SudokuSolver Forum

A forum for Sudoku enthusiasts to share puzzles, techniques and software
It is currently Wed May 22, 2019 5:39 am

All times are UTC




Post new topic Reply to topic  [ 4 posts ] 
Author Message
 Post subject: Assassin 372
PostPosted: Fri Mar 15, 2019 7:59 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 802
Location: Sydney, Australia
Attachment:
a372.JPG
a372.JPG [ 70.5 KiB | Viewed 280 times ]
This is an X-puzzle. 1-9 cannot repeat on either diagonal.

Assassin 372
Found this very difficult to crack first time though my optimised solution is very short. Made a zero version and the SSscore went up but didn't make any difference to how I did it. SS must use different cages than me so have gone with the vanilla. SScore=1.25 JSudoku uses a couple of chains. I used a difficult key step so will be interested to see what I missed.
code:
3x3:d:k:2048:7681:7681:7681:7681:4610:4610:4610:4099:2048:7681:2052:2052:7681:5893:5893:5893:4099:4870:3847:3847:1544:1544:3593:5893:2058:4099:4870:4870:1547:1547:6668:3593:5893:2058:1037:3854:3854:1551:1551:6668:6668:6937:6937:1037:3854:3089:3089:4114:4114:6668:6937:9232:6937:4884:3089:5909:4114:9232:9232:9232:9232:9232:4884:4884:5909:5909:9232:2582:3095:3095:3864:4884:3347:3347:5909:2582:2582:2582:3095:3864:
solution:
Code:
+-------+-------+-------+
| 3 4 8 | 9 1 5 | 6 7 2 |
| 5 2 1 | 7 6 3 | 4 8 9 |
| 7 9 6 | 2 4 8 | 1 3 5 |
+-------+-------+-------+
| 9 3 2 | 4 8 6 | 7 5 1 |
| 6 8 5 | 1 7 2 | 9 4 3 |
| 1 7 4 | 3 5 9 | 8 2 6 |
+-------+-------+-------+
| 2 1 9 | 8 3 7 | 5 6 4 |
| 8 5 3 | 6 9 4 | 2 1 7 |
| 4 6 7 | 5 2 1 | 3 9 8 |
+-------+-------+-------+
Cheers
Ed


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 372
PostPosted: Tue Mar 19, 2019 4:33 am 
Offline
Grand Master
Grand Master

Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1647
Location: Lethbridge, Alberta, Canada
Thanks Ed for your latest Assassin. I have no idea how SudokuSolver got that score; it felt quite a lot harder to me, more like our current level of Assassins.

Here is my walkthrough for Assassin 372:
Prelims

a) R12C1 = {17/27/35}, no 4,8,9
b) R2C34 = {17/27/35}, no 4,8,9
c) R3C23 = {69/78}
d) R3C45 = {15/24}
e) R34C6 = {59/68}
f) R34C8 = {17/27/35}, no 4,8,9
g) R4C34 = {15/24}
h) R45C9 = {13}
i) R5C34 = {15/24}
j) R89C9 = {69/78}
k) R9C23 = {49/58/67}, no 1,2,3
l) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
m) 26(4) cage at R4C5 = {2789/3689/4589/4679/5678}, no 1
n) 27(4) cage at R5C7 = {3789/4689/5679}, no 1,2
o) 10(4) cage at R8C6 = {1234}

Steps resulting from Prelims
1a. Naked pair {13} in R45C9, locked for C9 and N6, clean-up: no 5,7 in R3C8
1b. 27(4) cage at R5C7 now = {4689/5679}, 6,9 locked for N6, clean-up: no 2 in R3C8
1c. 2 in N6 only in R4C78 + R6C8, CPE no 2 in R2C8
1d. Naked quad {1234} in 10(4) cage at R8C6, CPE no 1,2,3,4 in R9C4
1e. 1 in N5 only in R456C4 + R6C5, CPE no 1 in R7C4
1f. 36(7) cage at R6C8 must contain 9, not now in R6C8, CPE no 9 in R7C4

2. 45 rule on C9 2 innies R67C9 = 10 = [46/64/82], no 5,7,9, no 8 in R7C9
2a. 5 in C9 only in 16(3) cage at R1C9, locked for N3
2b. 16(3) cage = {259/457}, no 6,8

3. 45 rule on R1234 2 innies R4C59 = 9 = [63/81]
3a. Variable hidden killer pair 3,7 in 26(4) cage at R4C5 and 16(3) cage at R6C4 for N5, 26(4) cage cannot contain more than one of 3,7 -> 16(3) cage must contain at least one of 3,7 = {178/349/358/367/457} (cannot be {169/259/268} which don’t contain 3 or 7), no 2

4. 45 rule on N7 2 outies R89C4 = 1 innie R7C2 + 10
4a. Min R89C4 = 11, no 1 in R8C4
4b. Max R89C4 = 17 -> max R7C2 = 7

5. 45 rule on N5 3 innies R45C4 + R4C6 = 1 outie R7C4 + 3
5a. Max R7C4 = 8 -> max R45C4 + R4C6 = 11, no 9 in R4C6, clean-up: no 5 in R3C6
5b. Min R45C4 + R4C6 = 8 -> min R7C4 = 5
5c. 26(4) cage at R4C5 = {2789/3689/4589/4679} (cannot be {5678} which clashes with R4C6), 9 locked for N5
5d. 9 in R4 only in R4C12, locked for N4 and 19(3) cage at R3C1, no 9 in R3C1
5e. 19(3) cage must contain 9 in R4C12 = {289/379/469}, no 5

6. 45 rule on R12 3(2+1) outies R34C7 + R3C9 = 13
6a. R34C7 cannot total 4 -> no 9 in R3C9

7. R3C23 = {69/78}, R3C6 = {689} -> combined cage R3C236 = {69}8/{78}6/{78}9, 8 locked for R3
7a. 19(3) cage at R3C1 (step 5e) = {289/379/469}
7b. 2 of {289} must be in R3C1 -> no 2 in R4C12
7c. Consider combinations for R4C34 = {15/24}
R4C34 = {15}, locked for R4 => R4C56 = {68}, locked for R4 => 19(3) cage = {379/469}
or R4C34 = {24}, R4C9 = 1 (hidden single in R4) => 3 in R4 only in R4C12 => 19(3) cage = {379}
-> 19(3) cage = {379/469}, no 2,8
[Maybe SudokuSolver sees this as a huge block 19(3) cage cannot be 2{89} because R4C123456 = {89}{24}[65] clashes with R4C78.]

8. 45 rule on N6 3 innies R4C78 + R6C8 = 14 must contain 2 for N6 = {248/257}
8a. Consider combinations for R4C34 = {15/24}
R4C34 = {15}, locked for R4 => R4C56 = {68}, locked for R4
or R4C34 = {24}, locked for R4 => R4C8 = {57} => R4C78 + R6C8 = {257}, no 8
-> no 8 in R4C7
8b. 8 in R4 only in R4C56, locked for N5
[Extending that forcing chain.]
8c. R4C34 = {15}, locked for R4 => R4C56 = {68}, locked for R4
or R4C34 = {24}, locked for R4 => R4C78 = {57}, locked for R4 => R4C56 = {68}
-> R4C56 = {68}, clean-up: no 9 in R3C6
8d. Naked pair {68} in R4C56, locked for R4 and N5
8e. Naked pair {68} in R34C6, locked for C6
8f. 26(4) cage at R4C5 (step 5c) = {2789/4589/4679} (cannot be {3689} because 6,8 only in R4C5), no 3
8g. 3 in N5 only in R6C45, locked for R6
8h. 16(3) cage at R6C4 (step 3a) must contain 3 = {358/367}, no 1,4 -> R6C45 = {35/37}, R7C4 = {68}
[At this stage I saw
1 in N5 only in R45C4, locked for C4, clean-up: no 7 in R2C3, no 5 in R3C5
Either R4C34 = [51] or R5C34 = [51] (locking cages) -> 5 in R45C3, locked for C3 and N4
but this quickly becomes unnecessary.]
8i. Killer pair 6,8 in R3C23 and R3C6, locked for R3, clean-up: no 2 in R4C8
8j. 19(3) cage at R3C1 = {379} (only remaining combination), no 4
8k. 19(3) cage = 7{39} (cannot be 3[79] which clashes with R34C8 = [17/35]) -> R3C1 = 7, R4C12 = {39}, 3 locked for R4 and N4 -> R45C9 = [13], clean-up: no 1 in R12C1, no 8 in R3C23, no 1 in R2C4, no 5 in R4C34
8l. R5C4 = 1 (hidden single in N5) -> R5C3 = 5, clean-up: no 3 in R2C4, no 5 in R3C5, no 8 in R9C2
8n. Naked pair {24} in R4C34, locked for R4 -> R4C78 = {57}, locked for N6
8o. R6C8 = 2 (hidden single in N6), clean-up: no 8 in R6C9 (step 2)
8p. Naked pair {46} in R67C9, locked for C9, clean-up: no 9 in R89C9
8q. Naked pair {78} in R89C9, locked for C9 and N9
8r. Naked triple {259} in 16(3) cage at R1C9, locked for N3
8s. Naked pair {69} in R3C23, locked for R3 and N1 -> R3C6 = 8, R4C6 = 6, placed for D/, R4C5 = 8, clean-up: no 2 in R12C1, no 2 in R2C4
8t. Naked pair {35} in R12C1, locked for C1 and N1 -> R4C12 = [93], clean-up: no 5 in R2C4

9. 36(7) cage at R6C8 = {2345679} (only remaining combination), no 1, 7 locked for N8
9a. 1 in N8 only in R8C6 + R9C56, locked for 10(4) cage at R8C6, no 1 in R9C7
9b. 1 in N9 only in 12(3) cage at R8C7 = {129/156}, no 3,4
9c. 2 of {129} must be in R8C7 -> no 9 in R8C7
9d. 36(7) cage = {2345679}, CPE no 6 in R7C4
9e. R7C4 = 8 -> R6C45 = 8 = {35}, 5 locked for N5
9f. R45C4 + R4C6 = R7C4 + 3 (step 5) -> R45C4 + R4C6 = 11, R4C6 = 6, R5C4 = 1 -> R4C4 = 4, placed for D\, R4C3 = 2, R2C3 = 1 -> R2C4 = 7, clean-up: no 2 in R3C5

10. R8C8 = 1 (hidden single on D\), R3C8 = 3 -> R4C8 = 5, R4C7 = 7
10a. 1 in N8 only in R9C56, locked for R9
10b. R3C7 = 1 (hidden single on D/), R3C5 = 4, R3C4 = 2, R3C9 = 5

11. 45 rule on N47 5(1+4) outies R3C1 + R4589C4 = 23, R3C1 = 7, R45C4 = [41] -> R89C4 = 11 = {56}, locked for C4, N8 and 23(4) cage at R7C3
11a. R6C4 = 3, placed for D/, R6C5 = 5
11b. 36(7) cage at R6C8 = {2345679} -> R7C7 = 5, placed for D\, 6 locked for R7 and N9 -> R8C7 = 2, R9C8 = 9, clean-up: no 4 in R9C23
11c. Naked pair {46} in R7C89, locked for R7 and N9 -> R9C7 = 3, R8C6 = 4
11d. R89C4 = 11 -> R78C3 = 12 = [93], 9 placed for D/ -> R1C9 = 2, placed for D/, R5C5 = 7, placed for both diagonals
11e. R9C1 = 4 (hidden single in R9), placed for D/
11f. R2C8 = 8, R34C7 = [17] -> R2C67 = 7 = [34]
11g. R8C2 = 5 (hidden single on D/), R9C1 = 4 -> R78C1 = 10 = [28]
11h. R56C1 = [61] -> R5C2 = 8 (cage sum)

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

Rating Comment:
I'll rate my walkthrough for A372 at Easy 1.5. I used the same forcing chain three times in slightly different ways.


Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 372
PostPosted: Sat Mar 23, 2019 8:43 pm 
Offline
Master
Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 183
Location: California, out of London
Thanks again Ed. Interesting puzzle! I found a couple of key steps which made the rest straightforward. Here is how I started - not using the diagonals at all. Andrew and I used the same basic 45s, IODs etc. - but in quite different ways.
Assassin 372 WT:
1. 4(2)n6 = {13}
-> Innies r1234 = r4c59 = +9(2) from [81] or [63]

2. 27(4)n6 = {69(48|57)}
Innies n6 = r4c78 + r6c8 = {2{48|57)}

3. Innies c9 = r67c9 = +10(2) = [82] or {46}

4! 36(7)r6c8 contains three of (1234)
If r89c8 were both from (1234) those values would be in 10(4) in n8 and neither in 36(7)
-> at most one of r89c8 is from (1234)
-> 12(3)n9 cannot be from [9{12}], [8{13}], [7{14}], [7{23}], [6{24}], [5{34}] (Important later)

5! r6c8
r6c8 from (24578)
IOD n89 -> r789c4 = r6c8 + 17
-> r6c8 is max 7
Trying r6c8 = 7 puts r4c78 = {25} contradicting 6(2)r4
Trying r6c8 = 4 puts 27(4)n6 = {5679} which leaves no solution for H10(2)r67c9
-> r6c8 from (25)
Trying r6c8 = 5 puts 5 in n9 in r8c7 ...
... puts 12(3)n9 = [5{16}] ...
... which leaves no solution for 8(2)c8
-> r6c8 = 2

Easy from here.

6. -> Remaining Innies n6 = r4c78 = +12(2) which can only be {57} (neither of (48) in r4c8)
-> 6(2)r4 = {24}
HS 1 in r4 -> 4(3)n6 = [13]
Innies r1234 -> r4c5 = 8
HS 3 in r4 -> 19(3)r3c1 = [7{39}]
-> NS 6 in r4 -> 14(2)r3c6 = [86]
-> 15(2)n1 = {69}
-> 8(2)n1 = {35}
-> r4c12 = [93]

7. 3 in n5 cannot be in 26(4) (since r4c6 = 6) - must be in r6c45
-> HS 1 in n5 -> 6(2)r5c3 = [51]
-> Remaining outies n4 = r4c4 + r7c2 = +5. Can only be r4c4 = 4 and r7c2 = 1.
-> r4c3 = 2
-> Remaining outie n5 -> r7c4 = 8
-> 16(3)n5 = [{35}8]
-> 12(3)n4 = [{47}1]

8. Remaining outies n3 = r12c6 = +8(2)
Only from {17} or {35}
-> 6(2)n2 = [24]
-> r3c789 = [{13}5]

9. Innies c9 r67c9 can only be [64]
-> 15(2)n9 = {78}
-> 16(3)c9 = [{29}5]
etc.


Last edited by wellbeback on Sun Mar 31, 2019 8:19 pm, edited 1 time in total.

Top
 Profile  
Reply with quote  
 Post subject: Re: Assassin 372
PostPosted: Sun Mar 24, 2019 10:35 pm 
Offline
Grand Master
Grand Master

Joined: Wed Apr 16, 2008 1:16 am
Posts: 802
Location: Sydney, Australia
Interesting! We all had to think carefully. As usual, wellbeback gets the prize for the most creative. A good read. My way is very close to Andrew, though as often happens, he used several easier steps while I make one complicated one (step 9).

SS does it very differently. Machines are good at some things so its score makes some sense! I have included its way after Andrew's step 6a. I started the continuation in Andrew's WT style but couldn't keep it up. Had to concentrate too hard!

SS key steps:
Prelims

a) R12C1 = {17/27/35}, no 4,8,9
b) R2C34 = {17/27/35}, no 4,8,9
c) R3C23 = {69/78}
d) R3C45 = {15/24}
e) R34C6 = {59/68}
f) R34C8 = {17/27/35}, no 4,8,9
g) R4C34 = {15/24}
h) R45C9 = {13}
i) R5C34 = {15/24}
j) R89C9 = {69/78}
k) R9C23 = {49/58/67}, no 1,2,3
l) 19(3) cage at R3C1 = {289/379/469/478/568}, no 1
m) 26(4) cage at R4C5 = {2789/3689/4589/4679/5678}, no 1
n) 27(4) cage at R5C7 = {3789/4689/5679}, no 1,2
o) 10(4) cage at R8C6 = {1234}

Steps resulting from Prelims
1a. Naked pair {13} in R45C9, locked for C9 and N6, clean-up: no 5,7 in R3C8
1b. 27(4) cage at R5C7 now = {4689/5679}, 6,9 locked for N6, clean-up: no 2 in R3C8
1c. 2 in N6 only in R4C78 + R6C8, CPE no 2 in R2C8
1d. Naked quad {1234} in 10(4) cage at R8C6, CPE no 1,2,3,4 in R9C4
1e. 1 in N5 only in R456C4 + R6C5, CPE no 1 in R7C4
1f. 36(7) cage at R6C8 must contain 9, not now in R6C8, CPE no 9 in R7C4

2. 45 rule on C9 2 innies R67C9 = 10 = [46/64/82], no 5,7,9, no 8 in R7C9
2a. 5 in C9 only in 16(3) cage at R1C9, locked for N3
2b. 16(3) cage = {259/457}, no 6,8

3. 45 rule on R1234 2 innies R4C59 = 9 = [63/81]
3a. Variable hidden killer pair 3,7 in 26(4) cage at R4C5 and 16(3) cage at R6C4 for N5, 26(4) cage cannot contain more than one of 3,7 -> 16(3) cage must contain at least one of 3,7 = {178/349/358/367/457} (cannot be {169/259/268} which don’t contain 3 or 7), no 2

4. 45 rule on N7 2 outies R89C4 = 1 innie R7C2 + 10
4a. Min R89C4 = 11, no 1 in R8C4
4b. Max R89C4 = 17 -> max R7C2 = 7

5. 45 rule on N5 3 innies R45C4 + R4C6 = 1 outie R7C4 + 3
5a. Max R7C4 = 8 -> max R45C4 + R4C6 = 11, no 9 in R4C6, clean-up: no 5 in R3C6
5b. Min R45C4 + R4C6 = 8 -> min R7C4 = 5
5c. 26(4) cage at R4C5 = {2789/3689/4589/4679} (cannot be {5678} which clashes with R4C6), 9 locked for N5
5d. 9 in R4 only in R4C12, locked for N4
5e. 19(3) cage at R3C1 must contain 9 in R4C12 = {289/379/469}, no 5, no 9 in R3C1

6. 45 rule on R12 3(2+1) outies R34C7 + R3C9 = 13
6a. R34C7 cannot total 4 -> no 9 in R3C9
Optimised SS steps from here
6b. R3c9 + R4c7 cannot total 4 or 5 -> no 8,9 in r3c7

7. 45 rule on N89 1 outie r6c8 + 17 = 3 innies R789C4
7a. Max R789C4 = 24 -> max r6c8 = 7

8. 45 rule on N6 3 innies R4C78 + R6C8 = 14 must contain 2 for N6 = {248/257}
8a. 8 in {248} must be in R4C7 -> no 4 in R4C7

9. "45" on r123: 2 innies r3c16 - 3 = 2 outies r4c78
9a. r4c78 cannot total 14 or 11 -> no 8 in r3c1

10. Hidden killer pair 8,9 in r3 in 15(2)r3c2 and r3c6
10a. -> r3c6 = (89), r4c6 = (56)

11. "45" on r123: 1 innie r3c1 + 11 = 3 outies r4c678
11a. r4c678 cannot total 17 -> no 6 in r3c1

12. from step 5e. 19(3)r3c1 = {289/379/469}
12a. 4 in {469} must be in r3c1 -> no 4 in r4c12

13. 4 in r4 only in 6(2)r4c3 = {24}: both locked for r4
13a. -> hidden single 2 in n6 -> r6c8 = 2

14. naked quad {5678} in r4c5678, all locked for r4

etc
.
My way:
Preliminaries
Cage 4(2) n6 - cells ={13}
Cage 6(2) n2 - cells only uses 1245
Cage 6(2) n45 - cells only uses 1245
Cage 6(2) n45 - cells only uses 1245
Cage 14(2) n25 - cells only uses 5689
Cage 15(2) n9 - cells only uses 6789
Cage 15(2) n1 - cells only uses 6789
Cage 8(2) n1 - cells do not use 489
Cage 8(2) n12 - cells do not use 489
Cage 8(2) n36 - cells do not use 489
Cage 13(2) n7 - cells do not use 123
Cage 19(3) n14 - cells do not use 1
Cage 10(4) n89 - cells ={1234}
Cage 27(4) n6 - cells do not use 12
Cage 26(4) n5 - cells do not use 1

1. 4(2)n6 = {13}: both locked for c9 and n6

2. 16(3)n3: {268} blocked by 15(2)n9 = 6 or 8
2a. = {259/457}(no 6,8)
2b. must have 5: locked for c9 and n3

3. "45" on c9: 2 innies r67c9 = 10 = {46}/[82](no 7,9; no 8 in r7c9)

4. "45" on r1234: 2 innies r4c59 = 9 = [81/63]

5. 27(4)n6 = {4689/5679}
5a. must have both 6,9: both locked for n6

6. 36(7)r6c8 must have 9 which must be in r7 or r8c5 -> no 9 in r7c4

7. "45" on n5: 4 outies r3c6 + r45c3 + r7c4 = 23.
7a. max. r45c3 + r7c4 = {458} = 17 -> min. r3c6 = 6
7b. -> no 9 in r4c6

8. 9 in r4 only in 19(3)r3c1
8a. 9 locked for n4 and no 9 in r3c1
8b. 19(3) = {289/379/469}(no 5)

The crack
9. "45" on r123: 5 outies r4c12678 = 30 and must have 7 & 9 for r4
9a. = {24789/35679}
9b. but {24789} as {29}[8]{47} blocked by 27(4)n6 = 4 or 7
9c. but {24789} as {79/49}[8](47)[2] blocked by [66] in r3c68
9d. but {24789} as {49}[827] blocked by [66] in r3c16
9e. -> all permuations for {24789} blocked
9f. r4c12678 = {35679}: 3,5 & 6 locked for r4

10. r4c59 = [81], r5c9 = 3

11. {57} in r4c78: both locked for n6 and r4
11a. r34c6 = [86](6 placed for D/)

12. r4c78 = 12 -> 1 innie r6c8 = 2

13. "45" on n36: 2 outies r12c6 = 8
13a. = {17/35}(no 2,4,9) = 1 or 5

14. 6(2)r3c4: {15} blocked by r12c6
14a. = {24} only: both locked for r3 and n2

15. r4c12 = {39} = 12, 3 locked for n4
15a. r3c1 = 7

16. {69} in r3c23: both locked for n1 and r3
16a. r3c9 = 5

17. r3c78 = {13}: both locked for n3

18. r67c9 = h10(2) = {46} only: both locked for c9
18a. 15(2)n9 = {78} only: both locked for n9: 7 for c9

19. r12c9 = {29}: both locked for n3
etc
Cheers
Ed


Top
 Profile  
Reply with quote  
Display posts from previous:  Sort by  
Post new topic Reply to topic  [ 4 posts ] 

All times are UTC


Who is online

Users browsing this forum: No registered users and 8 guests


You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum

Search for:
Jump to:  
cron
Powered by phpBB® Forum Software © phpBB Group