## I could use some advice on a kakuro

For fans of Kakuro

### I could use some advice on a kakuro

Hi everyone!
On April 4th 2015 i started a kakuro puzzle on a puzzle calendar i got as a present. Till today I have been trying to solve the kakuro with no success. The solution is on the backside but I dont get how to get to the solution.
I added two attachements: "Kakuro" shows the emty puzzle and "Kakuro 2" is how far I ve gotten till now.
I would love if someone could help me and give me a hint about how to proceed. Is this puzzle even solvable? I tried various Kakuro-Tools and they werent able to solve it correctly without giving them a lot more numbers (from the solution on the backside).

Attachments
Kakuro 2.png (6.13 KiB) Viewed 979 times
Kakuro.png (5.28 KiB) Viewed 979 times
Puzzlefan

Posts: 4
Joined: 05 March 2016

### Re: I could use some advice on a kakuro

I strongly suspect that this puzzle is invalid, i.e. that it has multiple solutions. This is typical of gadgets like "a puzzle calendar I got as a present".

If, indeed, the puzzle has multiple solutions, then you will never get anywhere, because nothing can be solved by logic alone. Of course, a puzzle with multiple solutions is a huge no-no in the kakuro / sudoku industry, but there is a lot of that sort of garbage floating around, even on some websites that ought to know better.

Also, I don't see how you got even as far as you got. I agree with your 1 and 6 in r7c3 and r8c3, but I don't see how you could conclude (at this early stage) that, at the top of column 8, the 8 goes above the 9 rather than the other way around. Also, at the bottom of that column, why does it have to be 7-6-5 rather than 9-8-1 or 8-7-3 or any of several others?

Incidentally, your notation is incorrect in several places. For example, "13\" and "9\" at the bottom of column 6 should be "\13" and "\9" respectively.

Maybe someone with a solving program (there used to be a bunch of such people on these forums) can test it for you, but it wouldn't surprise me at all if there were at least 100 solutions to this one.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: I could use some advice on a kakuro

The following are the specs I used:
Code: Select all
`  0\0  11\0  21\0   0\0   0\0  20\0   8\0  17\0   0\8    -     -   32\0  28\16   -     -     -    0\30   -     -     -     -     -     -     -    0\28   -     -     -     -     -   19\0   0\0  0\0   0\29   -     -     -     -     -   18\0  0\0  13\0  7\20    -     -     -     -     -    0\18   -     -     -     -    0\13   -     -    0\23   -     -     -    0\0   0\9    -     -  `

Assuming this is correct, the puzzle is hopelessly badly-formed, it has godknows how many solutions - I killed the solver after 1 million (about 4m 30s).

I give here the first one that I found:

KP0808_ForumProblem.jpg (48.3 KiB) Viewed 938 times

Mathimagics
2017 Supporter

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Joined: 27 May 2015
Location: Canberra

### Re: I could use some advice on a kakuro

Mathimagics: I'm curious. Are there any cells, other than the 1 and 6 at the bottom of column 2, that are uniquely determined? I'm willing to bet that the overwhelming majority of individual cells have multiple solutions.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: I could use some advice on a kakuro

No problem!

This shows problem state after setting up (ie. all forced moves + domain shaving) - you can see why there's so many valid combinations.
Attachments
KP0808_ForumProblem_InitialState.jpg (57.9 KiB) Viewed 930 times

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra

### Re: I could use some advice on a kakuro

Thank you! That picture would be hilarious if it weren't so pathetic.

Shame on you, whoever created this one.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: I could use some advice on a kakuro

Clearly some dodgy generation there!

Mathimagics
2017 Supporter

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Joined: 27 May 2015
Location: Canberra

### Re: I could use some advice on a kakuro

Thanks a lot for all your replies. It soothes me that the puzzle is unsolvable, because I ve been trying rly hard to solve it
Smythe Dakota wrote:Also, I don't see how you got even as far as you got. I agree with your 1 and 6 in r7c3 and r8c3, but I don't see how you could conclude (at this early stage) that, at the top of column 8, the 8 goes above the 9 rather than the other way around. Also, at the bottom of that column, why does it have to be 7-6-5 rather than 9-8-1 or 8-7-3 or any of several others?

I rechecked my solutions and I may have made a little mistake: the 1 and 6 in r7c3 and r8c3 are correct, I also was able to get to the solutions in r7c8, r7c9, r8c6,r8c7 and r8c8 through exclusion. However I have no idea how i got to the 8/9 in r8c2 and r8c3. It may have been the desperation that clouded my judgement

Anyways thanks a lot for your help, I appreciate it!
Puzzlefan

Posts: 4
Joined: 05 March 2016

### Re: I could use some advice on a kakuro

Also I now think this isnt even a "real kakuro". Because when I looked up some kakruos you suggested I found out that those have a different rule then my kakuro:

The difference is that in my kakuro numbers cant show up repeatedly in a row or column (instead of a word).

Maybe that was the reason why your solver wasnt able to solve it?
Puzzlefan

Posts: 4
Joined: 05 March 2016

### Re: I could use some advice on a kakuro

Well, with that additional restraint (no repeats within a row or column), certainly the number of solutions will be much smaller. Whether the number of solutions would be 1 (as it should be), or larger, remains unclear.

And, probably, no one has written a solver for that type of pseudo-Kakuro, so realistically, it might be a long time or an eternity before anybody jumps in with a proof, one way or the other.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: I could use some advice on a kakuro

I adapted my solver to enforce unique values in rows and cols and the number of solutions reduces to 9,797.

A couple of samples:

Code: Select all
`Solution #117..439327415879183...38657...417265139.67869..45........Solution #819162..358146253948196...75629...734155148.76869..27`

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra

### Re: I could use some advice on a kakuro

Mathimagics wrote:I adapted my solver to enforce unique values in rows and cols and the number of solutions reduces to 9,797.

A couple of samples:

Code: Select all
`Solution #117..439327415879183...38657...417265139.67869..45........Solution #819162..358146253948196...75629...734155148.76869..27`

well i guess that settles it then
Puzzlefan

Posts: 4
Joined: 05 March 2016

### Re: I could use some advice on a kakuro

That's a relief. Now I can still castigate the person(s) who created that puzzle.

Perhaps with a few more constraints (like every 8 must have a 9 immediately above or below it, and another 9 immediately to its left or its right, and vice versa) the number of solutions could be reduced to a few hundred.

Bill Smythe
Smythe Dakota

Posts: 564
Joined: 11 February 2006

### Re: I could use some advice on a kakuro

I think the publisher's dog ate the givens!

Mathimagics
2017 Supporter

Posts: 1762
Joined: 27 May 2015
Location: Canberra