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Small, but hard puzzles
vidar
Kwon-Tom Fan
Puzzles: 50
Best Total: 56m 22s
Posted - 2009.02.06 13:48:57
Hi all. I'm relatively new to this highly addictive puzzle form, but certainly not to puzzles in general.

In the sudoku world there is a "saying" that claims that as long as the puzzle has one single solution, there should be a logical path of deductions that solve it, without use of the infamous trial and error.

I wonder, does the same hold true for Loops? I've made a number of puzzles, all quite small, that I've verified only has one solution, but darned if I can crack them logically.

Here are two samples:





Any takers?
MondSemmel
Kwon-Tom Obsessive
Puzzles: 3890
Best Total: 7m 47s
Posted - 2009.02.06 14:07:22
Welcome to this site!
You'll probably learn a few more tricks and deductions as you solve more puzzles, but I'll help you with the two you posted now (using only logic):

First puzzle:

1)


leads to 2)


leads to 3)


leads to 4)


leads to the solution


Second puzzle:

1)


leads to 2)



leads to 3)



leads to 4)



leads to 5)



leads to 6)


leads to 7)


leads to the solution


(Actually, I'm experienced enough with Slither Link that I do all that instantly, but I figured it would be more helpful for you if I tried to do it step by step. If you have questions, you can refer to specific steps and I'll try to explain them to you .

EDIT: And yes, with a few exceptions (where trial & error is simply a lot faster than pure logic, although it would be possible even there) all the puzzles on this site can be used by logic alone.
I personally try to solve these puzzles as fast as I can, so that usually means pure logic except for when I'm stuck for more than a few seconds.
Last edited by MondSemmel - 2009.02.06 14:12:49
vidar
Kwon-Tom Fan
Puzzles: 50
Best Total: 56m 22s
Posted - 2009.02.06 15:04:59
Hi, thanks for your quick reply.

I have jotted down a number of patterns that I'm hoping to get more experienced with, including a lot of interesting ones based on coloring (or shading, as it seems to be called around these parts ).

Typical! As soon as I give the first puzzle a second look I spot the solution... (The three cells in the middle must be inside the loop, or they would cut off the lower right corner from the rest. I assume this is your step 4.) Oh well.

As for the second one, I'm not sure I see how you got from 3 to 4 - the lines over and under the 3. Care to elaborate?

And a bonus puzzle:
Para
Kwon-Tom Obsessive
Puzzles: 1911
Best Total: 19m 28s
Posted - 2009.02.06 17:49:12
I get 3 -> 4. It's about seeing inner loops. I would have done it a bit differently. Wouldn't have instantly seen the bottom line.

Puzzle 2

1) Standard lines:


2) Standard crosses:


3) Pattern: 3-1 in corner diagonally:


4) Standard crosses:


5) Line on the diagonal through 2:


6) Cross on 2:


7) Final step, cross + line:


Solution:


Bonus puzzle is harder. This is the best I can do logically. Maybe there's some patterns I am not aware of or some shading techniques I am no good at.

Bonus Puzzle

1) Standard lines:


2) The next step is a bit visualising. There's 4 ways to draw a 3 in the bottom right corner. Opening up: 2 lines up or 1 line up and left; Opening left: 2 lines left or 1 line up and left. You can't go 2 lines up from the 3 in the right bottom corner as it would create an inner loop. You also can't go 2 lines left as that would create an inner loop. So one line from the three goes up and one goes left. This give you the following cross, because now you always make an L around the 2 in R3C4.


3) Standard lines:


4) Standard cross:


5) Line on the diagonal through 2 2's:


6) Standard lines:


7) Last step: Line blocked as this would create an inner loop with the 3:


Solution unfolds now:

Last edited by Para - 2009.02.06 18:25:52
Nis
Kwon-Tom Obsessive
Puzzles: 1989
Best Total: 22m 1s
Posted - 2009.02.07 10:42:13
"Trial and error" is also deduction. It is also known as "reductio ad absurdum".

The only difference is whether you put your intermediate calculations down, or keep them in your head.

Nis
Tilps
Kwon-Tom Obsessive
Puzzles: 4230
Best Total: 20m 22s
Posted - 2009.02.09 11:32:14
I've written solving engines for both sudoku and loop-de-loop.  I've spent quite a bit more time on my loop-de-loop engine then I ever did on the sudoku one, but I make the following observation.

With all of the basic rule/coloring/counting/loop closing logic I've managed to put into my iterrative loop-de-loop solver, the recursive solver regually finds puzzles which the iterrative solver cannot solve with single trials.

My sudoku solver on the other hand, has fairly simple logic (simple doesn't mean easy for a human to see sometimes, but simple all the same) - but only about 1 in a million puzzles cannot be solved with single trial.

(Single trial is where you guess at one thing, and if it fails you assume the opposite - if it does not you try the opposite and if it fails you take the first.  If neither fails, you take whatever common changes.  When I was doing sudoku - I found that most advanced logic was an example of single trial with basic logic - but single trial is a bit stronger in practice.)
ferkel
Kwon-Tom Obsessive
Puzzles: 536
Best Total: 39m 18s
Posted - 2009.02.12 22:23:13
vidar - your user puzzle #371 is amazing! It's really hard. Nice work.

I don't know the answer to your question. I think slitherlink is a really interesting case where the human brain is able to internalise more and more rules with experience - look at the amazing speed of some of the solvers here. So certainly they can solve them without trial and error.

(What MondSemmel and Nis said, basically.

By contrast, the same can't be said about soduku, as far as I know. Are there speed solvers of soduku puzzles? Is there anyone that can do them in just a few seconds?
vidar
Kwon-Tom Fan
Puzzles: 50
Best Total: 56m 22s
Posted - 2009.02.12 23:50:14
Glad you like it, ferkel. (And there's a hidden message in the solution.

I'll try to provide some more interesting, small toughies soon.

I see your points regarding trial and error. I guess for me the difference boils down to simply giving up and just trying something random versus making a sound, logical deduction or at least a very educated guess.

I haven't put much effort into improving my speed yet, but I'm noticing that I keep getting faster nonetheless. (Nowhere near what some of you guys manage, though. Very impressive!)
vidar
Kwon-Tom Fan
Puzzles: 50
Best Total: 56m 22s
Posted - 2009.02.13 08:35:28
OK, here's a nice one:

Edit: Completely broken puzzle removed.
Last edited by vidar - 2009.02.13 12:19:29
MondSemmel
Kwon-Tom Obsessive
Puzzles: 3890
Best Total: 7m 47s
Posted - 2009.02.13 11:15:32
Quote:
Originally Posted by vidar
OK, here's a nice one:

Sorry, but that puzzle isn't unique (by a long shot).
vidar
Kwon-Tom Fan
Puzzles: 50
Best Total: 56m 22s
Posted - 2009.02.13 12:21:11
Argh, you're right, of course. Sorry about that. 561 solutions. I wonder how that happened...

Anyway, here's an equally sparse one:

Last edited by vidar - 2009.02.13 12:24:21
ttsoftt
Kwon-Tom Obsessive
Puzzles: 1642
Best Total: 26m 52s
Posted - 2009.02.18 13:38:32
One "field shortcut" to Bonus Puzzle, step 1->6 directly!
Let I(x) be boolean function "field "x" is inside loop";
1) I(A3).ne.I(B4); I(B4).ne.I(C3); I(B2).ne.I(C3) =>
I(A3).eq.I(C3).ne.I(B2).eq.I(B4)
2) I(C3).or.(IC4) (due to "?3?3" in row 4 - no separate loop)
=>3)I(C3)!!, due I(C3)=>I(C4) & separate loop in col 4!
=> I(A3).and.I(B2)'.and.I(B4), as shown in fig 6.
Last edited by ttsoftt - 2009.02.18 13:40:40

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