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 Post subject: Assassin 417
PostPosted: Sun May 15, 2022 7:54 am 
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Grand Master
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
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x-killer so 1-9 cannot repeat on either diagonal.

Assassin 417
Had a hard time getting this to the right level since I couldn't solve the previous versions. SudoduSolver gives it 1.40 and JSudoku uses just one 'advanced' step so should be an easier one. Not for me. Must have missed something important. No time for a WT yet so hoping you guys find a decent way through.

triple click code:
3x3:d:k:3584:3584:5889:5889:4866:4866:4866:4866:2563:5889:5889:5889:6411:6411:5655:5637:5637:2563:4102:3335:3335:2056:6411:5655:5637:5637:2825:4102:5386:5386:2056:6411:5655:5655:2825:2825:4102:5386:5386:4876:4876:5655:5133:5133:6926:4111:4111:4111:4111:4876:3600:5133:5133:6926:2833:2833:3858:5651:4876:3600:5133:6926:6926:4884:2833:3858:5651:5651:3600:4885:4885:4885:4884:4884:3858:5651:3350:3350:3350:1540:1540:
solution:
+-------+-------+-------+
| 9 5 4 | 7 2 8 | 6 3 1 |
| 1 8 3 | 4 5 6 | 2 7 9 |
| 2 6 7 | 3 9 1 | 5 8 4 |
+-------+-------+-------+
| 8 3 2 | 5 7 9 | 4 1 6 |
| 6 7 9 | 1 4 2 | 3 5 8 |
| 4 1 5 | 6 8 3 | 9 2 7 |
+-------+-------+-------+
| 5 4 8 | 2 6 7 | 1 9 3 |
| 7 2 1 | 9 3 4 | 8 6 5 |
| 3 9 6 | 8 1 5 | 7 4 2 |
+-------+-------+-------+
Cheers
Ed


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 Post subject: Re: Assassin 417
PostPosted: Fri May 20, 2022 6:32 pm 
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Joined: Tue Jun 16, 2009 9:31 pm
Posts: 280
Location: California, out of London
In my first attempt for the longest time I had two solutions which was only resolved by about a 10-step contradiction chain! My second attempt made that quite a bit shorter. Very intriguing (i.e., at first frustrating) puzzle. Thanks Ed!
Corrections thanks to Andrew.
Assassin 417 WT:
1. IOD n1 r1c4 = r3c1 + 5
-> r1c4 from (6789) and r3c1 from (1234)
Whatever is in r1c4 also goes in 13(2)n1
13(2)n1 cannot be {58} since that leaves no solution for 14(2)n1
[r1c4,r3c1] cannot be [94] since that leaves no place for 9 in n1
-> [r1c4,r3c1] from [61] or [72], 13(2)n1 = {67} and 14(2)n1 = {59}

2. Outies c6789 = r19c5 = +3(2) = {12}
Innies r1 = r1c349 = +12(3)
Since r1c4 from (67) and 5 already in r1 -> Max r1c3 = 4. (Also Max r1c9 = 4)
-> 8 in n1 in r2c123
-> 2 not in r1c9
Also since 9 already in r1 -> 19(4)r1 cannot contain both (12)
-> (12) not in r1c678
-> 2 in r1 only in r1c3 or r1c5

3. One of:
(A) r1c4 = 6 -> r1c39 = [24] and 19(4)r1 = [1{378}]
(B) r1c4 = 7 -> r3c1 = 2 -> r1c5 = 2 -> r1c39 = {14} and 19(4)r1 = [2{368}]

4. IOD n3 -> r1c56 = r3c9 + 6
-> Min r1c6 = 6
-> 3 in r1c78
-> Remaining Innies n3 = +10(2)
-> (57) not in innies n3 and nor in 10(2)n3
-> (57) in n3 in 22(4)n3 with 7 in r2c78
-> 7 in n2/r1 in r1c46

5. Outies n14 = r16c4 = +13(2)
-> r16c4 = {67}
-> 8(2)c4 = {35}
-> 22(4)n8 only from {1489}, {2389}, or {2479}

6! Consider Step 3(A)
This has r1c456 = [617], r6c4 = 7, r9c5 = 2, and 22(4)n8 = {1489}
But this puts r7c5 = 7 which puts r789c6 = +14(3) contradicting cage 14(3)c6
-> Step 3(B) must be correct

7. -> r1c4 = 7, r3c1 = 2, r1c5 = 2
-> (HS 2 in r2) 22(4)n3 = [{27}{58}]
-> 19(4)r1 = [28{36}]
-> r3c9 = 4 and 10(2)n3 = [19]
-> r1c3 = 4
-> r2c123 = {138} and r2c456 = [4{56}]
-> 8(2)c4 = [35]
-> r3c56 = [91]
-> 25(4)n2 = [4597]
-> r23c6 = [61]
Also 14(2)n1 = [95]
Also r4c89 = [16]
-> 16(3)c1 = [286]
Also r9c5 = 1, 6(2)r9 = [42]
Also (HS 1 in n9) r7c7 = 1
Also (HS 9 in 27(4)) r7c8 = 9
Also (Remaining Innie c9) r8c9 = 5
-> r8c78 = {68}
-> 13(3)r9 = [157] (cannot be [193] since 9 in 22(4)n8)
-> r7c9 = 3 and r56c9 = {78}
-> (Remaining Innie n6) r4c7 = 4
-> r45c6 = {29}
Also (HS 6 in c5)r7c5 = 6
etc.


Last edited by wellbeback on Tue Jun 14, 2022 5:30 pm, edited 1 time in total.

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 Post subject: Re: Assassin 417
PostPosted: Wed May 25, 2022 6:18 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1040
Location: Sydney, Australia
I started in a similiar way to wellbeback so have started from the end of his step 5. Not easy but one interesting step. [Thanks to Andrew for finding something I overlooked]
paste marks into A417 in SudokuSolver:
.-------------------------------.-------------------------------.-------------------------------.
| 59 59 124 | 67 12 678 | 368 368 14 |
| 12348 12348 12348 | 1249 34569 1234569 | 1245679 1245679 69 |
| 12 67 67 | 35 34589 1234589 | 124589 124589 1248 |
:-------------------------------+-------------------------------+-------------------------------:
| 123456789 123456789 123456789 | 35 3456789 123456789 | 123456789 12345678 12345678 |
| 123456789 123456789 123456789 | 12489 3456789 123456789 | 123456789 123456789 3456789 |
| 123456789 123456789 123456789 | 67 3456789 123456789 | 123456789 123456789 3456789 |
:-------------------------------+-------------------------------+-------------------------------:
| 12345678 12345678 123456789 | 12489 345678 12345678 | 123456789 3456789 3456789 |
| 23456789 12345678 123456789 | 12489 34789 12345678 | 23456789 23456789 23456789 |
| 23456789 23456789 123456789 | 12489 12 12345678 | 123456789 1245 1245 |
'-------------------------------.-------------------------------.-------------------------------'
alternate middle:
6. from step 4, r1c56 = r3c9 + 6
6a. and from step 3, 19(4)r1c5 = [17]{38}/[26]{38}/[28]{36}
6b. -> r1c56 = 8/10 -> r3c9 = (24)
6c. but r1c56 + r3c9 as [262] is blocked by iod n1 = -5 = [61]
6d. -> r1c56 + r3c9 = [172]/[284]

7. [17] in r1c56 -> 4 in r1c9
7a. [28] in r1c56 -> 4 in r3c9 (step 6d)
7b. -> 4 locked for n3 and c9
7c. no 2 in r9c8

8. 27(4)r5c9: {689}[4] blocked by r2c9 = (69)
8a. -> = {3789/5679}(no 4)

Key steps. Tough
9. "45" on c9: 1 outie r7c8 + 8 = 4 innies r3489c9
9a. no 1,2,4 in r7c8 -> the number in that cell can only repeat in c9 in r2c9 or r4c9
9b. if it repeats in r4c9 -> the remaining 3 innies c9 = 8
9c. but {125} as [2]{15} only, blocked by 6(2)r9c8 (Combo Crossover Clash CCC)
9d. and {134} blocked by r1c1 = (14)
9e. -> r7c8 cannot repeat in r4c9
9f. must repeat in r2c9 -> r7c8 = (69)

10. Looking at 5 in 27(4)r5c9 = {3789/5679}
10a. when 6 in r7c8 -> [462] in r123c9 (step 9f) -> 6(2)n9 = {15} -> no 5 in r7c9
10b. when 9 in r7c8 -> other 3 innies n9 = 11
10bi. but {128/146/245} all blocked by 6(2)n9
10bii. so is {137/236} -> no 5 in r7c9
10c. -> no 5 in r7c9
10d. -> r7c89 must have at least one of 7,9 (ie, can't be {38/56}

11. 19(3)n9: {379} blocked by step 10d
11a. {469} blocked by r7c8 = (69)
11a. = {289/478/568}(no 3)
11b. 8 locked for r8 and n9

12. r2c9 = r7c8 -> r123c9 + r7c8 = [1949/4626]
12a. 11(3)r3c9 must have 2 or 4 for r3c9 = {128/146/236/245}(no 7)
12b. but [263] blocked by 6 also in r7c8
12c. -> no 3 in r4c9

13. 3 in c9 only in 27(4)r5c9 = {3789} only
13a. -> r7c8 = 9 and r123c9 = [194]

On from there
Cheers
Ed


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 Post subject: Re: Assassin 417
PostPosted: Tue May 31, 2022 8:04 pm 
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Thanks for this Assassin! I've been busy on other things so only really got to spend time of this puzzle yesterday evening. So I haven't yet found time to go through wellbeback's walkthrough and Ed's 'alternative' middle. My way was mostly routine steps until I found the key one.

Here's my walkthrough for Assassin 417:
Prelims

a) R1C12 = {59/68}
b) R12C9 = {19/28/37/46}, no 5
c) R3C23 = {49/58/67}, no 1,2,3
d) R34C4 = {17/26/35}, no 4,8,9
e) R9C89 = {15/24}
f) 11(3) cage at R3C9 = {128/137/146/236/245}, no 9
g) 11(3) cage at R7C1 = {128/137/146/236/245}, no 9
h) 19(3) cage at R8C1 = {289/379/469/478/568}, no 1
i) 19(3) cage at R8C7 = {289/379/469/478/568}, no 1
j) 27(4) cage at R5C9 = {3789/4689/5679}, no 1,2

1a. 45 rule on C6789 2 outies R19C5 = 3 = {12}, locked for C5
1b. Killer pair 1,2 in R9C5 and R9C89, locked for R9
1c. 45 rule on R1 3 innies R1C349 = 12 = {138/147/237/246/345} (cannot be {129} which clashes with R1C5, cannot be {156} which clashes with R1C12), no 9, clean-up: no 1 in R2C9
1d. 27(4) cage at R5C9 = {3789/4689/5679}, CPE no 9 in R8C9

2a. R3C23 = {49/67} (cannot be {58} which clashes with R1C12), no 5,8
2b. Killer pair 6,9 in R1C12 and R3C23, locked for N1
2c. 23(5) cage at R1C3 = {13478/23468} (cannot be {12578/13568/14567/23567} which clash with R1C12), no 5
2d. 23(5) cage at R1C3 = {13478/23468}, CPE no 8 in R1C12, clean-up: no 6 in R1C12
2e. Naked pair {59} in R1C12, locked for R1 and N1, clean-up: no 4 in R3C23
2f. Naked pair {67} in R3C23, locked for R3, 7 locked for N1, clean-up: no 1,2 in R4C4
2g. 6,7 of 23(5) cage only in R1C4 -> R1C4 = {67}
2h. 23(5) cage at R1C3 = {13478/23468}, 3,4,8 locked for N1
2i. R3C1 = {12} -> R45C1 = 14,15 = {68/69/78} (cannot be {59} which clashes with R1C1)
2j. R1C349 (step 1c) = {147/237/246} (cannot be {138/345} because R1C4 only contains 6,7), no 8, clean-up: no 2 in R2C9
2k. R1C4 = {67} -> no 6,7 in R1C9, clean-up: no 3,4 in R2C9
2l. 8 in N1 only in R2C123, locked for R2, clean-up: no 2 in R1C9

3a. 45 rule on N4 2(1+1) outies R3C1 + R6C4 = 8 = [17/26]
3b. Naked pair {67} in R16C4, locked for C4, clean-up: no 1,2 in R3C4
3c. Naked pair {35} in R34C4, locked for C4
3d. R1C349 (step 2j) = {147/246} (cannot be {237} = [273] which clashes with R3C1 + R6C4), no 3, 4 locked for R1, clean-up: no 7 in R2C9
3e. 3 in N1 only in R2C123, locked for R2
3f. Naked triple {124} in R1C359, locked for R1
3g. Min R6C4 = 6 -> max R6C123 = 10, no 8,9 in R6C123

4a. 45 rule on N3 2 outies R1C56 = 1 innie R3C9 + 6
4b. Max R1C56 = 10 -> max R3C9 = 4
4c. Min R1C56 = 7, R1C5 = {12} -> no 3 in R1C6
4d. 3 in R1 only in R1C78, locked for N3
4e. 45 rule on N3 3 innies R1C78 + R3C9 = 13 = {36}4/{38}2, no 1,7
4f. 7 in R1 only in R1C46, locked for N2
4g. 11(3) cage at R3C9 = {128/146/236/245} (cannot be {137} because R3C9 only contains 2,4), no 7

5a. R1C349 (step 3d) = {147/246}
5b. Consider permutations for R3C1 + R6C4 (step 3a) = [17/26]
R3C1 + R6C4 = [17] => R1C4 = 6, R1C39 = [24] => R3C9 = 2
or R3C1 + R6C4 = [26] => R3C1 = 2
-> 2 in R1C3 + R3C1, locked for N1
and 2 in R3C19, locked for R3

6a. Min R567C5 = 12 -> no 8,9 in R5C4
6b. 8 in C4 only in R789C4, locked for N8
6c. 22(4) cage at R7C4 contains 8 = {1489/2389} (cannot be {1678/2578/3478/3568} because 3,5,6,7 only in R8C5), no 5,6,7, 9 locked for N9
6d. Killer pair 1,2 in 22(4) cage and R9C5, locked for N8
6e. Min R78C6 = 8 (cannot be {34} which clashes with 22(4) cage) -> max R6C6 = 6
6f. Max R9C56 = 9 -> min R9C7 = 4
6g. 45 rule on N8 3 innies R7C56 + R8C6 = 1 outie R9C7 + 10
6g. Max R7C56 + R8C6 = 18 -> max R9C7 = 8

7a. 45 rule on N69 2 innies R49C7 = 1 outie R3C9 + 7
7b. Max R3C9 = 4 -> max R49C7 = 11
7c. Min R9C7 = 4 -> max R4C7 = 7

8a. 9 in C6 only in 22(5) cage at R2C6 = {12379/12469/13459}, no 8
8b. R1C6 = 8 (hidden single in C6), R1C78 = {36}, 6 locked for R1 and N3, R2C9 = 9 -> R1C9 = 1, placed for D/, R1C35 = [42], R9C5 = 1, clean-up: no 5 in R9C89
8c. R1C78 = {36} -> R3C9 = 4 (step 4e), R9C9 = 2, placed for D\, R9C8 = 4
8d. Naked pair {58} in R3C78, 5 locked for R3 and N3 -> R3C456 = [391], R4C4 = 5, placed for D\ -> R1C1 = 9, placed for D\, R1C2 = 5
8e. R3C1 = 2 -> R45C1 = 14 = {68}, locked for C1 and N4
8f. R1C4 = 7, R6C4 = 6, placed for D/
8g. R2C4 = 4, R3C5 = 9 -> R24C5 = 12 = [57]
8h. R5C4 = 1 (hidden single in C4) -> R567C5 = 18 = {48}6, 4 locked for C5 and N5
8i. R6C6 = 3, placed for D\ -> R78C6 = 11 = {47}
8j. R9C6 = 5 (hidden single in C6), R9C5 = 1 -> R9C7 = 7 (cage sum), R2C7 = 2 -> R2C8 = 7, placed for D/

9a. R9C1 = 3 -> R8C1 + R9C2 = 16 = [79]
9b. R2C123 = [183], 8 placed for D\, R5C5 = 4, placed for D/, R6C5 = 8, R8C2 = 2, placed for D/, R8C8 = 6, placed for D\
9c. R8C2 = 2 -> R7C12 = 9 = [54], R7C3 = 8, placed for D/
9d. R6C14 = [46] -> R6C23 = 6 = [15]
9e. R2345C6 = [6192] = 18 -> R4C7 = 4
9f. R7C89 = [93] -> R56C9 = 15 = [87]

and the rest is naked singles.


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