interesting puzzles?

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interesting puzzles?

Postby ab » Thu Nov 08, 2007 6:45 pm

What makes a puzzle interesting for a solver. I realise this will be different for different people, but I think there are some general things that most might agree on. For instance difficulty. People often like difficult puzzles. But I think there are some things that make puzzles interesting that are not connected to difficulty. Variety of techniques required to solve a puzzle for instance. A puzzle might not be very difficult, but requires a nice variety of techniques, for example. In the inferior thread, I think it was Ruud that said that the narrowness of the solving path is interesting (although arguably this is connected with difficulty).

Also when considering this question it can be easier to ask what makes a puzzle uninteresting. If you place a candidate, a 7 say, and then all the remaining 7s can be placed in succession, that's not very nice. Similarly if you place a number in one house (box or line) and can then complete the rest of that house it makes for a less interesting puzzle.

These are some thoughts on what make for interesting/uninteresting puzzles, please add your own ideas and maybe post examples of interesting puzzles.
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Postby Chessmaster » Thu Nov 08, 2007 9:42 pm

I like one where at the begining 1 or maybe even more numbers are not given. For example you may be given no 7's at the begining of the puzzle. I like a puzzle that requieres you to think outside the box and explore new techniques.
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Postby m_b_metcalf » Thu Nov 08, 2007 10:14 pm

Chessmaster wrote:I like one where at the begining 1 or maybe even more numbers are not given.

The puzzle compilers amongst us would dearly love to see an example of a puzzle with more than 1 number not given.

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Postby Chessmaster » Thu Nov 08, 2007 11:16 pm

m_b_metcalf wrote:
Chessmaster wrote:I like one where at the begining 1 or maybe even more numbers are not given.

The puzzle compilers amongst us would dearly love to see an example of a puzzle with more than 1 number not given.

Regards,

Mike Metcalf

None exist yet? I actually now think it may not be possibe becasue you will have two unkown numbers left over if you could figure out all the other ones. this would leave many soultions which obviously makes it an invalid puzzle.
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Postby 999_Springs » Sat Nov 10, 2007 9:57 pm

Chessmaster wrote:I actually now think it may not be possible because you will have two unknown numbers left over if you could figure out all the other ones. This would leave many solutions which obviously makes it an invalid puzzle.

The 18 cells which should contain the 9 occurrences of the two digits will fom a 2-solution unavoidable set. This is because in a completed grid, all the (say) ones and twos could be interchanged and still leave a valid grid.

m_b_metcalf wrote:The puzzle compilers amongst us would dearly love to see an example of a puzzle with more than 1 number not given.

I doubt they will, as it has been proven that it would have multiple solutions, which they would know, and they would probably groan and say, "Another invalid puzzle..."
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Postby m_b_metcalf » Sat Nov 10, 2007 10:58 pm

999_Springs wrote:
m_b_metcalf wrote:The puzzle compilers amongst us would dearly love to see an example of a puzzle with more than 1 number not given.

I doubt they will, as it has been proven that it would have multiple solutions, which they would know, and they would probably groan and say, "Another invalid puzzle..."

Who knows? Maybe they understand irony too!

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Postby Smythe Dakota » Sun Nov 11, 2007 12:25 am

Chessmaster wrote:.... I actually now think it may not be possible ....

That's true, and the proof is easy. If, for example, there are no 4's and no 7's among the givens, then, when you find a solution, you can generate a second solution simply by replacing all the 4's with 7's and vice versa.

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Postby Para » Sun Nov 11, 2007 12:34 am

Well you could create a puzzle which holds only the digits 1-7 and leaves 2 squares blank in each row, column and block. That way such a puzzle would have a unique solution.
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Postby TTHsieh » Sun Nov 11, 2007 3:51 am

from 1,2,3,...,9
Code: Select all
. . . | 1 2 . | . . .
. . 7 | . . . | . 3 .
. . . | . . 4 | 6 . 5
- - - + - - - + - - -
. . 3 | 4 . . | . . 1
6 . 1 | . 5 . | 2 . 8
5 . . | . . 2 | 4 . .
- - - + - - - + - - -
1 . 4 | 3 . . | . . .
. 2 . | . . . | 5 . .
. . . | . 4 1 | . . .

    000120000007000030000004605003400001601050208500002400104300000020000500000041000
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Postby RW » Sun Nov 11, 2007 5:48 am

999_Springs wrote:The 18 cells which should contain the 9 occurrences of the two digits will fom a 2-solution unavoidable set.

or 2, 3, or 4 unavoidable sets, giving up to 16 solutions.

As for the original topic, the answer must be highly subjective. At least for me, an interesting puzzle is one where I find something new. Not neccessarily a new solving technique, it might be enough with a new twist to some technique I've used earlier. A puzzle that can be solved with nothing but straight forward basic techniques is thus not very interesting to me. If I had to come up with a universal rule about "interesting puzzles", my guess would be that the most interesting puzzles are those that are slightly above the solver's level. If they are too easy, it becomes routine (which usually is not interesting), if they are too hard, they are more frustrating than interesting. If they are just slightly above the solver's level, then they are within reach for the solver, but will also force the solver to think in a new and interesting way.

Then there is of course the ultra hards, which are interesting for other reasons than pure solving purposes.

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Postby TTHsieh » Mon Nov 12, 2007 10:52 am

I wrote:
Code: Select all
 . . . | 1 2 . | . . .
 . . 7 | . . . | . 3 .
 . . . | . . 4 | 6 . 5
 - - - + - - - + - - -
 . . 3 | 4 . . | . . 1
 6 . 1 | . 5 . | 2 . 8
 5 . . | . . 2 | 4 . .
 - - - + - - - + - - -
 1 . 4 | 3 . . | . . .
 . 2 . | . . . | 5 . .
 . . . | . 4 1 | . . .

    000120000007000030000004605003400001601050208500002400104300000020000500000041000

The Sudoku Explainer's rating is 1.2, the steps :
Code: Select all
1111-22222-333333-4444-55555-6666666-77777777-88888888-999999999

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Postby Pat » Mon Dec 10, 2007 2:11 pm

ab wrote:What makes a puzzle interesting for a solver?

I think there are some things that make puzzles interesting that are not connected to difficulty---


for me it is often the red herrings ( admittedly that's related to difficulty )
    say a puzzle is solved with a duo -- the puzzle only has this one duo, and that's all it takes -- not interesting

    whereas another puzzle is also solved with just one duo -- but this puzzle has 3 duos available, most of them are red herrings -- i'll probably be spending some time on a red herring, following its implications, trying to see how it solves the puzzle, until i concede it doesn't and move on to find the other duo which does solve it
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re: red herrings

Postby Pat » Tue Dec 18, 2007 3:39 pm

      here's an actual example --
        did you meet any red herrings, or did you get lucky ??
TTHsieh (2007.Dec.13) wrote:
Code: Select all
 . . . | . . . | . . .
 . . 1 | . 2 . | 3 . .
 . 4 5 | . 3 . | 6 1 .
-------+-------+------
 . . . | 2 . 6 | . . .
 . 7 6 | . . . | 5 8 .
 . . . | 7 . 1 | . . .
-------+-------+------
 . 5 9 | . 4 . | 2 3 .
 . . 3 | . 1 . | 8 . .
 . . . | . . . | . . .

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