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 Post subject: NC Repeat X 3 H
PostPosted: Sun Oct 16, 2016 2:00 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
NC Repeat X 3 H

The cages are maximum repeat so: XYZ-XYZ or TU-U.
It is NC.
It is X.


Below assassin level - views?

Image

Solution:
583927146
146385729
729641583
297164835
461538297
835792461
358279614
614853972
972416358


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 Post subject: Re: NC Repeat X 3 H
PostPosted: Mon Oct 24, 2016 10:39 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 another interesting puzzle. Not sure why part of the instructions was in small type; that part made it clearer and didn't give anything away.

Maybe I missed something but I found it quite hard, definitely Assassin level. I used several forcing chains; I would expect that using contradictions would be similarly hard. Second time through, while checking my walkthrough, I managed to find some simplifications.

Thanks HATMAN for pointing out that I’d carelessly included {167167} in the possible combinations for the 28(6) double cage. I’ve changed step 1c without that combination.

Here is my walkthrough:
Non-consecutive (NC), killer-X. The cages are maximum repeat so: XYZ-XYZ or TU-U.
After step 3, most statements about NC have been omitted.

Prelims

a) 22(3) cage at R3C3 = {499/688/877}, no 1,2,3,5
b) 22(6) double cage at R3C4 = {137137/146146} (cannot be {128128/236236/245245} because of double-row NC), no 2,5,8,9
c) 26(6) double cage at R4C3 = {139139/148148/157157/247247} (cannot be {238238/256256/346346} because of double-row NC), no 6
d) 28(6) double cage at R4C6 = {149149/158158/248248/257257} (cannot be {167167/239239/347347/356356} because of double-row NC), no 3,6
e) The blank double cage at R6C4 cannot contain consecutive numbers because of double-row NC

1a. 22(6) double cage at R3C4 = {137137/146146}, 1 locked for R34 + N25
1b. Killer pair 1,2 in 22(6) double cage at R4C3 and 26(6) double cage at R4C6, locked for N5 -> no 1,2 in R456C5
1c. 28(6) double cage at R4C6 = {158158/248248/257257} (cannot be {149149} which clashes with 26(6) double cage at R4C3), no 9
1d. No 1 in R6C456 -> no 1 in blank double cage at R6C4

2a. 6 in N5 only in R456C5, locked for C5
2b. R456C4 = 13, R456C6 = 14 -> R456C5 = 18 = {369/468/567}
2c. R456C5 = {369} (cannot be {468} which clashes with 22(6) double cage at R3C4 = {146146}, cannot be {567} because of NC), locked for C5 and N5
2d. No 3,9 in R456C4 -> no 3,9 in 26(6) double cage at R4C3
2e. 28(6) double cage at R4C6 = {158158/248248/257257}, R4C6 = {147} -> no 4,7 in R56C6

3a. 26(6) double cage at R4C3 = {157157/247247} (cannot be {148148} which clashes with 22(3) cage at R3C3), no 8, 7 locked for C34 + N45
3b. 28(6) double cage at R4C6 = {158158/248248}, no 7, 8 locked for C67 + N6
3c. 22(3) cage at R3C3 = {499/688} -> R4C2 + R5C1 must contain at least one of 8,9 -> no 8,9 in R4C1 + R5C2 (NC)
3d. R6C12 must contain one of 8,9, R6C56 must contain one of 8,9 (R5C56 cannot be [98] because of NC) -> killer pair 8,9 in R6C12 and R6C56, locked for R6

4a. 22(6) double cage at R3C4 = {137137} => R456C4 = 7{24} => R456C3 = {247} => 22(3) cage at R3C3 = {688}
or 22(6) double cage at R3C4 = {146146}, 4 locked for R34
-> no 4 in R3C3 + R4C2
4b. 22(3) cage at R3C3 = {499/688}
4c. 4 of {499} must be in R5C1 -> no 9 in R5C1
4d. 8 in N6 only in R45C7 -> 22(3) cage cannot be 6[88] -> no 6 in R3C3

5. 22(6) double cage at R3C4 = {137137} => R4C456 = [731] => R456C6 = 1{58}
or 22(6) double cage at R3C4 = {146146} => R4C456 = [164] => R456C6 = [482] (cannot be [428] because R5C5 + R6C6 = [98] clashes with R3C3) => R456C5 = [639]
or 22(6) double cage at R3C4 = {146146} => R4C456 = [461] => R456C6 = [185] (cannot be [158] because R5C5 + R6C6 = [98] clashes with R3C3) => R456C5 = [639]
-> no 2 in R5C6, no 3 in R6C5

6a. 22(6) double cage at R3C4 = {137137} => R4C456 = [731] => R456C6 = [185] (cannot be [158] because R5C5 + R6C6 = [98] clashes with R3C3) => R456C5 = [369]
or 22(6) double cage at R3C4 = {146146} => R456C5 = [639]
-> R6C5 = 9
6b. R4C2 = 9 (hidden single in N4) -> 22(3) cage at R3C3 = [994], 9 placed for D\
6c. R5C6 = 8 (hidden single in N5), R4C7 = 8 (hidden single in R4)
6d. R6C5 = 9 -> 9 in R7C46 (because of blank double cage at R6C4), locked for R7 and N8
6e. No 3,6,8 in R6C46 -> no 3,6,8 in R7C46
6f. R6C12 = [83] (hidden pair in N4)
6g. R5C1 = 4 -> 26(6) double cage at R4C3 = {157157}, locked for C34 + N45 -> R5C2 = 6, R4C1 = 2, R4C4 = 1 (hidden single in N5), placed for D\, R4C6 = 4, placed for D/, R5C5 = 3, placed for both diagonals, R6C6 = 2, placed for D\, R4C5 = 6, R5C3 = 1
6h. R4C456 = [164] -> 22(6) double cage at R3C4 = {146146}, locked for R3 and N2

7a. Naked pair {57} in R6C34, locked for R6 -> R6C7 = 4, R5C7 = 2, R3C7 = 5, placed for D/, R6C4 = 7, placed for D/
7b. R6C456 = [792] -> blank double cage at R6C4 = {279279}, 2,7 locked for R7 and N8 -> R7C7 = 6, placed for D\, R7C3 = 8, placed for D/
7c. R3C1 = 7, R1C1 = 5, placed for D\, R3C2 = 2, R8C2 = 1, placed for D/, R7C12 = [35], R1C2 = 8, R2C2 = 4, placed for D\, R12C3 = [36], R8C3 = 4
7d. R1C4 = 9, R7C4 = 2, R2C4 = 3, R7C5 = 7, R8C5 = 5, R8C46 = [83]

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


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 Post subject: Re: NC Repeat X 3 H
PostPosted: Thu Nov 03, 2016 5:03 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
I noticed from Andrew's solution that 6 is forced in R456c5 my approach had been an unsatisfactory multicase one this reduced it to an (in my view) acceptable multicase one, so:

Non-consecutive (NC), killer-X. The cages are maximum repeat so: XYZ-XYZ or TU-U.

Prelims

a) 22(3) cage at R3C3 = 9{49}/8{68}/7{87}, 7/8/9 & no 1,2,3,5
b) 22(6) double cage at R3C4, 11(3)*2 = {137137/146146} (cannot be {128128/236236/245245} because of double-row NC), no 2,5,8,9
c) 26(6) double cage at R4C3, 13(3)*2 = {139139/148148/157157/247247} (cannot be {238238/256256/346346} because of double-row NC), no 6
d) 28(6) double cage at R4C6, 14(3)*2 = {149149/158158/248248/257257} (cannot be {167167/239239/347347/356356} because of double-row NC), no 3,6
e) The blank double cage at R6C4 cannot contain consecutive numbers because of double-row NC (this is the fundamental concept for the design of the puzzle and why I used small letters)

1a. 22(6) double cage at R3C4 = {137137/146146}, 1 locked for R34 + N25
1b. 6 not in 26(6) double cage at R4C3 or 28(6) double cage at R4C6, r456c5 = 45-1/2*26 - 1/2*28 = 18(3) = {369} not {678} = 3{69}/6{39}
1c. 11(3) @r4c456 = [137/731/164/461]
1d. N5:13(3) = {148/157/247} = 1{48}/1{57}/4{27}/7{24}
1e. N5:14(3) = {158/248/257} = 1{58}/4{28}/7{25}

2 there are four cases for the 11(3) at r4c4
2a. case [137]: 14(3) = 7{25}; 13(3) = 1{48}
2b. case [731]: 14(3) = 1{58}; 13(3) = 7{24}
2c. case [461]: 14(3) = 1{58}; 13(3) = 4{27}
2d. case [164]: 14(3) = 4{28}; 13(3) = 1{57}

Consider the case combinations allowing for NC

3 case [137]: r56c4,5,6 = {48}{69}{25}
3a. r5 = 495, r6 = 862 22(3) fail on 9 at r5c5 and {148} r4c3
3b. r5 = 862, r6 = 495 fail (cage at r6c4)

4 case [731]: r56c4,5,6 = {24}{69}{58}
4a. r5 = 268, r6 = 495 fail (cage at r6c4)
4b. r5 = 295, r6 = 468 fail 798 on d\ clash r3c3
4c. r5 = 468, r6 = 295 22(3) fail [68] at r5c56 and {247} r4c3
4c. r5 = 495, r6 = 268 fail 798 on d\ clash r3c3

5 case [461]: r56c4,5,6 = {27}{39}{58}
22(3) = [886], r6c6 = 5, r5c6 = 8, r5c5 = 3, r5c4 = 7, r6c4 = 2, r6c5 = 9
fail N4 no room for 5

6 case [164]: r56c4,5,6 = {57}{39}{28}
6a. r5 = 592, r6 = 738 fail (cage at r6c4)
6b. r5 = 792, r6 = 538 fail D\ 98 r3c4 and {157} clash r3c3
6c. r5 = 538, r6 = 792 OK so far
6d. r5 = 738, r6 = 592 OK So far

7 N5: c4 =1{57}, c5 = [639], c6 = [ 482]

8 NC on 89 at r3c3, r4c2
8a. N4 HS r4c2 = 9 22(3) = [994]

Singles and simple NC from here

Difficulty: nothing very hard for NC and the set of cases reasonable so difficulty less than 1.0.

How many cases is acceptable I wonder? My original 48 is in my view not acceptable. Of course it is not just the number it is the shortness of the elimination in each case, but most of mine died very easily and a couple died easily enough.

I often post puzzles where I have a solution which I do not consider acceptable - I cannot remember a case where someone did not come up with an acceptable one.


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