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 Post subject: SinKiller GT 1&2
PostPosted: Thu Jul 15, 2021 5:39 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Sinkiller GT 1
I think I may have done this before.

Each killer cage contains singletons only.

Inequalities are between the cage totals.

Not to difficult once you are used to the variant.


Image

CORRECTED Solution:

513784296
264193758
897256413
328649175
649517832
751328649
982431567
475962381
136875924


Last edited by HATMAN on Wed Jul 28, 2021 8:36 pm, edited 2 times in total.

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 Post subject: Re: Sinkiller GT 1
PostPosted: Thu Jul 15, 2021 7:43 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
It looks familiar but I can't find that puzzle title in my saved, solved HATMAN puzzles.

Presumably the = only applies to the cages at R8C2 and R9C5, which have the largest cage totals in the chain of GT symbols. M is at least two less than T.


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 Post subject: Re: Sinkiller GT 1
PostPosted: Sat Jul 17, 2021 1:20 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Correct Andrew

I probably used a different name for them


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 Post subject: Re: SinKiller GT 1&2
PostPosted: Wed Jul 28, 2021 8:48 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
SinKiller GT 2

The dashed cages are all singleton cages. The continuous cage is not, i.e. two or three numbers are consecutive.

This is a much harder one - enjoy.


Image

Solution:
863425197
724198356
159376248
346519782
281647539
975832461
432981675
618753924
597264813


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 Post subject: Re: SinKiller GT 1&2
PostPosted: Thu Jul 29, 2021 8:04 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
Quote:
Each killer cage contains singletons only.
Maybe I'm missing a point. What does this mean? It's not a term I'm familiar with. The second puzzle says that one cage contains two or three consecutive numbers. Does that mean that cages containing singletons have three numbers which aren't consecutive, different from non-consecutive which means that adjacent numbers aren't consecutive.

Andrew


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 Post subject: Re: SinKiller GT 1&2
PostPosted: Wed Aug 04, 2021 6:43 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Hi Andrew

The Singleton terminology comes from the Sindokus I've been posting. Quadrata originally called them isolated, but Isodoku was used by Motris a few years ago, so I changed the name.
In this usage it means that no number in a cage is adjacent to another number in the cage, so for example 9(3) can only be {135}.

It significantly reduces the cage combinations, so we have to use zero killers.

I hope that this clarifies.

Maurice


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 Post subject: Re: SinKiller GT 1&2
PostPosted: Wed Aug 04, 2021 7:17 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 Maurice. As you said it significantly reduces the cage combinations; it also prevents some cage totals including 6(3) to 8(3) and 22(3) to 24(3).

After posting my message I tried GT1 again and it came out easily.
There are clues:
at each end of the long chain, in addition to the chain itself.

I've started GT2. An easy start but clearly some hard work to come.

Andrew


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 Post subject: Re: SinKiller GT 1&2
PostPosted: Fri Aug 06, 2021 4:10 am 
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Grand Master
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Joined: Wed Apr 23, 2008 6:04 pm
Posts: 1893
Location: Lethbridge, Alberta, Canada
Finished now. A long solving path but I didn't use anything harder than the 'singletons' and interactions between cages; that's not giving anything away because it's obvious from the diagram.

Here's how I solved SinKiller GT 2:
Cages are chained by greater-than signs and with equal signs; letters also indicate some cages with the same totals. Cage R1C456 contains two or three consecutive numbers, assumed not necessarily adjacent. All the other cages contain ‘singletons’, so no consecutive numbers within each of those cages.

Cages M at R8C1, R8C4 and R8C7 are all equal so must total 15. This also places 15(3) cages at R5C1, R5C3, R5C9, R6C2 and R7C5, also R34C3 = 15 = {69}, locked for C3. 15(3) = {159/168/249/258/357}, so only {168/249/357} for R8

Cages L less than cages M -> cages L = 12,13,14, R9C123 = 17,19,21 = {269/359/368/379/469/579} (cannot be {179} which clashes with cage M at R8C1), no 1
2,4 of {269/469} must be in R9C3 -> no 2,4 in R9C12

R7C123 = 9,11,13 (no restriction on ‘singletons’)
R7C123 cannot be {139} which clashes with cage M at R8C1, no 9 in R7C12

Cages K at least two greater than cages M = 17,18,19 -> R1C456 = 7,9,11, all of which can contain two or three consecutive numbers
R1C456 = {124/126/234/128/236/245}, no 7,9
R1C456 cannot be {124} because that would only leave {379} for both cages K
R1C456 cannot be {126/234} which clash with only valid 18(3) combinations {279/369/468}
-> cages K must total 17, R1C456 = 11
Cages K in R1 = {179/269/359/368}, no 4 -> R1C456 = {245}, locked for R1 and N2 -> cages K in R1 = {179/368}
Killer pair 6,9 in cage K at R1C1 and R3C3, locked for N1
Cage K at R4C5 = {179/359/368} (cannot be {269} which clashes with R4C3), no 2,4
Killer pair 6,9 in R4C3 and cage K, locked for R4

Cage K+1 at R1C5 = 18 = {279/468} (cannot be {369} because R1C5 only contains 2,4,5), no 1,3,5

Cages N at R2C6 and R2C9 = 16 = {169/259/268/358}, no 4,7
Cage N at R2C9 = {259/268/358} (cannot be {169} = {69}1 which clashes with cage K at R1C7), no 1
4 in N3 only in R3C78, locked for R3
4 in R3C78 -> no 3,5 in cage L at R3C6
Cage L = {147/246/148/247/149/248}
6 of {246} must be in R3C6 -> no 6 in R3C78
Cage K at R1C7 = {179/368} -> combined cage with cage N at R2C9 = {179}{268}/{179}/{358}/{368}{259} (cannot be {368}{268}/{368}{358}) -> 9 in R1C789 + R23C9, locked for N3
Cage N at R2C6 = {259/268/358} (cannot be {169} = 9{16} which clashes with cage K at R1C7), no 1
3 of {358} must be in R2C78 (cannot be 3{58} which blocks both cage K = {368} and cage N at R2C9 = {358} leaving no 3 in N3) -> no 3 in R2C6
3 in N2 only in R23C4, locked for C4

Hidden killer pair 1,7 in cage K at R1C7 and cage L at R3C6 for N3, cage K contains both or neither of 1,7 but cage L cannot contain all of 1,4,7 in R3C78 -> cage K at R1C7 = {179}, locked for R1 and N3
Cage K at R1C1 = {368}, locked for N1 -> R34C3 = [96]
9 in R4 only in cage K at R4C5 = {179/359}, no 8
Cage N at R2C9 = {268/358}, 8 locked for C9
Hidden killer pair 3,6 in R2C78 and R23C9 for N3, each can only contain one of 3,6 -> cage N at R2C6 = {268/358} with 3,6 in R2C78 -> R2C6 = 8, cage N at R2C9 = {268/358} with 3,6 in R23C9, no 3 in R4C9
Cage K+1 at R1C5 = {279} = [297]
Cage K at R4C8 = {269/359/368} (cannot be {179} which clashes with R1C8), no 1,4,7

Cage L at R3C6 = 1{48}/6{24} = 12,13 -> cage L at R9C4 and R9C7 = 12,13 -> R9C123 = 19,21 = {379/469/579}, no 2,8, 9 locked for R9 and N7
Cage M at R8C1 = {168/357}, no 2,4
2 in N7 only in R7C123, locked for R7
Cage M = 15, R9C123 = 19,21 -> R7C123 = 9,11 containing 2 = {126/234/128/245} (cannot be {236} which clashes with cage M), no 7
Cages L at R9C4 and R9C7 = 12,13 = {138/246/148/157} (cannot be {147/247} which clash with R9C123)
One of them must contain 8 for R9 -> cages L at R9C4 and R9C7 = {138/246} (cannot be {157} which clashes with {138/148} and cannot be {148} which clashes with {138/246}), no 5,7 -> cages L = 12
R9C123 = {579} (hidden triple in R9), 5,7 locked for N7 -> cage M at R8C1 = {168}, locked for R8 and N7 -> R7C123 = {234}, 3,4 locked for R7
Cage M at R7C5 = {159/168}, no 7, 1 locked for R7
45 rule on N8 1 innie R7C4 = 1 outie R7C7 + 3 -> R7C4 = {89}, R7C7 = {56}
1 in R7 only in R7C56, locked for N8
Cage L at R9C4 = {246}, locked for R9 and N8
Cage M at R8C4 = {357}, locked for R8, 5 locked for N8
Naked triple {189} in R7C456, 8,9 locked for R7
Cage M at R5C1 = {249/258/357} (cannot be {159/168} because R7C1 only contains 2,3,4), no 1
3 of {357} must be in R7C1 -> no 3 in R56C1
Similarly cage M at R6C2 = {249/258/357} (cannot be {159/168} because R7C2 only contains 2,3,4), no 1
3 of {357} must be in R7C2 -> no 3 in R6C23
9 of {249} must be in R6C2 -> no 4 in R6C2
Cage M at R5C9 = {159/168/258/357} (cannot be {249} which clashes with R8C9), no 4
R8C9 = 4 (hidden single in C9)
Cage K at R4C8 = {359/368} (cannot be {269} which clashes with R8C8), no 2, 3 locked for C8 and N6
Cage M at R5C9 = {159/168/249/258}, no 7
R7C8 = 7 (hidden single in R7)
R1C9 = 7 (hidden single in C9)
Killer pair 8,9 in R19C8 and cage K at R4C8, locked for C8 -> R8C8 = 2, R8C7 = 9, R1C78 = [19], R9C8 = 1 (hidden single in C8) -> R9C79 = [83]
R2C7 = 3 (hidden single in C7), R2C6 = 8 -> R2C8 = 5 (cage sum)
R3C8 = 4 (hidden single in C8), R3C7 = 2 -> R3C6 = 6 (cage sum)
R23C9 = [68] -> R47C9 = [25], R23C4 = [13]
R7C7 = 6 -> R7C56 = [81], R7C4 = 9
R4C6 = 9 (hidden single in R4) -> R4C57 = [17/35]

Cage at R2C1 must be less than 15 and cannot be {257} which clashes with cage M at R5C1 -> no 2 in R2C1
2 in C1 only in cage M = {249/258}, no 3,7
Cage at R2C1 must contain 1 (cannot be {357} which totals 15), locked for C1

Cage M at R5C3 = {168/258} (cannot be {357} = 3{57} which clashes with R8C4), no 3,4,7
Hidden killer pair 2,6 in cage M and R9C4 for C4, cage M cannot contain both of 2,6 -> R9C4 = {26} and cage M must contain one of 2,6 in R56C4, no 2 in R5C3

Cage M at R5C1 = {249/258}, cage M at R6C2 = {249/258/357} -> killer pair 5,9 in R56C1 and R6C23, locked for N4
Naked pair {18} in R58C3, locked for C3 -> R1C3 = 3
Naked pair {68} in R18C1, locked for C1
R7C2 = 3 (hidden single in R7) -> cage M at R6C2 = {357}, R6C23 = {57}, locked for R6 and N4 -> R6C7 = 4
R4C1 = 3 (hidden single in C1), R4C5 = 1, R4C6 = 9 -> R4C7 = 7 (cage sum), R4C248 = [458]
Naked pair {29} in R56C1, 2 locked for C1 and N4 -> R7C1 = 4
Cage M at R5C3 = {168} -> R5C3 = 1, R56C4 = {68}, 6 locked for C4 and N5

and the rest is naked singles.


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 Post subject: Re: SinKiller GT 1&2
PostPosted: Tue Aug 10, 2021 7:28 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 693
Location: Saudi Arabia
Nice solution Andrew


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