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A question on Pic-A-Pix solving techniques

 
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A question on Pic-A-Pix solving techniques - 7/19/2019 4:44:09 AM   
RobotArm

 

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I'm working on one of the black-and-white Pic-A-Pix puzzles from last week and I'm really quite stuck. I've made a good start, but I've been studying this for a while and can't see a next move. So I have a couple questions:

1. Some of the other puzzle types here sometimes require proof by contradiction to make any progress; If a square is either black or white, guess that it's black and if that leads to an impossible situation then you know it must be white. Then you can undo your moves back to where you made the guess, set the square to white, and continue. I hate using that method in the Pic-A-Pix puzzles, though. Does anyone know if some Pic-A-Pix puzzles require that method to solve, or is there always a deduction that can be reached just by looking at the puzzle in its current state?

2. Depending on the answer to question 1, if I'm still stuck, can I post the puzzle here and get a nudge in the right direction, or is that frowned upon?
Post #: 1
RE: A question on Pic-A-Pix solving techniques - 7/19/2019 8:42:52 AM   
dave

 

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The best way is to post here a scan/photo of the puzzle at the point in which you are stuck. I'm sure some of our fans will quickly suggest which next steps can be taken and why

Thanks, Dave

(in reply to RobotArm)
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RE: A question on Pic-A-Pix solving techniques - 7/19/2019 12:33:48 PM   
RobotArm

 

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Many thanks for any help. Hopefully I should just need the next move and can start making progress from that.




Attachment (1)

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RE: A question on Pic-A-Pix solving techniques - 7/21/2019 12:40:01 PM   
RobotArm

 

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It makes me feel a little better to think that everyone else is stumped, too.

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RE: A question on Pic-A-Pix solving techniques - 7/22/2019 5:44:01 AM   
CharleneTX

 

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I usually help with these, but I'm traveling at the moment and can't attempt to find a solution using my phone. I can look at it in August.

(in reply to RobotArm)
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RE: A question on Pic-A-Pix solving techniques - 7/22/2019 7:10:18 PM   
Ahlyis

 

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First, let me say that I am not the right person to ask about pic-a-pix puzzles. I love trying to help here when people ask, but pic-a-pix is not one of my strong points.

I just wanted to comment on something else you said in your first post.

quote:

ORIGINAL: RobotArm

1. Some of the other puzzle types here sometimes require proof by contradiction to make any progress; If a square is either black or white, guess that it's black and if that leads to an impossible situation then you know it must be white. Then you can undo your moves back to where you made the guess, set the square to white, and continue. I hate using that method in the Pic-A-Pix puzzles, though. Does anyone know if some Pic-A-Pix puzzles require that method to solve, or is there always a deduction that can be reached just by looking at the puzzle in its current state?


I understand that sentiment. I truly do. I had a friend (sadly no longer with us) who used to say the same thing to me. And I agreed with him at the time even though it bothered me. So eventually I stopped and thought about it some more. What was bothering me about that argument? Well, what bothered me is that it is completely arbitrary and essentially bogus.

EVERY puzzle requires that. Even the simplest pic-a-pix requires it at EVERY point!

Consider the puzzle you posted and the row that starts with 45. How do you know that the 45 starts in the very first column? Well, because if you mark that column empty then you no longer have room to fit everything. This clue was simple enough that you did not need to fill in blocks to "try" it. You could immediately see what would happen if you tried in your head, without needing markers to help. But the logic is EXACTLY the same.

Once I realized the underlying logic was the same thing, then I wondered why is one acceptable and the other not? Most puzzle solvers can immediately see in their head one or two placements. Things like, if I mark this square for the across clue, then the vertical clue will no longer work. The question then becomes, how many "moves" can you keep straight in your head before it gets too confusing to keep track of. And here, everyone is different.

As an example, suppose Bob can only keep track of about 3 moves while Tom is able to track 5 moves in his head. There is a point in the puzzle where you need to look 4 moves out. For Tom, this is "easy" and he makes the appropriate mark. But Bob cannot see the move unless he "takes a guess and marks it one way to test it", he then finds the contradicting result 4 moves out.

Why is it wrong for Bob to resort to making a mark as a visual aid? Tom did not need the visual aid, but Bob did. Should only Tom be considered to have "properly" solved the puzzle? Why?

Don't get me wrong. I hate not being able to find a spot within my mental tracking range too. I hate having to resort to the "try it and see" sort of thing... but it is EXACTLY the same thing you do for EVERY piece of the puzzle you solve. You make a mark (whether it is just black or white for pic-a-pix, or a number for a sudoku square) because you know that making any other mark in that spot will lead to a contradiction. It doesn't matter if the contradiction is immediate, or a few moves down... does it?

Just something to think about. ;)

(in reply to RobotArm)
Post #: 6
RE: A question on Pic-A-Pix solving techniques - 7/23/2019 3:43:50 AM   
RobotArm

 

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quote:

ORIGINAL: CharleneTX

I usually help with these, but I'm traveling at the moment and can't attempt to find a solution using my phone. I can look at it in August.
I didn't mean to call anyone out. This is my first time participating here and I wasn't sure how active this forum is or how long a reply might take. Any help will be appreciated, even in August.



quote:

ORIGINAL: Ahlyis

I understand that sentiment. I truly do. I had a friend (sadly no longer with us) who used to say the same thing to me. And I agreed with him at the time even though it bothered me. So eventually I stopped and thought about it some more. What was bothering me about that argument? Well, what bothered me is that it is completely arbitrary and essentially bogus.

EVERY puzzle requires that. Even the simplest pic-a-pix requires it at EVERY point!

Consider the puzzle you posted and the row that starts with 45. How do you know that the 45 starts in the very first column? Well, because if you mark that column empty then you no longer have room to fit everything. This clue was simple enough that you did not need to fill in blocks to "try" it. You could immediately see what would happen if you tried in your head, without needing markers to help. But the logic is EXACTLY the same.

Once I realized the underlying logic was the same thing, then I wondered why is one acceptable and the other not? Most puzzle solvers can immediately see in their head one or two placements. Things like, if I mark this square for the across clue, then the vertical clue will no longer work. The question then becomes, how many "moves" can you keep straight in your head before it gets too confusing to keep track of. And here, everyone is different.

As an example, suppose Bob can only keep track of about 3 moves while Tom is able to track 5 moves in his head. There is a point in the puzzle where you need to look 4 moves out. For Tom, this is "easy" and he makes the appropriate mark. But Bob cannot see the move unless he "takes a guess and marks it one way to test it", he then finds the contradicting result 4 moves out.

Why is it wrong for Bob to resort to making a mark as a visual aid? Tom did not need the visual aid, but Bob did. Should only Tom be considered to have "properly" solved the puzzle? Why?

Don't get me wrong. I hate not being able to find a spot within my mental tracking range too. I hate having to resort to the "try it and see" sort of thing... but it is EXACTLY the same thing you do for EVERY piece of the puzzle you solve. You make a mark (whether it is just black or white for pic-a-pix, or a number for a sudoku square) because you know that making any other mark in that spot will lead to a contradiction. It doesn't matter if the contradiction is immediate, or a few moves down... does it?

Just something to think about. ;)
I can see what you're getting at. All the puzzles involve some form of deduction, analysis, and prediction. The distinction I draw with Pic-A-Pix puzzles is that I like any row or column to provide some conclusive fact on its own. If a puzzle is 15 columns wide, and one row has a block of 10, I know that the middle 5 squares have to be colored in. Once I know that, I can look at each of those columns, in turn, and maybe draw some further conclusions about them. So far, that has worked for me. It can be quite difficult, but I've always been able to look at a row or column, draw some definite conclusion from it, and use that information to draw the next conclusion. I can't remember a time when I've had to guess a square, fill in that row, fill in some columns, check the adjacent rows, etc., and see if my guess was right.

I found a website once that would solve Sudoku puzzles, and you could step through the solution process and the site would show you which technique it was using to arrive at each conclusion. It used the same techniques I did, in roughly the same order of difficulty. But it went on to more levels of analysis that I'd never even thought of, with names like "unique rectangles", and "digit forcing chains". There are puzzles types here that make a distinction between whether basic or advanced techniques are required to solve them. Even when I know the advanced methods, I try not to use them when solving a basic puzzle. I've always suspected that this site has solving algorithms for each type of puzzle, to prove that they can be solved by known methods.

As I said, I've never done a Pic-A-Pix that I couldn't solve by examining one row or column at a time, and I've done quite a lot of them. That just makes me think that there's something in this puzzle that I'm not seeing. Or, if anyone knows that Proof by Contradiction (taking data from multiple rows and/or columns) can be required for some puzzles, I'd like to know that, too.

(in reply to Ahlyis)
Post #: 7
RE: A question on Pic-A-Pix solving techniques - 7/23/2019 5:09:34 AM   
GWW

 

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Here's a way forward. In row 5 continue your part-filled 31 block as far right as possible and then fill in the down blocks that follow. You will then see that in row 6 a block of 2 arises to the left of the 18 block, which is a contradiction.

(in reply to RobotArm)
Post #: 8
RE: A question on Pic-A-Pix solving techniques - 7/23/2019 3:11:46 PM   
RobotArm

 

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quote:

ORIGINAL: GWW

Here's a way forward. In row 5 continue your part-filled 31 block as far right as possible and then fill in the down blocks that follow. You will then see that in row 6 a block of 2 arises to the left of the 18 block, which is a contradiction.
I see what you're describing. Good eye, and many thanks.

I still wonder if that's necessary, though. I've never seen one of these puzzles that required taking information from multiple rows and columns to deduce the next move. Sometimes it wasn't easy, but I could always figure something out based on the clues in a single row or column, along with the squares whose state was already known.

For those who solve Pic-A-Pix puzzles, do you resort to the multiple rows approach often?

(in reply to GWW)
Post #: 9
RE: A question on Pic-A-Pix solving techniques - 7/23/2019 8:30:38 PM   
Ahlyis

 

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quote:

ORIGINAL: RobotArm

I've always suspected that this site has solving algorithms for each type of puzzle, to prove that they can be solved by known methods.


Hmm... I've always assumed that they built the puzzles using algorithms guaranteed to make the puzzle have a unique solution. Which algorithms they used to build the puzzle often dictating the difficulty level.

I do not know that they do that. It is just what I have always assumed was the case. And it is sort of the same thing you are saying, just from the other end.

quote:

ORIGINAL: RobotArm

For those who solve Pic-A-Pix puzzles, do you resort to the multiple rows approach often?


I use whatever logic I know of. Not just for the rare pic-a-pix that I do, but for any of the different puzzle types.

Cross-a-pix puzzles almost always involve that type of logic, sometimes to multiple layers, even for the easiest difficulties.

Fill-a-pix very often requires looking at chain reactions. Things like if I mark this square here, then it forces this to be empty, which then forces that over there to be filled which then makes too many filled for that number way over there. I do not consider that to be guessing. I consider that to be solid logic.

*shrug*

(in reply to RobotArm)
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RE: A question on Pic-A-Pix solving techniques - 7/26/2019 10:09:49 PM   
dave

 

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All our Pic-a-Pix puzzles can be solved by analyzing one row (or column) at a time. Although there are sometimes "edge techniques" which can be used in certain cases on the sides of the grid, these steps are "assistive only" and are not essential to finish a puzzle. This means there is some row-only (or column-only) technique hiding somewhere in the grid.

Thanks, Dave

(in reply to RobotArm)
Post #: 11
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