Can You Solve This Without Trial and Error?

For fans of Kakuro

Re: Can You Solve This Without Trial and Error?

Postby kakuroatk » Thu Jan 23, 2014 2:18 am

30 minutes? I'm impressed. I'm intrigued that you could do it without T&E. Maybe I'll try it again.


Again, I use the keyboard arrow keys, copy/paste and it really allows me to focus on the logic rather than inputting values... of course I can use the mouse's number pad.. it just takes longer to input pencil marks and it would've taken longer than 30 minutes... however, using the mouse and number pad, if you enter for example 345 for a cell, you can then move to another cell and enter ? and it will simply repeat the 345... it is like an instant paste... or you can use "C" copy and "V" paste... easier to enter repeated pencil marks...

M73131 it is done using elimination. I look at the sums and determine which pencil mark can be removed... I get to a point where there are a lot of doubles and triples which is how a medium puzzle should be. Of course, like I said, M73131 may be a medium plus...

I didn't realize you could use caps lock to toggle the state. I use "P". In an app I wrote for KenKen, I didn't use a state. If you hold the shift key down when pressing a number key, it's an answer; otherwise, it's a candidate. I like that a lot.


Initially I set it up to use "P" which was difficult on the keyboard when working a puzzle ... so I found <Caps Lock> a lot easier to use so I set the toggle pencil mark to that as well... you can also toggle by clicking the pencil icon at the top or the pencil icon on the number pad... so technically there is 4 ways to toggle pencil mark in an attempt to make things super smooth when solving ... I did outline <Caps Lock> in my "Quick Help" link at the bottom of the screen

I use "A" and "D" a lot, too. I hadn't realized until just now that they work if you're positioned in one of the white cells. I had thought you had to be positioned on the clues. is this a recent enhancement, or have I just never tried it out before?


yes you can be on a white cell and use "A" and "D"... it has always been there... it simply refers to the sum that is associated with that cell by either moving left or up to its related sum... :)
kakuroatk
 
Posts: 10
Joined: 17 September 2013

Re: Can You Solve This Without Trial and Error?

Postby Mani » Thu Jan 23, 2014 7:17 am

Latest Modification ATK has added to their site is very interesting and useful. I often find it inconvenient to toggle to bold mode and enter digits into cells where a unique number has been discovered. Am happier without this distraction, to continue on in the pencil mode till I complete the sum. The new feature now allows you to press the + key and get all the pencil marks converted to bold digits. And, if the solution is right, to do the special music and multicolour dazzling. Really nice modification!

Am just publicising a feature just added for benefit of fellow Kakuro solvers.
Mani
 
Posts: 33
Joined: 13 December 2013

Re: Can You Solve This Without Trial and Error?

Postby denis_berthier » Thu Jan 23, 2014 7:19 am

In several posts of this thread, there are claims that a puzzle has been solved without T&E.
(Sometimes, this is written as w/o T&E/guessing, which reveals a confusion between T&E and guessing - although they are totally different concepts.)

In any case, as no one says what he means by T&E and no one says which rules (or kinds of reasoning) he uses instead, such claims are rather pointless. As a result, this thread is turning into an enumeration of puzzles with various personal evaluations of their difficulty but with no technical content.



Take the last puzzle discussed above (M73131) as an example (kakuroatk, there's nothing personal here):

kakuroatk wrote:M73131 it is done using elimination.

this contains no real information

kakuroatk wrote:I look at the sums and determine which pencil mark can be removed...

this contains no real information

kakuroatk wrote:I get to a point where there are a lot of doubles and triples

There are indeed pairs and triplets appearing in the resolution path, but this is very far from sufficient to solve the puzzle.
Some kinds of chain rules are necessary.
So, as long as you haven't explained which kind of eliminations you are doing apart from the pairs and triplets, you haven't said much about your solution.
denis_berthier
2010 Supporter
 
Posts: 1253
Joined: 19 June 2007
Location: Paris

Re: Can You Solve This Without Trial and Error?

Postby saul » Thu Jan 23, 2014 3:58 pm

denis_berthier wrote:
In any case, as no one says what he means by T&E and no one says which rules (or kinds of reasoning) he uses instead, such claims are rather pointless.


In my view, the definition of T&E is operational; you fill in a square, see what the consequences are, fill in other squares, or erase candidates, until you arrive at a contradiction; now you know the original assumption is wrong, assuming that you hadn't made any prior mistakes. When kakuroatk says he was able to do the puzzle without resorting to this, it conveys definite information to me about the difficulty of the puzzle, even though I might not be able to duplicate the feat because of my inferior memory, lower intelligence, or whatever.

I agree that it would be even more valuable if he could tell me exactly how he arrived at this solution, but this is a lot to ask. You've developed a descriptive language for the chain of inferences, but manually keeping a log of the solution would be beyond most people, I think. It would certainly be beyond me.

What I was planning to do, if I take up this puzzle again, and still find myself compelled to use T&E, is to post the point puzzle at that point, and ask for instructions on how to proceed.

The problem I have with a formal description of the kind you've posted from time to time, is that it's laborious and error-prone to follow it. If I make a mistake at some point, it invalidates all that follows.

Also, I'm not entirely sure that I understand what the starting point is. I know you've introduced variables in addition to the cell values, and I understood you to say that their domain is the set of all combinations that can satisfy a segment, but I don't know how you use these. Is it any more than saying that the cell at the intersection of two segments must have a value drawn from the intersection of the possible values of those segments?

To put it another way, if I trace through your solution using ATK, do the known cells, the pencil marks, the Across and Down clues, and the lists of possibilities that you get by clicking on the clues convey everything that is needed to follow the solution, or is there more? (We've said before that it would be nice if the lists were adjusted to take account of the answers already entered, but let's assume that this is done mentally.)

denis_berthier wrote:Some kinds of chain rules are necessary.

Please explain what you mean by "chain rules."

denis_berthier wrote:As a result, this thread is turning into an enumeration of puzzles with various personal evaluations of their difficulty but with no technical content.

What do you suggest? Should we spin off a separate thread? Personally,I certainly find the technical discussions to be of more lasting interest, but I also value having entertaining puzzles pointed out to me. I prefer having all the information in one place, but I'll go with whatever the group wants.
saul
 
Posts: 105
Joined: 01 February 2013
Location: Kansas City

Re: Can You Solve This Without Trial and Error?

Postby kakuroatk » Thu Jan 23, 2014 5:31 pm

In my view, the definition of T&E is operational; you fill in a square, see what the consequences are, fill in other squares, or erase candidates, until you arrive at a contradiction; now you know the original assumption is wrong, assuming that you hadn't made any prior mistakes.


I agree Saul ... that is exactly what I thought T&E is...

What I was planning to do, if I take up this puzzle again, and still find myself compelled to use T&E, is to post the point puzzle at that point, and ask for instructions on how to proceed.


If you plan on trying M73131 (or any other puzzle) and get stuck, post a screen shot of where you are at and I can try and explain the next step (and why it is the next step) ...

In general, I am not sure what everyone's strategy is but can do my best to assist...
kakuroatk
 
Posts: 10
Joined: 17 September 2013

Re: Can You Solve This Without Trial and Error?

Postby saul » Thu Jan 23, 2014 6:45 pm

Picking up the thread of my last post, here's the end of a puzzle from authority's site:
Selection_014.png
Selection_014.png (6.51 KiB) Viewed 429 times

Part of the top and bottom rows is cut off. The cells in that part have already been determined.

I'm going to refer to the two unsolved columns as columns 1 and 2. If I put a 1 in the first row of either column, then there will also be a 2 and 3 in that column, so if the 1 goes in column 1, I will need a 9 and a 5 to complete the column. If the 1 goes in column 2, I will need a 9 and a 4. In the latter case, then, I will have a 1 in row 1 and a 4 in row 5 of column 2, which means I'll have a 5 in column 1 in those two rows, so the 1 must go in column 1.

To reiterate my point of view on T&E, I can perhaps make all these inferences in my head; then it's not T&E. If I make these exact same inferences by writing on the diagram, then it is T&E.

Now, Denis, do you actually have a name for a chain of inferences like this? If so, what is it?

It has occurred to me that by "chain rule" you may be referring to the "chains" in your book, not a chain of inferences. But if this is so, wouldn't you be assuming that everyone uses your model of kakuro?

I must be missing something.
saul
 
Posts: 105
Joined: 01 February 2013
Location: Kansas City

Re: Can You Solve This Without Trial and Error?

Postby saul » Thu Jan 23, 2014 6:49 pm

Mani wrote:The new feature now allows you to press the + key and get all the pencil marks converted to bold digits ... Really nice modification!

I really like this, too. I press the + sign intermittently, as I go along. On my system, though, if I press the + sign on the numeric keypad, it doesn't work. I have to use the shift key and the = sign.
saul
 
Posts: 105
Joined: 01 February 2013
Location: Kansas City

Re: Can You Solve This Without Trial and Error?

Postby Authority » Thu Jan 23, 2014 7:41 pm

saul wrote:Picking up the thread of my last post, here's the end of a puzzle from authority's site:
Selection_014.png

Part of the top and bottom rows is cut off. The cells in that part have already been determined.

The medium-difficulty puzzles on my site should not need guessing, and it took me a while to figure out the logical deduction here. The difficulty here comes from the possible combos of the left column. There are only two: 12359 and 13457. The other combos have either a 6 or 8, which are not present as candidates in any of the cell. Both remaining combos have the number 3 in them, and only a single cell has that as a candidate, so that cell must be a 3. Which causes the rest of the puzzle to fall into place.
Authority
 
Posts: 11
Joined: 09 December 2013

Re: Can You Solve This Without Trial and Error?

Postby kakuroatk » Thu Jan 23, 2014 8:12 pm

To reiterate my point of view on T&E, I can perhaps make all these inferences in my head; then it's not T&E. If I make these exact same inferences by writing on the diagram, then it is T&E.


yes, lets take a simple example lets say you have 3 cells in a row: 12 12 123 ... now for the 123 you can randomly choose a value like 2 and see if you run into a dead end which you would because of the 12 and 12... Or you logically deduce that since you have doubles 12 and 12 that the only possible value for the 123 candidate is 3 using ... that is using logic instead of T&E.

If you "save game"... try a scenario, find out it doesn't work then "restore game" to go back to a certain point in time then that is T&E/guessing.

30 minutes? I'm impressed. I'm intrigued that you could do it without T&E. Maybe I'll try it again.


when I play a hard level it can take hours or even days with breaks rather than 30 - 45 minutes for a medium...
:roll:
kakuroatk
 
Posts: 10
Joined: 17 September 2013

Re: Can You Solve This Without Trial and Error?

Postby denis_berthier » Thu Jan 23, 2014 10:15 pm

saul wrote: I know you've introduced variables in addition to the cell values, and I understood you to say that their domain is the set of all combinations that can satisfy a segment, but I don't know how you use these. Is it any more than saying that the cell at the intersection of two segments must have a value drawn from the intersection of the possible values of those segments?

Of course, it's much more. They participate in all the chain rules.

denis_berthier wrote:Some kinds of chain rules are necessary.
saul wrote:Please explain what you mean by "chain rules."

bivalue-chains, whips, braids, ... See my book for details.


saul wrote:
denis_berthier wrote:As a result, this thread is turning into an enumeration of puzzles with various personal evaluations of their difficulty but with no technical content.

What do you suggest? Should we spin off a separate thread? Personally,I certainly find the technical discussions to be of more lasting interest, but I also value having entertaining puzzles pointed out to me. I prefer having all the information in one place, but I'll go with whatever the group wants.

I agree it's interesting to have puzzles pointed out.
What I suggest is, more information is also given on how one solved a puzzle.
Last edited by denis_berthier on Thu Jan 23, 2014 11:27 pm, edited 1 time in total.
denis_berthier
2010 Supporter
 
Posts: 1253
Joined: 19 June 2007
Location: Paris

Re: Can You Solve This Without Trial and Error?

Postby denis_berthier » Thu Jan 23, 2014 10:45 pm

saul wrote:If I put a 1 in the first row of either column, then there will also be a 2 and 3 in that column, so if the 1 goes in column 1, I will need a 9 and a 5 to complete the column.

This is where you refer to the possible combinations in this column, i.e. you are implicitly using "my" additional hrc and vrc CSP variables. As I wrote before, considering combinations is a very standard idea.

saul wrote:To reiterate my point of view on T&E, I can perhaps make all these inferences in my head; then it's not T&E. If I make these exact same inferences by writing on the diagram, then it is T&E.

But then, your definition of T&E depends on your memory, your concentration, how much coffee or beer you've drunk...

saul wrote:Now, Denis, do you actually have a name for a chain of inferences like this? If so, what is it?

I could probably write it as a whip or braid, but I need to know the combinations remaining in the rows and columns.
Notice however that this puzzle is in W3 and it therefore requires only much simpler chains than above.

saul wrote:It has occurred to me that by "chain rule" you may be referring to the "chains" in your book, not a chain of inferences.

Chains in my book are chain patterns, physically visible on the grid; they allow conclusions to be drawn but they are not chains of inferences in the usual sense.
In your above description, your "chains of inference" occur within the context of a hypothesis ("If I put a 1 in the first row of either column"...), which is the usual definition of T&E.

saul wrote:But if this is so, wouldn't you be assuming that everyone uses your model of kakuro?

You are already using combinations.
It's up to you do define more kinds of chain patterns. What I said is only, if you want to avoid T&E, the puzzles discussed in this thread can't be solved without using chains (e.g. using only pairs, triplets, ...).
denis_berthier
2010 Supporter
 
Posts: 1253
Joined: 19 June 2007
Location: Paris

Re: Can You Solve This Without Trial and Error?

Postby denis_berthier » Thu Jan 23, 2014 10:50 pm

kakuroatk wrote:If you "save game"... try a scenario, find out it doesn't work then "restore game" to go back to a certain point in time then that is T&E/guessing.

Assuming that "try a scenario" means "try a candidate":
- it is T&E if "doesn't work" means "leads to a contradiction" and you delete the candidate you have tried;
-it is guessing if it leads to a solution and you accept it.

I think it's very confusing to write T&E/guessing.
denis_berthier
2010 Supporter
 
Posts: 1253
Joined: 19 June 2007
Location: Paris

Re: Can You Solve This Without Trial and Error?

Postby denis_berthier » Fri Jan 24, 2014 1:01 am

saul wrote:The problem I have with a formal description of the kind you've posted from time to time, is that it's laborious and error-prone to follow it. If I make a mistake at some point, it invalidates all that follows.

That's not due to my description itself. I think this is a general problem with Kakuro (and it gets worse and worse as grid size increases): it requires lots of eliminations, most of which are obvious or almost obvious, after you've gained some familiarity with the game. Many logic puzzles are plagued with the same problem.

If you consider that individual eliminations that rely on the situation in only one sector (including the combinations for this sector) are obvious (which, I think, is now your case) and if you don't write them explicitly, resolutions paths can be quite short. For example, for the above M73131, one gets:

Code: Select all
x-wing-in-horiz-sectors: n7{r8 r10}{c4 c6} ==> r6c6 ≠ 7, r5c6 ≠ 7
biv-chain[3]: r4n7{c7 c8} - r2n7{c8 c5} - r2n5{c5 c7} ==> vr0c7 ≠ 2368
whip[3]: c6n1{r8 r9} - r9n4{c6 c4} - vr6c4{n1357 .} ==> r8c4 ≠ 1
whip[3]: r7c4{n2 n1} - vr6c4{n2347 n1267} - r9c4{n3 .} ==> r8c4 ≠ 2
naked-pairs-in-verti-sector: c2{r4 r6}{n8 n9} ==> r3c2 ≠ 8

(I kept the naked-pairs, although they can also be considered as whips[2], because they are somewhat exceptional cases of whips.
I kept the x-wings, although they can also be considered as whips[2], because they rely on several sectors - and they are also exceptional).

As you can see in the second line, "my" chains can also be used to eliminate combinations.

How to use this abstract of the full resolution path? For each line, see which of the candidates remaining on your grid (including the candidate-combinations) should be eliminated to make the pattern valid and try to eliminate them using only one sector at a time. Knowing that these intermediate eliminations don't rely on possible interactions between different sectors (but they may require other eliminations of the same kind) should make them quite obvious.

Of course, this is not the only possible resolution path. Depending on how you start, you can find different paths. But, what my CSP-Rules software guarantees is, you can't find a path with only shorter whips, braids or smaller subsets.
denis_berthier
2010 Supporter
 
Posts: 1253
Joined: 19 June 2007
Location: Paris

Re: Can You Solve This Without Trial and Error?

Postby saul » Fri Jan 24, 2014 1:38 pm

saul wrote:
Mani wrote:The new feature now allows you to press the + key and get all the pencil marks converted to bold digits ... Really nice modification!

I really like this, too. I press the + sign intermittently, as I go along. On my system, though, if I press the + sign on the numeric keypad, it doesn't work. I have to use the shift key and the = sign.


Withdrawn. I rebooted, and now the numeric + works fine.
saul
 
Posts: 105
Joined: 01 February 2013
Location: Kansas City

Re: Can You Solve This Without Trial and Error?

Postby Mani » Sun Jan 26, 2014 7:02 am

All too silent here.

H81402 was a nice sum, with a forced T&E being necessary. Luckily, my first assumption landed me the answer.
Mani
 
Posts: 33
Joined: 13 December 2013

PreviousNext

Return to Kakuro