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Ed
 Post subject: Assassin 248
PostPosted: Thu Oct 25, 2012 9:37 pm 
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An encouraging start gets you hooked into this one. Then I used a couple of harder steps that are interesting enough for this to be an Assassin. It gets a high SudokuSolver score of 1.70 but JSudoku gets it out without much struggle. Two months till Christmas so we should hit the 250 by then. I'm very busy for a good bit of that time so will be very limited how much I can contribute. From memory, HATMAN still has a couple of "hidden" Assassins lying around??? If so, please keep them coming!

Assassin 248

Image

code:
3x3::k:11264:11264:11264:11264:5633:9730:9730:9730:9730:11264:3587:3587:2564:5633:4101:2566:2566:9730:11264:3587:2564:5633:5633:5633:4101:2566:9730:11264:4103:4103:1544:10505:2570:5131:5131:9730:11264:4103:1544:10505:10505:10505:2570:5131:9730:2316:2829:2829:4366:10505:5647:2832:2832:3089:2316:2316:4366:10505:10505:10505:5647:3089:3089:1554:1554:4627:4366:2836:5647:3093:2070:2839:2584:2584:4627:4627:2836:3093:3093:2070:2839:
solution: 
+-------+-------+-------+
| 6 7 2 | 4 5 3 | 8 1 9 |
| 5 4 1 | 7 8 9 | 2 3 6 |
| 8 9 3 | 6 2 1 | 7 5 4 |
+-------+-------+-------+
| 9 1 7 | 2 6 4 | 3 8 5 |
| 3 8 4 | 5 1 7 | 6 9 2 |
| 2 5 6 | 3 9 8 | 4 7 1 |
+-------+-------+-------+
| 1 6 5 | 8 3 2 | 9 4 7 |
| 4 2 8 | 9 7 5 | 1 6 3 |
| 7 3 9 | 1 4 6 | 5 2 8 |
+-------+-------+-------+
Cheerio
Ed
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HATMAN
 Post subject: Re: Assassin 248
PostPosted: Fri Oct 26, 2012 9:54 pm 
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Joined: Wed Apr 30, 2008 9:45 pm
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Location: Saudi Arabia
I do indeed - but am a bit busy.

As you probably all remember I'm a widower.

I've been going out with a beautiful, intelligent (you will of course take that for granted - none of us can deal well with boredom) young Nigerian lady for about six months. We got engaged last month and yesterday we decided to get on with it and get married.

My sudoku addiction amuses her so I will keep posting.

Please wish us well.

Maurice

PS By the way her name is Queen Elizabeth Wayas - the vicar would not accept Queen as a proper christian name.

Actually I had the same problem as a baby I was presented as "Maurice" and the stupid priest had not heard of the roman soldier marthyr so I ended having Michael attached.

It goes further than that but I'll leave it to another time.
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Andrew
 Post subject: Re: Assassin 248
PostPosted: Sun Oct 28, 2012 2:53 am 
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Maurice

Congratulations to you and your fiancée! :applause: Very best wishes for your future!

I trust that she accepts your addiction, as well as being amused by it.

Andrew
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Andrew
 Post subject: Re: Assassin 248
PostPosted: Sun Oct 28, 2012 3:01 am 
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Thanks Ed for another challenging Assassin. I'll be interested to find out whether your harder steps are the same as the ones I used.

Here is my walkthrough for Assassin 248:
Minor errors corrected

Prelims

a) R2C4 + R3C3 = {19/28/37/46}, no 5
b) R2C6 + R3C7 = {79}
c) R4C4 + R5C3 = {15/24}
d) R4C6 + R5C7 = {19/28/37/46}, no 5
e) R6C23 = {29/38/47/56}, no 1
f) R6C78 = {29/38/47/56}, no 1
g) R8C12 = {15/24}
h) R89C5 = {29/38/47/56}, no 1
i) R89C8 = {17/26/35}, no 4,8,9
j) R89C9 = {29/38/47/56}, no 1
k) R9C12 = {19/28/37/46}, no 5
l) 10(3) cage at R2C7 = {127/136/145/235}, no 8,9
m) 20(3) cage at R4C7 = {389/479/569/578}, no 1,2
n) 9(3) cage at R6C1 = {126/135/234}, no 7,8,9
o) 22(3) cage at R6C6 = {589/679}
p) 44(8) cage at R1C1 = {23456789}, no 1
q) 38(8) cage at R1C6 = {12345689}, no 7
r) 41(8) cage at R4C5 = {12356789}, no 4

Steps resulting from Prelims
1a. Naked pair {79} in R2C6 + R3C7, CPE no 7,9 in R2C789 + R3C456
1b. Caged X-Wing for 9 in R2C6 + R3C7 and 22(3) cage at R6C6, no other 9 in C67, clean-up: no 1 in R4C6 + R5C7, no 2 in R6C8
1c. 7 in N3 only in R3C78, locked for R3, clean-up: no 3 in R2C4
1d. 1 in N6 only in R456C9, locked for C9
1e. 1 in C1 only in R6789C1, CPE no 1 in R7C2

2. 45 rule on R89 2 innies R8C46 = 14 = {59/68}
2a. R89C5 = {29/38/47} (cannot be {56} which clashes with R8C46), no 5,6

3. 45 rule on C1234 3 innies R357C4 = 19 = {289/379/469/478/568}, no 1

4. 45 rule on C6789 3 innies R357C6 = 10 = {127/136/145/235}, no 8

5. 45 rule on N7 1 innie R7C3 = 2(1+1) outies R6C1 + R9C4 + 2
5a. Min R6C1 + R9C4 = 2 -> min R7C3 = 4
5b. Max R6C1 + R9C4 = 7, no 7,8,9 in R9C4
5c. Min R7C3 + R8C4 = 9 -> max R6C4 = 8

6. 45 rule on N9 1 innie R7C7 = 2(1+1) outies R6C9 + R9C6 + 2
6a. Max R6C9 + R9C6 = 7, no 7,8,9 in R6C9 + R9C4
6b. 7 in C9 only in R789C9, locked for N9, clean-up: no 1 in R89C8
6c. R89C9 = {29/38/47} (cannot be {56} which clashes with R89C8), no 5,6

7. 45 rule on N7 3 innies R789C3 = 1 outie R6C1 + 20
7a. Max R789C3 = 24 -> max R6C1 = 4
7b. Min R789C3 = 21, no 1,2,3

8. 45 rule on N6 4 innies R456C9 + R5C7 = 14 contains 1 = {1238/1247/1256/1346}, no 9
8a. 9 in N6 only in R456C8, locked for C8
8b. 38(8) cage at R1C6 = {12345689}, 9 locked for C9 and N3 -> R3C7 = 7, R2C6 = 9, clean-up: no 1 in R3C3, no 3 in R4C6, no 4 in R6C8, no 5 in R8C4 (step 2), no 2 in R89C9
8c. 22(3) cage at R6C6 = {589/679} -> R7C7 = 9, R68C6 = [58/76/85], no 6 in R6C6
8d. Min R7C3 + R8C4 = 10 -> max R6C4 = 7
8e. 20(3) cage at R4C7 = {389/479/569/578}
8f. 4 of {479} must be in R4C7 -> no 4 in R45C8

9. 1 in N1 only in 14(3) cage = {149/158/167}, no 2,3
9a. 9 of {149} must be in R3C2 -> no 4 in R3C2

10. 45 rule on N3 3 outies R1C6 + R45C9 = 10, no 8 in R1C6 + R45C9

11. R7C3 = R6C1 + R9C4 + 2 (step 5)
11a. Max R7C3 = 8 -> max R9C4 = 5

12. R357C4 (step 3) = {289/379/469/478/568}
12a. 9 of {289/379} must be in R5C4, 3 of {379} must be in R3C5 -> no 2,3 in R5C4, no 3 in R7C4
[There’s more complicated analysis of R357C4, but I didn’t find it until later.]

13. 7 in N8 only in R7C456 + R89C5, CPE no 7 in R456C5
13a. 7 in C6 only in R4567C6, CPE no 7 in R5C4

14. 45 rule on C789 3 remaining outies R149C6 = 13 = {148/238/247/346} (cannot be {157/256} which clash with R68C6), no 5
14a. 8 of {238} must be in R4C6 -> no 2 in R4C6, clean-up: no 8 in R5C7
14b. 2 in N5 only in R4C45 + R5C56 + R6C45, CPE no 2 in R7C4

15. R456C9 + R5C7 (step 8) = {1256/1346}, 6 locked for N6, clean-up: no 5 in R6C78
15a. R7C7 = R6C9 + R9C6 + 2 (step 6), R7C7 = 9 -> R6C9 + R9C6 = 7 = {16/34}/[52], no 2 in R6C9

16. R456C9 + R5C7 (step 15) = {1256/1346}, R1C6 + R45C9 = 10 (step 10) = {136/145/235}
16a. 4 of {145} must be in R1C6 (R45C9 cannot contain both of 4,5), no 4 in R45C9
16b. 3 of {235} must be in R1C6 (R45C9 cannot contain both of 2,3 or both of 3,5), no 2 in R1C6

17. 45 rule on N8 5 remaining innies R7C456 + R9C46 = 20 contains 1 = {12368/12467/13457} (cannot be {12458} which clashes with R8C46)
17a. 17(3) cage at R6C4 = {179/269/359/368/458/467} (cannot be {278} which clashes with R7C456 + R9C46)
17b. 2,3 of {269/368} must be in R6C4, 6 of {467} must be in R8C4 -> no 6 in R6C4
17c. 6 in N5 only in R4C56 + R5C456 + R6C5, CPE no 6 in R7C6

18. R89C8 = {26/35}, R89C9 = {38/47} -> combined cage R89C89 = {26}{38}/{26}{47}/{35}{47}
18a. 12(3) cage at R8C7 = {138/156/246/345}
18b. R89C7 cannot be {46}, which clashes with R89C89 -> no 2 in R9C6, clean-up: no 5 in R6C9 (step 15a)
[Can eliminate 4 from R7C9 but I’ll leave that for now.]

19. R8C46 (step 2) = [68/86/95], R7C456 + R9C46 (step 17) = {12368/12467/13457}
19a. R357C4 (step 3) = {379/478/568} (cannot be {289} because [298] which clashes with R8C46 = [68], cannot be {469} = [496] which clashes with R8C46 = [86]), no 2
19b. 5 of {568} must be in R35C4 (cannot be {68}5 which clashes with R8C46 = [95]), no 5 in R7C4

20. 1 in R6 only in R6C1459
20a. 45 rule on R6 5 innies R6C14569 = 23 = {12389/12479/12569/13478/13568/14567} (cannot be {12578/13469} which clash with the 11(2) cages in R6)
20b. 9 of {12389/12479/12569} must be in R6C5 -> no 2 in R6C5

21. 17(3) cage at R6C4 (step 17a) = {179/269/359/368/458} (cannot be {467} = {47}6 which clashes with R7C4 + R8C46 = [768])
21a. 1 of {179} must be in R6C4 -> no 7 in R6C4
21b. 7 in N5 only in R456C7, locked for C7

22. R149C6 (step 14) = {148/346}, no 7, 4 locked for C6, clean-up: no 3 in R5C7

23. R456C9 + R5C7 (step 15) = {1256/1346}
23a. 4 of {1346} must be in R5C7 (R456C9 cannot be {134} which clashes with R89C9) -> no 4 in R6C9, clean-up: no 3 in R9C6 (step 15a)
23b. R149C6 (step 22) = {148/346}
23c. 3 of {346} must be in R1C6 -> no 6 in R1C6

24. 45 rule on N2 3 remaining innies R1C46 + R2C4 = 14 = {158/248/347/356} (cannot be {167} which clashes with R357C4, cannot be {257} because no 2,5,7 in R1C6)
24a. 1 of {158} must be in R1C6 -> no 1 in R2C4, clean-up: no 9 in R3C3
24b. 5 of {356} must be in R1C4 -> no 6 in R1C4

25. R89C89 (step 18) = {26}{38}/{26}{47}/{35}{47}
25a. 12(3) cage at R8C7 = {138/156/246/345}
25b. 4 of {246} must be in R9C6 (R89C7 cannot be {24} which clashes with R89C89), 4 of {345} must be in R9C6 -> no 4 in R89C7
25c. 12(3) cage at R6C9 = {138/147/156/345} (cannot be {237/246} which clash with R89C89), no 2
25d. 6 of {156} must be in R6C9 (cannot be 1{56} which clashes with R89C89) -> no 6 in R7C89
25e. Hidden killer pair 4,7 in 12(3) cage at R6C9 and R89C9 for N9, R89C9 contains both or neither of 4,7 -> 12(3) cage at R6C9 must contain both or neither of 4,7 = {138/147/156} (cannot be {345} which only contains one of 4,7)
25f. 7 of {147} must be in R7C9 -> no 4 in R7C9
25g. 1 of {156} must be in R7C8 -> no 5 in R7C8

26. 2 in C6 only in R357C6 (step 4) = {127/235}, no 6
26a. 7 of {127} must be in R5C6 -> no 1 in R5C6

27. 6 in C6 only in R489C6 + 6 in 41(8) cage at R4C5, locked for N58, clean-up: no 8 in R8C6 (step 2), no 5 in R6C6 (step 8c)

28. R68C6 (step 8c) = [76/85], R8C46 (step 2) = [86/95] -> R6C6 + R8C4 = [78/89], CPE no 8 in R5C4
[Alternatively R68C6 = 13 (step 8c), R8C46 = 14 (step 2) -> R8C4 = R6C6 + 1 …]
28a. 8 in 41(8) cage at R4C5 only in R456C5 + R7C45, CPE no 8 in R89C5, clean-up: no 3 in R89C5

29. 3 in N8 only in R7C56 + R9C4 -> R7C456 + R9C46 (step 17) = {12368/13457}
29a. 7 of {13457} must be in R7C4 -> no 7 in R7C5

30. 8 in C6 only in R46C6, locked for N5
30a. 8 in 41(8) cage at R4C5 only in R7C45, locked for R7 and N8 -> R8C4 = 9, R8C6 = 5 (step 2), R6C6 = 8 (step 8c), clean-up: no 2 in R5C7, no 3 in R6C23, no 3 in R6C78, no 1 in R8C12, no 2 in R89C5, no 3 in R9C8

[I thought about using Naked pair {46} in R4C6 + R5C7, CPE no 4,6 in R4C79 + R5C45 but the naked pairs in the next two steps are just as powerful and technically simpler.]

31. Naked pair {24} in R8C12, locked for R8 and N7 -> R89C5 = [74], clean-up: no 6,8 in R9C12, no 6 in R9C8, no 7 in R9C9

32. Naked pair {38} in R89C9, locked for C9 and N9 -> R8C8 = 6, R9C8 = 2, R89C7 = [15], R9C6 = 6, R7C89 = [47], R4C6 = 4, R5C7 = 6, R5C4 = 5, R6C9 = 1, R45C9 = [52], R6C7 = 4, R6C8 = 7, R7C4 = 8
[Routine clean-ups omitted from here.]

33. 10(3) cage at R2C7 = {235} (only remaining combination) -> R2C7 = 2, R23C8 = {35}, locked for N3 -> R1C78 = [81], R1C6 = 3

34. R789C3 = R6C1 + 20 (step 7)
34a. R6C1 = {23} -> R789C3 = 22,23 = {589/689} (cannot be {679} because 7,9 only in R9C3) -> R8C3 = 8, R9C3 = 9, R9C4 = 1 (cage sum), R7C56 = [32], R4C4 = 2, R5C3 = 4, R6C4 = 3, R7C3 = 5 (cage sum), R6C1 = 2, R6C3 = 6, R6C5 = 9, R6C2 = 5

35. R2C4 + R3C3 = [73] (only remaining permutation)

36. R2C3 = 1, R23C2 = 13 = [49]

37. R5C5 = 1, R4C3 = 7, R45C2 = 9 = [18]

and the rest is naked singles.

What a lot of CPEs! The 41(8) cage at R4C5 was clearly a key feature of the cage pattern.

Rating Comment:
I'll rate my walkthrough for A248 at Hard 1.5, as much for the difficulty in finding the harder steps as for their technical difficulty.
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Ed
 Post subject: Re: Assassin 248
PostPosted: Thu Nov 01, 2012 8:16 am 
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Joined: Wed Apr 16, 2008 1:16 am
Posts: 1044
Location: Sydney, Australia
Congratulations HATMAN and all the very best. You've found a real gem!

I really enjoyed Andrew's walk-through even though it is much longer than my optimised one. Andrew's method of including all the redundant steps gives a really good insight into how many will find this puzzle - in fact, the way I found the puzzle in practice. Much, much harder than my short optimised WT makes it look. So many of Andrew's steps are very simple and elegant. We ended up making the same key elimination (Andrew's 30a, my 10e) but got there quite differently [edit].

A248 Walk-in
10 steps:
1. 16(2)r2c6 = {79}
1a. 22(3)r6c6 = {589/679}(no 1,2,3,4)
1b. both require 9 -> no other 9 in c67 (Caged X-Wing)

2. "45" on n6: 4 innies r5c7+r456c9 = 14 (no 9)

3. 38(8)r1c6 must have 9 which is only in n3: 9 locked for n3
3a. r3c7 = 7
3b. r2c6 = 9
3c. 22(3)r6c6 must have 9 -> r7c7 = 9

4. "45" on r89: 2 innies r8c46 = 14 = [95]/{68}(no 1,2,3,4,7; no 5 in r8c4)

5. "45" n9: 2 outies r6c9+r9c6 = 7 (no 7,8)

6. "45" on n7: 1 innie r7c3+2 = 2 outies r6c1+r9c4
6a. max. r7c3 = 8 -> max. 2 outies = 6 (no 6,7,8,9)

7. 41(8)r4c5: no 4
7b. 11(2)n8: {56} blocked by h14(2)r8c46 = [5/6,,]
7c. = {29/38/47}(no 1,5,6)

8. "45" on r6789: 4 innies r6c5+r7c456 = 22 and can't have repeats because all belong to the same cage
8a. {2578} blocked by 11(2)n8 = [2/7/8..]
8b. {2569} can only be [9]{256} but this clashes with h14(2)r8c46 = [5/6..]
8b. = {1579/1678/2389/3568}

9. 9 in n8 in 11(2) = {29} or h14(2)r8c46 = [95]
9a. ->h22(4)r6c5+r7c456: {1579} as [9]{157} would leave no 9 for n8
[or 9 in n8 in 11(2) = {29} or h14(2)r8c46 = [95], both block h22(4)r6c5+r7c456 = {1579} (Locking-out cages). Thanks Andrew]
9b. h22(4) = {1678/2389/3568}
9c. must have 8 -> 8 locked for 41(8) (no 8 in r4c5+r5c456); and no 8 in r89c5 since it sees all of r6c5+r7c456 (CPE)
9d. no 3 in 11(2)n8

10. 8 in n8 in h14(2) = {68} or in h22(4)r6c5+r7c456 = {1678/2389/3568} (step 9b)
10a. -> 6 in r7c456 must also have 8 in r7c456 or there would be no 8 for n8 (Locking-out cages)
10b. and 6 in r6c5 -> no 8 in r6c5
10c. and 9 in r6c5 -> no 8 in r6c5
10d. in summary, {1678/3568} must have 8 in r7c456 (because of 10a or b) and {2389} can only be [9]{238} -> no 8 in r6c5 [This is an unusual Locking-out cages because it doesn't eliminate a combination, just a couple of permutations, and does not give the elimination on it's own.]
10e. -> 8 locked in r7c456 for r7 and n8
10f. no 6 in h14(2)r8c46

This effectively cracks the puzzle with cage sums, cage placement and basic moves left.
Cheerio
Ed
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enxio27
 Post subject: Re: Assassin 248
PostPosted: Mon Jan 07, 2013 7:27 pm 
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HATMAN wrote:
I've been going out with a beautiful, intelligent (you will of course take that for granted - none of us can deal well with boredom) young Nigerian lady for about six months. We got engaged last month and yesterday we decided to get on with it and get married.

Congratulations!!
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