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Domino puzzles
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Para
Yokozuna
Yokozuna


Joined: 08 Nov 2006
Posts: 384
Location: The Netherlands

PostPosted: Thu Nov 29, 2007 8:29 pm    Post subject: Reply with quote

Here's some more things you can take into consideration.

Blocked isolation
Code:
 +   +   +
 | 1   n
 +   +   +
 | 5   8 
 +---+---+   +
 | n   1   5
 +   +   +   +
 | n   n |
 +   +   +
 | n   n |
 +   +   +   +
 | n   8   5
 +---+---+   +

The lowest area can't be [15] and [85] in R3 and R6 as it would conflict the 5 in R2C1 as it needs to be either of [15] or [58]

Tunneling
Code:
 +   +   +
 | 9   n
 +   +   +
 | 2   7 
 +---+---+---+---+---+   +
 | 9   n   n   n   2   7
 +   +---+---+---+---+   +
 | 2
 +   +
The lower tunnel either end in [29] or [27]. This creates a pair [27] [29] with the 2 in R2C1 eliminating these stones from the rest of the grid.
Tunneling can be done with any odd isolated area.

greetings

Para
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Ruud
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PostPosted: Sat Dec 01, 2007 7:34 pm    Post subject: Reply with quote

If you have installed the new DominoCue program, you can find a nice example of the sixpack isolation technique in the following puzzle:

Code:
20517012434872240340125867669434970026756654047310221872717133905689672559958831189910354725954481693833880696


State where the sixpack isolation can be used:
Code:
205170124348722403401258676694xe9700c6756gf40473l0c2l872#b#b3390568jghc5599588x1l$9910354725954481g93s33i80696


Ruud
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cowgirl
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PostPosted: Sun Dec 02, 2007 10:49 pm    Post subject: Reply with quote

hoi,

Ruud, i download this new puzzel.
i want ask, you must find al the variaties, you sie in the right site.
when you mark 2 same combie's, than he marked it red. thats wrong i think.

i want ask in dutch now, because i don't now how to write this ask in english . sorry Sad

is de zoektocht naar combie's altijd van links naar rechts en van hoog naar laag, qua nummering?
als voorbeeld, als ik 6.8 markeer is die goed,
maar 8.6 is dus altijd onmogelijk. Heb ik dit zo goed gezien, en alle combies die rechts staan, moeten gevonden worden.

alvast bedankt voor je antwoord.
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Ruud
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PostPosted: Mon Dec 03, 2007 6:33 pm    Post subject: Reply with quote

Gemma,

je kan in elke volgorde zoeken, maar voor het overzicht zijn alle mogelijke combinaties in oplopende volgorde rechts op het scherm geplaatst.

Je moet denken aan echte dominostenen. De combinatie 8-6 is gelijk aan 6-8 als je de steen omdraait.

Het leuke is dat diverse oplostechnieken vergelijkbaar zijn met Sudoku. Zo heb je 'naked singles', hidden singles', paartjes, triples en diverse andere technieken. Aangezien hier nog niet door zoveel mensen over is nagedacht, kan je zelf nog nieuwe methodes vinden. Een belangrijk hulpmiddel is het tellen van de resterende vakjes in bijna afgesloten gedeelten. Omdat elke steen 2 vakjes gebruikt, moeten er dus altijd een even aantal lege vakjes in een afgesloten ruimte zitten. Halve dominostenen kennen we niet.

Ruud
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cowgirl
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PostPosted: Mon Dec 03, 2007 7:48 pm    Post subject: Reply with quote

Hoi Ruud,

Thanks for this answer.
I have try first the little puzzels Smile .
generate 0-3 t/m 0-6 , i can make them , and i understand thisone.
the biggest is not easy, but i understand now the possibility. I hope Very Happy

bedankt voor het antwoord.
ik ben begonnen met de kleinere puzzels.
generate 0-3 t/m 0-6 heb ik kunnen maken, dus ik begrijp nu de bedoeling.
de grootste 0-9 is niet gemakkelijk, maar ik begrijp de bedoeling. hoop ik Very Happy.
de technieken zal ik nog uit moeten vinden voor deze puzzels.
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Para
Yokozuna
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PostPosted: Mon Dec 03, 2007 9:23 pm    Post subject: Reply with quote

Here's another uniqueness move.

Code:

 +   +   +   +            +   +   +   +
       5   4                    5 | 4   
 +   +   +   +    -->>    +   +   +---+
   4   5   5                4   5   5   
 +   +---+   +            +   +---+   +


The 4 in R1C3 can't be use to create for [45] as this would block R2C12 and create an non-unique square with the [55].
Found this in 2 puzzles already.

Here's a no initial singles puzzle, in which you can use this technique to break open this puzzle.

Code:
.-------------------------------.
| 1   5   1   6   6   1   3   6 |
|   +   +   +   +   +   +   +   |
| 6   6   1   3   4   4   3   5 |
|   +   +   +   +   +   +   +   |
| 2   3   1   5   1   2   2   5 |
|   +   +   +   +   +   +   +   |
| 0   2   6   0   4   0   2   2 |
|   +   +   +   +   +   +   +   |
| 1   0   4   0   3   0   5   2 |
|   +   +   +   +   +   +   +   |
| 2   0   6   5   0   6   3   4 |
|   +   +   +   +   +   +   +   |
| 4   4   4   5   1   3   3   5 |
'-------------------------------'


It's pretty hard to list all techniques as most techniques are very easily combined with non-unique squares. I still think uniqueness is probably what i use most when solving domino puzzles.

greetings

Para
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Ruud
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PostPosted: Mon Dec 03, 2007 9:40 pm    Post subject: Reply with quote

Here is a lovely move:

Code:
.-------------------------------------------.
| 3 | 5   6 | 5 | 0   3   0   1   7 | 4   4 |
|   +---+---+   +   +---+   +   +   +---+---|
| 4 | 1   8 | 5 | 0   7   6 | 3   8 | 8 | 3 |
|---+---+---+---+   +   +   +   +   +   +   |
| 2   6 | 6   9 | 5   9 | 6   8   8 | 9 | 7 |
|---+---+---+---+   +   +---+---+   +---+---|
| 0   4 | 2 | 5   7   4 | 3   5 | 8   6   7 |
|---+---+   +   +   +   +---+---+---+---+   |
| 1   2 | 8 | 0   1   9   0   2   5   4   5 |
|---+---+---+   +---+   +   +---+---+---+   |
| 1   6   3   6   4   7   0   6   6   0   2 |
|   +---+---+---+   +   +   +   +   +---+---|
| 9 | 1   4 | 3   9   0   5   1   0 | 3   3 |
|   +   +   +   +---+---+   +   +   +---+---|
| 9   4   7   8 | 5 | 2 | 7   9   9 | 4   8 |
|   +   +---+---+   +   +   +   +   +---+---|
| 1   6 | 1   1 | 8 | 9 | 9   1   5 | 0   8 |
|   +---+---+---+---+---+   +---+---+---+---|
| 3   2   7   2   4   2   3 | 2   2 | 7   7 |
'-------------------------------------------'

What can be deduced from the 3-9 possibilities?

Ruud
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rep'nA
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PostPosted: Mon Dec 03, 2007 9:53 pm    Post subject: Reply with quote

Here is a puzzle I've been working on:
42567881230465800871153445132236865692931502253469754330012528880694447089181671071066462320997399478779913557

I get to here:
4256788b23046580ki7vlf344513wmxq86569m9nl50m2534qt75433k01c5wsiia694ee7ks9bsb6710r10@qe6mxc09j7ntj47i#rjt13557

where there is a sixpack move that brings the grid to:
Code:
.-------------------------------------------.
| 4   2   5   6   7   8   8 | 1   2   3   0 |
|   +   +   +   +   +---+   +   +---+---+   |
| 4   6   5   8   0   0 | 8   7 | 1   1 | 5 |
|   +   +   +   +   +   +---+---+---+---+   |
| 3   4   4   5   1   3 | 2   2 | 3   6   8 |
|   +   +   +   +---+   +---+---+   +   +---|
| 6   5   6   9   2   9   3   1   5   0   2 |
|   +   +   +   +---+---+   +   +   +   +   |
| 2   5   3   4   6   9   7   5   4   3   3 |
|---+---+   +   +   +---+---+   +   +   +   |
| 0   0 | 1 | 2   5 | 2   8 | 8 | 8 | 0   6 |
|   +   +   +   +   +---+---+   +   +---+   |
| 9   4 | 4 | 4   7   0   8   9 | 1   8 | 1 |
|   +   +   +   +---+   +   +---+---+   +   |
| 6   7 | 1   0   7   1   0 | 6   6 | 4   6 |
|---+---+   +   +   +   +   +---+---+   +   |
| 2 | 3 | 2   0   9 | 9   7   3   9 | 9   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 7 | 8 | 7   7 | 9   9   1   3   5   5   7 |
'-------------------------------------------'

Any help out there?
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Ruud
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PostPosted: Mon Dec 03, 2007 10:04 pm    Post subject: Reply with quote

Just a little step:

both candidates for {0-5} eliminate {0-6} in r3-4c10. This leaves a hidden single {0-6} elsewhere in the grid.

Ruud

(Edit:)

Candidates for {6-8}: when r3c10-11 is true, a tunnel forces r1c5-6 to {7-8}. The alternative {6-8} is r1-2c4. Eliminate r1c4-5.

The next step is a contradiction from r1c10-11 {0-3} forcing {0-3} into r2-3c6. (T&E or a simple forcing chain?)
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Para
Yokozuna
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Location: The Netherlands

PostPosted: Mon Dec 03, 2007 10:40 pm    Post subject: Reply with quote

Ruud wrote:
Here is a lovely move:

Code:
.-------------------------------------------.
| 3 | 5   6 | 5 | 0   3   0   1   7 | 4   4 |
|   +---+---+   +   +---+   +   +   +---+---|
| 4 | 1   8 | 5 | 0   7   6 | 3   8 | 8 | 3 |
|---+---+---+---+   +   +   +   +   +   +   |
| 2   6 | 6   9 | 5   9 | 6   8   8 | 9 | 7 |
|---+---+---+---+   +   +---+---+   +---+---|
| 0   4 | 2 | 5   7   4 | 3   5 | 8   6   7 |
|---+---+   +   +   +   +---+---+---+---+   |
| 1   2 | 8 | 0   1   9   0   2   5   4   5 |
|---+---+---+   +---+   +   +---+---+---+   |
| 1   6   3   6   4   7   0   6   6   0   2 |
|   +---+---+---+   +   +   +   +   +---+---|
| 9 | 1   4 | 3   9   0   5   1   0 | 3   3 |
|   +   +   +   +---+---+   +   +   +---+---|
| 9   4   7   8 | 5 | 2 | 7   9   9 | 4   8 |
|   +   +---+---+   +   +   +   +   +---+---|
| 1   6 | 1   1 | 8 | 9 | 9   1   5 | 0   8 |
|   +---+---+---+---+---+   +---+---+---+---|
| 3   2   7   2   4   2   3 | 2   2 | 7   7 |
'-------------------------------------------'

What can be deduced from the 3-9 possibilities?

Ruud


I assume you mean that either R7C45 or R910C7 has to be [39] and they can't be both. So 1 three is an innie and 1 an outie. The fact that an isolated area has to be even then gives you that there needs to be a border between R67C1. The easier thing of course is the unique square in R78C23.
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Para
Yokozuna
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PostPosted: Mon Dec 03, 2007 10:49 pm    Post subject: Reply with quote

rep'nA wrote:

Code:
.-------------------------------------------.
| 4   2   5   6   7   8   8 | 1   2   3   0 |
|   +   +   +   +   +---+   +   +---+---+   |
| 4   6   5   8   0   0 | 8   7 | 1   1 | 5 |
|   +   +   +   +   +   +---+---+---+---+   |
| 3   4   4   5   1   3 | 2   2 | 3   6   8 |
|   +   +   +   +---+   +---+---+   +   +---|
| 6   5   6   9   2   9   3   1   5   0   2 |
|   +   +   +   +---+---+   +   +   +   +   |
| 2   5   3   4   6   9   7   5   4   3   3 |
|---+---+   +   +   +---+---+   +   +   +   |
| 0   0 | 1 | 2   5 | 2   8 | 8 | 8 | 0   6 |
|   +   +   +   +   +---+---+   +   +---+   |
| 9   4 | 4 | 4   7   0   8   9 | 1   8 | 1 |
|   +   +   +   +---+   +   +---+---+   +   |
| 6   7 | 1   0   7   1   0 | 6   6 | 4   6 |
|---+---+   +   +   +   +   +---+---+   +   |
| 2 | 3 | 2   0   9 | 9   7   3   9 | 9   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 7 | 8 | 7   7 | 9   9   1   3   5   5   7 |
'-------------------------------------------'

Any help out there?


Easy one: R45C10 = [03] -> R45C11 = [23] blocked by R1C10: border between R45C10

I spotted Ruud's final chain like this. R12C5 = [70], forces 2 domino's [03]( R23C6 and R1C1011): Border between R12C5. Noticed this before the [68] move.
Which is also easier now as R12C4 = [68] forces the R3C1011 to [68]. So border betweens R12C4. And a hidden single and the rest works out quickly.

greetings

Para
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Para
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PostPosted: Tue Dec 04, 2007 12:18 am    Post subject: Reply with quote

What about the size of this isolation block in R1234C123456789.

Code:
.-------------------------------------------.
| 0   0   3   9   5   5   6   8   4 | 2   9 |
|   +   +   +   +   +   +---+---+   +---+---|
| 5   6   3   7   2   6 | 8 | 1   5   3   0 |
|   +   +   +---+   +   +   +   +   +   +   |
| 0   2   6 | 0 | 4 | 7 | 8 | 4   5 | 3   4 |
|   +   +   +   +   +   +---+---+   +   +---|
| 5   8   9 | 1 | 1   5   7   7   7   1   1 |
|---+---+---+---+---+---+   +---+   +   +   |
| 1   7 | 0   2 | 9   9 | 1   6   2   8   9 |
|   +   +   +   +---+---+   +   +   +   +   |
| 1   9 | 4   2   8   1   6   5   7   3   6 |
|---+---+   +   +   +   +   +   +   +   +   |
| 4   7 | 8   0   7   3   6   8   1   3   8 |
|---+---+   +   +   +   +   +   +   +---+---|
| 4   5 | 2   3   6   9 | 2   2   7 | 4   6 |
|   +   +---+   +   +---+   +   +   +---+---|
| 9 | 9   3 | 0   6   0   0   8   3 | 1 | 4 |
|   +---+   +   +   +   +   +   +   +   +   |
| 0   9   4 | 7   8   3   2   5   5 | 2 | 4 |
'-------------------------------------------'


greetings

Para
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unkx80
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PostPosted: Sat Dec 15, 2007 10:41 am    Post subject: Reply with quote

Ruud wrote:
Locked pairs, triples, etc.

N cells can only be used in N combinations. Eliminate remaining candidates for this combination in the grid.


This is an easy one, but I don't think is implemented in DominoCue:

Hidden pairs, triples, etc.

Probably easiest to say it via an example:

Code:
+   +   +   +          +   +   +   +
  n   2   n              n   2   n 
+   +   +   +          +   +   +   +
  3   1   n              3   1 | n 
+   +   +   +          +   +---+   +
  n   n   n              n   n   n 
+---+---+---+   --->   +---+---+---+
  n   n   n              n   n   n 
+   +   +   +          +   +---+   +
  n   1   2              n | 1   2 
+   +   +   +          +   +   +   +
  n   3   n              n   3   n 
+   +   +   +          +   +   +   +


Suppose there are only two places to place the tile 1-2, and only two places to place the tile 1-3, as shown in the diagram on the left. Then we can add separators as shown on the right diagram.
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rep'nA
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PostPosted: Mon Dec 17, 2007 1:21 pm    Post subject: Reply with quote

Here is a an example I found of a hidden pair:
Code:
6712318075115xnj1744948euq205623495273g865743826q9c837668471m498030937392uj951904024ae173110156p86#50822788zpj

Code:
.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7   5   1 |
|   +   +---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +   +   +   +   +   +   |
| 8 | 4 | 0   6   2   0   5   6   2   3   4 |
|   +   +   +   +   +   +   +   +   +   +   |
| 9   5   2   7   3 | 6   8   6   5   7   4 |
|   +   +   +   +---+   +   +   +   +   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +   +   +---+   +   +   +   +   |
| 6   8   4   7   1   2   4   9   8   0   3 |
|   +   +   +   +   +   +   +---+   +   +   |
| 0   9   3   7   3   9   2 | 0 | 9   9   5 |
|   +   +   +   +   +   +   +   +   +   +   |
| 1   9   0   4   0   2   4 | 0 | 4   1   7 |
|   +   +   +   +   +   +   +---+   +   +---|
| 3   1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +   +   +   +   +---+---+   |
| 5   0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'

Look at [22] and [27] and after cleaning up a little, look at [26] and [66]. This will get you to
Code:
6712318075115xnj1744948euqc05@23495wr3@86574382qq9c8376684r1m49803k937392uj951904024ae173110156p86#5082m788zpj

Code:
.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7   5   1 |
|   +   +---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +   +   +---+   +   +   |
| 8 | 4 | 0   6 | 2   0   5 | 6   2   3   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 9   5 | 2   7   3 | 6   8   6   5   7   4 |
|   +   +   +---+---+   +   +   +   +   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2   4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +   |
| 0   9   3   7   3   9   2 | 0 | 9   9   5 |
|   +   +   +   +   +   +   +   +   +   +   |
| 1   9   0   4   0   2   4 | 0 | 4   1   7 |
|   +   +   +   +   +   +   +---+   +   +---|
| 3   1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+   +   +   +---+---+   |
| 5   0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'

Where to now?

Edit: And here is a puzzle that solves with hidden pairs, but DominoCue runs out of steam on.
Code:
05831811355524799153012344406944841275817699005721401134988769652329074037968673980100366237257926368482672585

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unkx80
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Joined: 26 Aug 2006
Posts: 33
Location: Singapore

PostPosted: Thu Dec 27, 2007 10:06 am    Post subject: Reply with quote

Non-unique blocks

As Para mentioned, there are many ways uniqueness constraints can be put to use. I just list some 2x2 and 3x2 commonly found patterns below (the 2x2 one is already widely known in this forum but included simply for completeness sake). What these mean is that if we encounter the pattern on the left hand side, then we cannot place borders as shown on the right hand side to form a non-unique block that has multiple solutions. Such 2x2 and 3x2 patterns are particularly interesting because square isolation and six-pack isolation can often be included in part of the uniqueness or non-uniqueness arguments. Note that the letters need not represent distinct digits, e.g., the results still hold if both A and B are the digit 1.

Code:
+   +   +                  +---+---+
  A   B                    | A   B |
+   +   +   --->   (No!)   +   +   +
  C   A                    | B   C |
+   +   +                  +---+---+

+   +   +   +                  +---+---+---+
  B   A   B                    | B   A   B |
+   +   +   +   --->   (No!)   +   +   +   +
  C   A   C                    | C   A   C |
+   +   +   +                  +---+---+---+

+   +   +   +                  +---+---+---+
  B   A   C                    | B   A   C |
+   +   +   +   --->   (No!)   +   +   +   +
  C   A   B                    | C   A   B |
+   +   +   +                  +---+---+---+

+   +   +   +                  +---+---+---+
  A   B   A                    | A   B   A |
+   +   +   +   --->   (No!)   +   +   +   +
  A   C   A                    | A   C   A |
+   +   +   +                  +---+---+---+


A very simple application is as follows. In the situation below, we can add a border to avoid a 2x2 non-unique block.

Code:
+   +   +          +   +   +
  A   B              A | B 
+---+---+   --->   +---+---+
| C   A |          | B   C |
+---+---+          +---+---+


Uniqueness patterns can often be combined with other constraints to add borders. Sounds obvious, but not always obvious how to apply. Razz For example, in the situation below, we can add two borders to avoid a 2x2 non-unique block.

Code:
+   +   +   +          +   +   +   +
  A   B   A              A   B   A 
+   +   +   +   --->   +---+   +---+
  C   A   C              C   A   C 
+   +---+   +          +   +---+   +


The last result can be used to advance rep'nA's puzzle above, but I have not yet figured out how this puzzle can be advanced further.
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