## Can You Solve This Without Trial and Error?

For fans of Kakuro

### Re: Can You Solve This Without Trial and Error?

Mani wrote:No one has replied to my request, how to paste kakuro grids as Saul has done before in this trail.

Did you miss Saul's answer? http://forum.enjoysudoku.com/can-you-solve-this-without-trial-and-error-t30960-234.html

Mani wrote:I would add H31452, which I just solved, where again such T&E or simulation was called for.

This is very much easier than the previous ones. You must have missed some easy eliminations. All those I need are in-sector contradictions (whips[2]), except:

- an x-wing (the only whips[2] that lie on more than a single sector):
x-wing-in-horiz-sectors: n4{r2 r5}{c5 c7} ==> r4c7 ≠ 4, r4c5 ≠ 4, r3c7 ≠ 4, r3c5 ≠ 4

- a single bivalue-chain[5]:
biv-chain[5]: r3c5{n2 n3} - r3c4{n3 n2} - r4c4{n2 n1} - hr4c3{n25 n16} - r4c5{n5 n6} ==> vr0c5 ≠ 13459
denis_berthier
2010 Supporter

Posts: 1261
Joined: 19 June 2007
Location: Paris

### Re: Can You Solve This Without Trial and Error?

H62352 before TnE.docx
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

Denis,
Thanks for clarifying, sorry I missed Saul's post. Hope you are able to see my upload, to me it shows a file still embedded, which is fine but I wanted to see it inline, which I chose.
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

Mani wrote:Denis,
Hope you are able to see my upload, to me it shows a file still embedded, which is fine but I wanted to see it inline, which I chose.

That's because you uploaded a docx file, which the application is unable to display. If you want to insert an image, I suggest using a png file. When you use the snipping tool to capture a rectangle from the screen you have the option of saving the snip to a file, rather than pasting it to the clipboard. Choose this option, and save it as a png. Once you've posted your reply with the image attached, you can trash the file, if you like.

I'm not using Windows at present, so I can't give step-by-step instructions. I know there's a snipping tool in Windows 7 and 8, but I can't remember if it's present in earlier versions.

http://windows.microsoft.com/en-us/windows/snipping-tool-faq#1TC=windows-7
saul

Posts: 105
Joined: 01 February 2013
Location: Kansas City

### Re: Can You Solve This Without Trial and Error?

H62352 Position.png (136.87 KiB) Viewed 506 times

Thanks Saul, hope this works!
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

The pic I inserted is H62352 status before I started on a limited trial and error to reach the solution
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

Another nice puzzle, again ATK, was H24562 which forced a TnE to get to the answer
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

Mani wrote:Another nice puzzle, again ATK, was H24562 which forced a TnE to get to the answer

I thought I was on the point of solving it without trial and error, but when I got down to the end I realized I had made a mistake somewhere.
H24562.png (88.03 KiB) Viewed 491 times

I had a lot of difficulty with this puzzle. I started working at it when I read Mani's post, and have been attacking it from time to time, saving my work as I went along. I hadn't even gotten to the point where I could see how to attempt trial and error, when this morning I saw a hidden single that I'd overlooked. I then made lots of progress, but all for naught.

I'm not sure I'll have the heart to try again.
saul

Posts: 105
Joined: 01 February 2013
Location: Kansas City

### Re: Can You Solve This Without Trial and Error?

Saul,
Do you want me to share the answer?
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

Mani wrote:Saul,
Do you want me to share the answer?

No, thanks.
saul

Posts: 105
Joined: 01 February 2013
Location: Kansas City

### Re: Can You Solve This Without Trial and Error?

H33901 - liked soving this one too!
Mani

Posts: 33
Joined: 13 December 2013

### Re: Can You Solve This Without Trial and Error?

Mani wrote:H33901 - liked soving this one too!

I enjoyed this one, a bit easier than usual, although I had to use T&E near the end.
Authority

Posts: 11
Joined: 09 December 2013

### Re: Can You Solve This Without Trial and Error?

Well, I solved H24562 using trial and error, with the emphasis on error, but then I realized that it can be solved completely deductively, in hindsight. I had gotten to this point without T&E, which is about the point where I was stuck previously:
H24562-1.png (94.13 KiB) Viewed 307 times

(I think I probably accidentally erased a candidate, leading to an incorrect deduction.)

Anyway, I was stuck, so I decided to try T&E. I assumed r2c3 = 6, and after some time I got a contradiction:
H24562-2.png (91.93 KiB) Viewed 307 times

Now I knew that r2c3 = 3, but that hardly propagated at all, except to tell me r2c2 = 45. (I use this notation to mean that r2c2 is one of 4 and 5.) I tried T&E again, therefore assuming r2c2=5 and got a contradiction, after about as much work as I'd needed before. Now however, the fact that r2c2 = 4, propagated to all parts of the puzzle, but I got a contradiction at the very end. I tried again, being as careful as I could, and once again got a contradiction. I therefore decided that I must have made a mistake after assuming r2c2 = 5. (Of course, I might have made a mistake earlier, but you're always stuck with the assumption that what you've done so far is correct, in chain kind of logical reasoning.)

Under that view of the matter, T&E and just shown r2c2<>4 so r2c2=5. I plugged that in again, and this time I was able to complete the puzzle.

While working the puzzle so many times, I noticed that under every path, I got r4c6 = 1, and that this had many consequences. I thought that if I could deduce this directly, I might be able to solve the puzzle without T&E. Go back to the first puzzle above, and note that in the first segment in row 4, the unknown cells must collective be 136 or 235. Suppose first that r4c6 = 36. Then r4c2=1, r3c2 = 2, r6c2 = 4, r2c2 = 5, r7c2 = 6. But then r7c1 = 7, so we must have r8c1 = 6, r6c1 = 4, but this is a contradiction, since we already decided r6c2 = 4. Now we can erase the candidates 3 and 6 from r4c6.

Suppose then that r4c6 = 25. Then r4c3 = 3, r2c3 = 6, and r2c2 = 12. Then we have the same contradiction as before, because r6c2 = 4, r2c2 = 5, r7c2 = 6, and we again have n r7c1 = 7, r8c1 = 6, r6c1 = 4.

At this point, we known that r4c6 = 1, and it turns out to be straightforward to complete the puzzle.

This is all easier to visualize that it may seem when written out, though I did it over in my head several times to be sure I wasn't making a mistake. Of course, I wouldn't even have tried this but for my experience with T&E.

Denis, do you happen to have analyzed this one?
saul

Posts: 105
Joined: 01 February 2013
Location: Kansas City

### Re: Can You Solve This Without Trial and Error?

Authority wrote:
Mani wrote:H33901 - liked soving this one too!

I enjoyed this one, a bit easier than usual, although I had to use T&E near the end.

The forum is picking up a few new members, I glad to see. Happy to have you here, Authority. On my first attempt, I had to use T&E, but I went back and tried it again, and did it without T&E, or excessively long chains of deductions. I was stuck on a batch of cells about three quarters of the way down on the left, before I saw what to do. I can recreate it and post my reasoning, if you're interested.
saul

Posts: 105
Joined: 01 February 2013
Location: Kansas City

### Re: Can You Solve This Without Trial and Error?

saul wrote:
Authority wrote:
Mani wrote:H33901 - liked soving this one too!

I enjoyed this one, a bit easier than usual, although I had to use T&E near the end.

The forum is picking up a few new members, I glad to see. Happy to have you here, Authority. On my first attempt, I had to use T&E, but I went back and tried it again, and did it without T&E, or excessively long chains of deductions. I was stuck on a batch of cells about three quarters of the way down on the left, before I saw what to do. I can recreate it and post my reasoning, if you're interested.

You are a braver man than I; as soon as I finish a kakuro I never want to see it again! I was stuck briefly on the part you described, but what took the trial and error was the bottom two-thirds of the right side. I got a lot of the cells down to two candidates but could not find any more deductions. I'm sometimes mistake-prone with the candidates, which causes a lot of problems at times. That's probably what happened with this one.
Authority

Posts: 11
Joined: 09 December 2013

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