C6 = 7 (hidden single in C6) -> R9C5 = 3
10f. 2 in N2 only in 19(4) cage at R1C4 (step 8d) = {2368/2458}, no 1,7, 8 locked for N2
10g. 4,6 only in R2C3 -> R2C3 = {46}
10h. Consider combinations for 19(4) cage
19(4) cage = {2368}, 3 locked for N2 => 12(3) cage = {147}
or 19(4) cage = {2458}, 5 locked for N2 => R2C5 = 7 => 12(3) cage = {147}
-> 12(3) cage = {147}, R2C5 = 7, R12C6 = {14}, locked for C6 and N2
[Ed pointed out that I’d missed the simpler 12(3) cage = {147} (cannot be {345} which clashes with 19(4) cage.]
10i. 23(4) cage = {1589/3569} (cannot be {1679} because R3C4 only contains 3,5), no 7, 5 locked for C4
10j. R6C4 = 7 (hidden single in C4) -> R6C123 = {358}, locked for N4

11. R4C6 = 3 -> 35(7) cage at R1C9 (step 7c) = {2345678} (only remaining combination) -> R4C7 = 7, R1234C9 = {4568}, locked for C9 -> R59C9 = [39]
11a. 8 in N6 only in R5C78, locked for R5
11b. 9 in R4 only in R4C23 = {19}, locked for R4 and N4 -> R45C1 = [67]
11c. Naked pair {58} in R4C45, locked for R4 and N5 -> R4C9 = 4, R5C45 = [16], R8C45 = [62]
11d. R3C5 = 9, R5C4 = 1 -> R34C4 = 13 = [58]
11e. R12C4 = {23}, R1C5 = 8 -> R2C3 = 6 (cage sum)
11f. R2C13 + R3C1 (step 8f) = {136} (only remaining combination), 1,3 locked for C1 and N1 -> R1C1 = 5, clean-up: no 3 in R1C78, no 8 in R3C23

and the rest is naked singles.
Thanks Ed for pointing out a couple of things that I'd missed.

Rating Comment:
I'll rate my WT for A350 at 1.5. I used several fairly short forcing chains; I also used combination analysis, when solving I felt I was doing a lot of that but, on checking my WT it didn't seem so much.


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 Post subject: Re: Assassin350
PostPosted: Sun May 20, 2018 7:06 pm 
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Posts: 280
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Thanks again Ed. A fine puzzle!

I made an error in A349 spotted by Ed - I hope I haven't done the same thing again here since I did not find it too difficult.

Assassin 350 WT:
1. Outies n7 -> r6c1234 + r7c4 = +32(5)
Min r6c56789 = +21
-> Max r6c1234 = +24
-> Min r7c4 = 8
-> 16(2)r7c3 = [79]

2. -> Remaining innies n7 = r789c1 = +15(3)
-> r6c1234 = +23(4)
-> Remaining innies r6 = r6c569 = +7(3) = {124}
-> (35) in r6c1234
-> 38(7) = {2345789}
-> (24) in r789c1
-> r789c1 = {249} with 9 in r89c1
-> r6c1234 = {3578}
-> 15(2)r6 = {69}

Also 6(2)n7 = {15}
and 17(3)n7 = {368}

3. r6c9 from (124)
-> Innies - Outies n9 -> r8c7 from (457)
Remaining Innies - Outies n8 -> r7c56 = 5 + r8c7
Since 5 already in r9 -> r8c7 cannot be 5. (Leaves no place for 5 in n8).
-> r8c7 from (47) and r6c9 from (14)

4. (89) in n9 only in 24(4)
-> 7 in n9 in r8c7 or r8c9
-> 10(3)r6c9 and 8(2)r7c7 from [127] and {35}, or [4{15}] and {26}
-> 2 in n9 only in r7

-> r7c1 = 4 and r89c1 = {29}
-> Remaining Innies - Outies r89 -> r8c9 = r7c2 + 1
Since r8c9 from (157) and r7c2 from (368)
-> r7c2 = 6 and r8c9 = 7
-> 17(3)n7 = [6{38}] and 10(3)r6c9 = [127]
-> 8(2)n9 = {35}
and r8c7 = 4
and 24(4)n9 = [1{689}]

5. -> r89c1 = [92]
-> r9c456 = [4{37}]
-> r8c456 = [{26}5]
-> r7c56 = {18}
Also r5c6, r6c5, r6c6 from [942] or [724]

6! Breakthrough
At this point 9 in c6 in one of:
a) r5c6 -> (HS 9 in n4) 10(2)n4 = {19}
b) r4c6
c) r12c6 -> 12(3)n2 = {129} -> 1 in n5 in r45c4

In none of those cases can 1 be in r4c6!
-> 1 not in 35(7)r1c9
-> 35(7) = {2345678}

(Note there are other ways to do the above step.
E.g., it is easy to prove that 9 in c6 can only go in r5c6 using very short chains).


7. Continuing
-> HS 9 in c9 -> r9c9 = 9
-> 9 in n3 in 16(3)
-> 8 in n3 in r123c9
Also 6 in c9 in r123c9
-> r5c9 from (345)
-> whatever is in r5c9 must be in the 35(7) in r4c6
-> Since 4 already in n5 and 5 already in c6 -> r4c6 = r5c9 = 3
-> HP in 35(5) -> r4c78 = {27}
-> Remaining outies n3 = r3c6 + r4c9 = +10(2)
Since r4c9 only from (45) and 5 already in c6
-> r3c6 = 6 and r4c9 = 4
-> r3c7 = 2 and r123c9 = {568}
-> 8(2)n3 = [17]
-> 16(3)n3 = {349} with 4 in r23c8
Also r4c78 = [72]
Also r5c78 = {58}

8. More
r9c56 = [37]
-> r56c6 = [92] and r6c5 = 4
-> (4 in n2/c6) -> 12(3)n2 = [471]
-> r7c56 = [18]
Also 10(2)n4 = {19}
Also HS 1 in r3 -> r3c1 = 1
Also HS 7 in n1 -> 11(2)n2 = [74]
-> HP in n4 -> r5c23 = [42]
-> 6 in n4 in r45c1
-> Remaining innies n1 -> r2c13 = [36]

9. Even more
HS 1 in r5/n5 -> r5c4 = 1
Since remaining Innies n2 = r3c45 = +14(2) -> 23(4)r3c4 = [5981]
-> HS r1c5 = 8
-> 24(4)n1 = [5298]
etc.


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 Post subject: Re: Assassin350
PostPosted: Mon May 21, 2018 8:16 pm 
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Loved wellbeback's first step!
It's not often:
that max/min is used in this way, particularly here where zero cells is used in the min.


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 Post subject: Re: Assassin350
PostPosted: Sat May 26, 2018 8:14 pm 
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Posts: 1039
Location: Sydney, Australia
Andrew wrote:
Loved wellbeback's first step!
Me too!

Love step 3 too. I've found them occasionally, are like an inverse IOE.
Attachment:
step3.JPG
step3.JPG [ 29.18 KiB | Viewed 10607 times ]

Quote:
3. Remaining Innies - Outies n8 -> r7c56 = 5 + r8c7
Since 5 already in r9 -> r8c7 cannot be 5. (Leaves no place for 5 in n8).
-> r8c7 from (47)
I see it slightly differently, "since r8c7 sees all 5 in n8 apart from the innies so must repeat there, but the IOD of 5 would also have to be in the innies -> no 5 in r8c7"

Here's my very long start WT. I get wellbeback's ! step 6 elimination in step 28! I started like Andrew but then did the middle differently.

A350
start:
Big thanks to Andrew for many corrections. Wasn't just the solving that was hard!!
Preliminaries courtesy of SudokuSolver
Cage 16(2) n78 - cells ={79}
Cage 6(2) n7 - cells only uses 1245
Cage 15(2) n6 - cells only uses 6789
Cage 8(2) n9 - cells do not use 489
Cage 8(2) n3 - cells do not use 489
Cage 8(2) n23 - cells do not use 489
Cage 10(2) n4 - cells do not use 5
Cage 11(2) n1 - cells do not use 1
Cage 10(3) n69 - cells do not use 89

Note: no clean-up done unless stated.

1. 38(7)r6c1 = {1256789/1346789/2345789}
1a. must have both 7 & 9 which can't both go in r6 since 15(2) = {69/78}; also can't both go in n7 since r7c3 = (79) -> must have one in r6 and one in n7
1b. killer pair 7,9 in r6c123478: locked for r6
1c. killer pair 7,9 in r789c1 & r7c3: both locked for n7

2. 17(3)n7; {458} blocked by 6(2)n7 needing 4/5
2a. = {368} only: all locked for n7

3. 38(7)r6c1 must have 8 which is only in r6: locked for r6

4. 15(2)n6 = {69} only: both locked for r6 and n6

5. 38(7)r6c1 must have 9 which is only in n7: locked for n7 and c1
5a. r7c34= [79]

6. 38(7)r6c1 = {2345789} only (no 1)

7. 1 in n7 only in 6(2) = {15} only: both locked for r9 and 5 for n7

8. naked triple {249} in r789c1: locked for c1 and 38(7) cage: no 2,4 in r6c234

9. naked quad {3578} in r6c1234: 3,5 locked for r6

10. "45" on n9: 1 outie r6c9 + 3 = 1 innie r8c7
10a. r8c7 = (457)

11. 10(3)r6c9: [2]{35} blocked by 5 also in r8c7 (iodn7=+3)
11a. = {127/136/145}
11b. must have 1: locked for c9

12. 8(2)n9 = {26/35}(no 1): must have 3 or 6
12a. 10(3)r6c9: [1]{36} blocked by 8(2)
12b. = {127/145}(no 3,6)
12c. 7 in {127} must be in r8c9 -> no 2 in r8c9

13. hidden killer pair 3,6 in n9 -> 24(4) must have 3/6 (and both 8,9 for n9)
13a. = {1689/3489}(no 2,5,7)

14. 2 in n9 only in r7: locked for r7
14a. r7c1 = 4

15. "45" on r6789: 1 outie r5c6 - 5 = 1 innie r6c5
15a. r5c6 = (679)

Lucky to have found this: not usually what I look for. But each combo has just one (or none) valid permutation and they just kept coming!
16. 20(4)r5c6:
16a. {1379} blocked by 7,9 only in r5c6
16b. {1469} as [94]{16} only, blocked by 4 in r6c5 (from iodr6789=-5)
16c. {1568} as [61]{58} only, blocked by 1 already in r6c5 (from iodr6789=-5)
16d. {2369} as [92]{36} only, blocked by 8(2)n9 needing 3/6
16e. {2378} as [72]{38} only, blocked by 2 already in r6c5 (from iodr6789=-5)
16f. {2459/2468} blocked by 2,4 only in r6c6
16g. {2567} as [72]{56} only, blocked by 2 already in r6c5 (ditto)
16h. {3458} blocked by no 6,7,9 for r5c6
16i. {3467} as [74]{36} only, blocked by 8(2)n8 needing 3 or 6
16j. = {1289/1478}: must have {18} -> r7c56 = {18} both locked for r7 and n8
16k. r56c6 = [92/74]
16l. -> r6c5 = (24) (iodr6789=-5)

17. naked pair {24} in r6c56: both locked for r6 and n5
17a. r6c9 = 1
17b. -> r8c7 = 4 (iodn9=+3)
17c. r78c9 = [27]

18. 8(2)n9 = {35} only: 3 locked for r7 and n9
18a. r7c2 = 6
18b. r8c23 = {38}: both locked for r8

19. hidden single 4 in n8 -> r9c4 = 4
19a. -> r8c45 = 8 = {26} only: both locked for n8 and r8
19b. r8c6 = 5, r89c1 = [92], r8c8 = 1

Now it gets hard again!
20. r4c78 sees all 3,4,5 in c9 -> no 3,4,5 in r4c78

21. 35(7)r1c9 must have two of {278} for r4c78 = {1235789/1245689/2345678}
21a. must have 2 which is only in r4c78: 2 locked for r4 and n6
21b. must have 5 -> no 5 in r5c9
21c. must have 1 in r4c6 or be {2345678} -> must have 3,8 in r4c6 to avoid clashing with r5c9
21d. -> r4c6 = (138)

22. hidden killer triple 2,4,9 in n4 which are only in r45c23 in n4
22a. 10(2) must have one of them = {19}/[46](no 3,7,8)
22b. r5c23 must have two of 2,4,9 = {249}

23. r5c236 = three of {2479} -> r5c789 cannot have more than one of 4,7
23a. hidden killer pair 4,7 in n6 -> r4c789 must have at least one of 4,7
23b. -> 35(7)r1c9 must have 4,7 or both in n6
23c. but {14} from {1245689} in r4 blocked by 10(2)r4c2 which must have one of 1 or 4
23d. = {1235789/2345678}
23e. must have 7 which is only in r4c78 -> r4c78 = {27}: 7 locked for r4 and n6

Some tricky recursive moves now.
24. "45" on n3: 5 outies r3c6 + r4c6789 = 22
24a. r4c78 = 9 -> r3c6 + r4c69 = 13
24b. but [1][84] blocked by r7c6
24c. but [3] blocked by can't make 10 from r4c69
24d. no 1,3 in r3c6
24e. 8(2)r3c6 = {26}[71]

25. "45" on n3: 4 innies r123c9 + r3c7 = 21 and must have 1,2,6 for r3c7
25a. but {3468} as [6]{348} only blocked by r5c9
25b. = {1389/1569/2469/2568}- all combinations must have 1,2 in r3c7
25c. -> no 6 in r3c7
25d. no 2 in r3c6

26. "45" on n3: 5 outies r3c6 + r4c6789 = 22
26a. r4c78 = 9 -> r34c6 + r4c9 = 13
26b. = [63][4]/[71][5]; note, must have 3/7 in r34c6
26c. r4c6 = (13), r4c9 = (45)

27. killer pair 3,7 in r349c6: both locked for c6
27a. r5c6 = 9 -> r6c6 = 2 (cage sum), r6c5 = 4

28. naked pair {24} in r5c23: 4 locked for r5 and n4
28a. -> 10(2)n4 = {19} only: 1 locked for r4 and n4
(finally got wellbeback's key elimination: no 1 in r4c6!!!)

29. r4c6 = 3, r4c9 = 4 (hsingle n6)

30. 8 must be in 35(7)r1c9: locked for c9 and n3
31a. ->r123c9 = 19 (cage sum) = {568}: 5,6 locked for n3 and 6 for c9


much easier now!! Phew!
Ended up a significant puzzle. Perfect for a milestone.

Cheers
Ed


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 Post subject: Re: Assassin350
PostPosted: Tue Jun 05, 2018 9:13 pm 
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Grand Master
Grand Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
Thank you for the nice comments. I liked those steps too!
I see Step 3 just like Ed did - but he wrote a better and more complete version.

BTW - I've stopped receiving emails when a Private Message has been posted to me. Anyone else? Maybe the GDPR means our email addresses have been deleted in the site!


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 Post subject: Re: Assassin350
PostPosted: Tue Jun 05, 2018 9:20 pm 
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Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 1039
Location: Sydney, Australia
wellbeback wrote:
I've stopped receiving emails when a Private Message has been posted to me. Anyone else?
I still get the notification. Might be worth emailing Richard. Probably better to email as he doesn't visit here often.


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