Okay, okay, so I'm not the world's greatest puzzle solver -- whether it's 2-3-4 or regular. I usually end up using guess-and-check in the more difficult regular puzzles, too.
Anyway, when I floated the idea of a 2-3-4 puzzle, I did so half-jokingly. But now that I've seen a few real examples, I find I enjoy them. Got any more?
Bill Smythe
2-3-4 Sudoku
28 posts
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by udosuk » Fri Jul 07, 2006 6:26 am
The 1st puzzle, as I queried, requires turbot fish to solve...
The 2nd puzzle is a little bit easier... Just a simple x-wing is enough... Here is the stage where you need the x-wing to crack it open:
The 3rd is the easiest of them all, only basic techniques (naked/hidden sets, locked candidates) are needed...
Here're the solution pics:
http://i6.tinypic.com/1z6fjg1.png
http://i6.tinypic.com/1z6fss1.png
http://i6.tinypic.com/1z6ft4g.png
The 2nd puzzle is a little bit easier... Just a simple x-wing is enough... Here is the stage where you need the x-wing to crack it open:
The 3rd is the easiest of them all, only basic techniques (naked/hidden sets, locked candidates) are needed...
Here're the solution pics:
http://i6.tinypic.com/1z6fjg1.png
http://i6.tinypic.com/1z6fss1.png
http://i6.tinypic.com/1z6ft4g.png
- udosuk
- Posts: 2698
- Joined: 17 July 2005
by Smythe Dakota » Tue Oct 03, 2006 5:59 am
Well, I solved it, with the help of just one T&E. My first guess led to a solution, so I am assuming the solution is unique and that I found THE solution.
Some solvers (of regular Sudokus) like to use uniqueness to rule out possibilities. For example, "r4c7 can't be a 5, because then there would be a dual solution involving 3's and 8's in r45c26."
Those who embrace such uniqueness techniques can REALLY have a field day here. For example, the digits in the top two corners of the upper-right box must be the same, because if they were different, they could be interchanged creating a second solution. Likewise, the three digits in the middle radius of the lower-right box must all be the same. From here it is a small step to conclude that all five of these digits must be 4's. Then the solution follows rather quickly, if we're allowed to take Pyrrhon's word for it that the solution is unique.
Somehow, however, this seems to short-circuit the intended solution path.
Bill Smythe
Some solvers (of regular Sudokus) like to use uniqueness to rule out possibilities. For example, "r4c7 can't be a 5, because then there would be a dual solution involving 3's and 8's in r45c26."
Those who embrace such uniqueness techniques can REALLY have a field day here. For example, the digits in the top two corners of the upper-right box must be the same, because if they were different, they could be interchanged creating a second solution. Likewise, the three digits in the middle radius of the lower-right box must all be the same. From here it is a small step to conclude that all five of these digits must be 4's. Then the solution follows rather quickly, if we're allowed to take Pyrrhon's word for it that the solution is unique.
Somehow, however, this seems to short-circuit the intended solution path.
Bill Smythe
- Smythe Dakota
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- Joined: 11 February 2006
by Smythe Dakota » Sun Oct 08, 2006 1:47 pm
I'm surprised nobody (including Pyrrhon) has yet jumped on this. (Did I discover a technique Pyrrhon didn't want me to discover?)
With this particular type of grid, the content of ANY two cells within the same outer box and on the same spoke ("spokes" and "tangents" are better terms here than rows and columns) can be interchanged without affecting the validity of the puzzle. Not surprisingly, in this puzzle, all but two of the 18 spokes start with at least two givens. The remaining two lend themselves to this most heavy-handed of uniqueness techniques.
Bill Smythe
With this particular type of grid, the content of ANY two cells within the same outer box and on the same spoke ("spokes" and "tangents" are better terms here than rows and columns) can be interchanged without affecting the validity of the puzzle. Not surprisingly, in this puzzle, all but two of the 18 spokes start with at least two givens. The remaining two lend themselves to this most heavy-handed of uniqueness techniques.
Bill Smythe
- Smythe Dakota
- Posts: 564
- Joined: 11 February 2006
by udosuk » Sun Oct 08, 2006 3:28 pm
Smythe Dakota wrote:I'm surprised nobody (including Pyrrhon) has yet jumped on this. (Did I discover a technique Pyrrhon didn't want me to discover?)
Perhaps this puzzle is a bit too easy for the need of this technique... After singles, you could reach this state, where a simple grouped x-wing would solve it (the green cells must contain two 3s, thus the red cells cannot contain 3s, hence the yellow cell must be 3)...
Of course, you can use a simple uniqueness reasoning alternatively: the 3 green cells in a row must all be 4s, etc... But serious users would only consider those types of techniques as a last resort when hopelessly stuck, and would prefer to establish uniqueness themselves rather than assuming them... And for a puzzle as easy as this (which I'm quite surprised when you said you need T&E to solve it
) these techniques wouldn't give us much shorter routes anyway...So no need to get excited... Just baby stuffs (as Carcul likes to put it)...
- udosuk
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by Pyrrhon » Sun Oct 08, 2006 5:16 pm
I'm agree with udosuk. Unfortunately it seems not to be possible with this nice grid to make a tough puzzle. So there is no need of uniqueness techniques. I've never thought about uniqueness techniques and so in no of my puzzles there are necessary. But may be if I would consider such kind of techniques a tougher puzzle with this grid would be possible. But I guess the contrary would be.
Uwe
Uwe
- Pyrrhon
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28 posts
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