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Both Windows AN

 
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HATMAN
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Joined: 06 Jan 2008
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Location: Britain, Turkey

PostPosted: Thu Jan 10, 2008 8:56 pm    Post subject: Both Windows AN Reply with quote

BWAN 1: Both Window sets and Anti-kNight


I've been working for some time (with Udosuk's help) on generic restrictions to give minimal solution spaces. This is the best that I've found without some form of sequence constraint (LE, GE or anti-consecutive). This puzzle type has 36880 solutions - which can be reduced with symmetry (with sequencing I've got down to one with 36 solutions).

The puzzle: You have two sets of windows which each with hidden windows and hidden stiles. It is also Anti-kNight - cells 2,1 away from each other cannot be the same.

This is solvable without any big vanilla - provided you use the Law of Leftovers fully.

Some of you will know I almost always create killers - but I feel this type works better as a vanilla - and this appears the best place to post it. In addition I need to practice creating these in order to do a vanilla OverKiller.

Ruud - thanks for many hours of frustration with your assassins - I took ages on 84 then tried Gary W's way and it rolled out.




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Nasenbaer
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PostPosted: Fri Jan 11, 2008 1:18 pm    Post subject: Reply with quote

Welcome, HATMAN,

that was a very interesting puzzle. It took me some time (and a restart) until I realized what you mean by Anti-kNight because I don't play chess. The symmetry of the puzzle helped a lot to solve it.

Here are some observations on uniqueness (each number exists exactly once in the given area) for Both Window sets based on this puzzle (I don't know if it works for all puzzles of this type). They might help to get a better grip on the puzzle.

Uniqueness exists in ...

1. the grey zone
1a. r123c234
1b. r123c678
1c. r789c234
1d. r789c678

2. the clear zone
2a. r234c123
2b. r234c789
2c. r678c123
2d. r678c789

3. the grey houses (the area between and around the grey zones)
3a. r123c159
3b. r789c159
3c. r456c234
3d. r456c678

4. the clear houses (the area between and around the clear zones)
4a. r234c456
4b. r678c456
4c. r159c123
4d. r159c789

5. the extra houses (based on the grey and clear houses)
5a. r159c456
5b. r456c159

... and, of course, the usual nonets n1 through n9.

Are these observations correct? Do they apply to all puzzles of this type?

Thanks again for this nice puzzle.

Here is the solution:
Quote:

8 9 4|7 2 5|6 3 1
7 2 5|6 3 1|8 9 4
6 3 1|8 9 4|7 2 5
-----+-----+-----
9 4 8|2 5 7|3 1 6
2 5 7|3 1 6|9 4 8
3 1 6|9 4 8|2 5 7
-----+-----+-----
4 8 9|5 7 2|1 6 3
5 7 2|1 6 3|4 8 9
1 6 3|4 8 9|5 7 2


Cheers,
Nasenbaer
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HATMAN
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PostPosted: Fri Jan 11, 2008 4:14 pm    Post subject: Reply with quote

Nasenbaer

Your description is correct and they apply to all puzzles of this type.

Maurice
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HATMAN
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PostPosted: Sun Feb 10, 2008 11:00 am    Post subject: Reply with quote

DW AN 2

I've managed to sort out a symmetrical minimal one.

Serious use of LOL and anti-knight but no big vanilla.



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sublue
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Joined: 12 Oct 2007
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Location: Champaign, Illinois, USA

PostPosted: Mon Feb 11, 2008 1:02 am    Post subject: Reply with quote

Maurice,
Just a quick note to let you know that your puzzles are being done "somewhere." I got the same solution (always a good thing) on BWAN: 1. I'm about to start DW AN2.
Susan
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sublue
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Joined: 12 Oct 2007
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Location: Champaign, Illinois, USA

PostPosted: Mon Feb 11, 2008 6:14 pm    Post subject: DW AN2 Solution Reply with quote


586721934
934586721
721934586
658934586
493658172
172493658
865217349
349865217
217349865

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HATMAN
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PostPosted: Tue Feb 12, 2008 9:52 am    Post subject: Reply with quote

Thanks Susan - you do sometimes feel that you are posting puzzles into thin air - particularly on a forum you are new to.
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