## Can all kakuro be solved with pure logic

For fans of Kakuro

### Can all kakuro be solved with pure logic

I have written a small software to solve kakuro puzzles by pure logic. However, there are some puzzles that cannot be solved by my solver. I can solve it using brute force. My question is : can all kakuro puzzles be solved with pure logic or we have to resort to trial and error method at some point ?

Thanks,
Surendra
surendra.jain

Posts: 27
Joined: 15 August 2015
Location: India

### Re: Can all kakuro be solved with pure logic

The answer depends on where you draw the line between pure logic and trial and error. That is not at all a well defined boundary. It is perfectly possible to define a purely logical procedure that that methodically tries every possibility. The more you look into the boundary between logic and guessing the more you will realize that there is a continuum of possibilities and no clear places to draw the line.

JasonLion
2017 Supporter

Posts: 640
Joined: 25 October 2007
Location: Silver Spring, MD, USA

### Re: Can all kakuro be solved with pure logic

My Kakuro solver program can solve the kakuro puzzles that are labelled "very hard" in this website : http://www.menneske.no/kakuro/7x7/eng/
But it cannot solve the kakuro puzzles that are labelled "super hard". I tried solving the super hard puzzles by hand and got stuck in the middle. I had to resort to trying different possible combinations without any apparent logic to solve it.
surendra.jain

Posts: 27
Joined: 15 August 2015
Location: India

### Re: Can all kakuro be solved with pure logic

JasonLion wrote: .... The more you look into the boundary between logic and guessing the more you will realize that there is a continuum of possibilities and no clear places to draw the line.

Amen.

For example, if you say that such-and-such a cell must be either a 1 or a 3, but it can't be a 3 because that would force a 6 somewhere else, and you already have a 6, is that trial and error? At the most elementary level, it probably would have to considered such.

Bill Smythe
Smythe Dakota

Posts: 546
Joined: 11 February 2006