# Feedback and Questions

I've received a lot of interesting comments and questions from Sudoku fans over the last few years and this page
is where I try to answer them. Please feel free to drop me a note on the side of the page or try the Facebook
comment box. Or you can email me directly at andrew@str8ts.com.
**Post a Comment or Question here...**

## Thursday 21-Aug-2014

## ... by: Didi, Austria

1) Solution path could imply 'try any strategy at this point' and see what can be eliminated. In actuality one wants to work through a list in order - some strategies just don’t make sense if easier strategies haven't cleared off the obvious eliminations. This is why after every successful tough elimination I always go back to the start of the list. So it's practical to limit the number of solution paths to those than follow a complexity order. However, I don’t pretend to assert that the order on my solver is the best order, just the one I've settled on as best for me. There is an element of subjectivity in that ordering, although the larger groupings (basic, tough etc) shouldn’t be controversial. So complexity order is one way to reduce the number of solution paths.

2) My grader has the notion of "opportunities to eliminate" which means that given the state of the board there may well be several places that the same strategy can eliminate candidates. This happens a lot with Pairs and Triples, for example. My rule is that the new state of the board shouldn't feed back into the algorithm and loop until exhausted. Even though a human with pencil and paper might want to exhaust the possibilities with a chain reaction of eliminations. I have this rule mainly for presentation reasons, in that it's not possible to show 'knock on' effects on the solver board and it would confuse people when they try and work out what the solver has done. Also, there is a logical reason - eliminations should be 'pattern based', ie based on the state of the board as it is, not what it may be after "in-loop" eliminations. If there are 5 "opportunities to eliminate", eg five Naked Pairs in a step, we should take them as a single step in the solution path. But if they lead to more Naked Pairs, the solver will stop and go back to Naked Singles and clear first.

3) "Solution Path" may imply "how many different strategies are that that will eliminate candidate X?" I think this is what most people mean when they ask the question. If we didn't know about, say "X-Wings" then a more complex strategy would probably do the same job. But I am coming round to the notion that this approach is a red herring. Does it matter which strategy gets X? Its like some light bulbs can be changed by one man, but some need two men - one to hold the ladder. Are they really different operations? Since my and most peoples solvers don’t contain every tool in the box or implement each strategy completely (very hard to prove) then we could accidentally balloon the count of solution paths artificially merely by being incomplete. This line of thinking means that the actual number of solution paths is constrained to be less than or equal the number of candidates on the board. Which is several hundred, but certainly not "millions" and most candidates are cleared off quickly.

The problem then becomes, what is the optimal solution path? What is the least number of operations required to solve it - allowing that each step can eliminate a slew of candidates in one loop. The answer to this question is exactly what the solver currently does. But the controversy becomes the order of the strategy list. Now, I have wondered, is my ordering optimal? Highly unlikely for all Sudoku puzzles. Probably for some. But impossible to know which. So what I need to do is take a bunch of puzzles and solve them using a tree/branch method that tries every possible order (leaving basic strategies at the start). This can't be done on a web page but could be done in my offline version. This is where I'm hoping to go next with my research and others, with solvers, would find it fun to explore this.

## Wednesday 20-Aug-2014

## ... by: Didi, Austria

Is that true? Do you know any artificial intelligence approaches to let computers detect known and unknown solving logics?

It would be great to have an AI developed, that could at least find the most basic solving techniques! I believe that without such basic AI real Androids will never ever exist. Sudoku could be a nice starting project.

I do believe there will be artificial intelligences that will be equal and superior to human minds but they will be evolved, not written, and they will exhibit the intuitive trait required to solve these types of problems. But if we asked them to explain how they did it, or dumped their "software" it would be as complex and useless to us as a physical brain dump.

However, there may well be some clever people out there who do work on algorithms that create algorithms. Some of these are tricks though, like slime moulds solving the Travelling Salesman problem.

## Tuesday 19-Aug-2014

## ... by: bruce, U.S. of A.

Bruce

## Tuesday 19-Aug-2014

## ... by: NiZhiyang, China

.5..1..6.4..2.3..8..........4.....5.6.......7.8.....9..........3..1.2..6.1..3..7.

See,this is harder than yours!

Do leave an email address next time!

## Thursday 14-Aug-2014

## ... by: john, us

## Wednesday 13-Aug-2014

## ... by: Larry Doe, Hyde Park, NY

Load Sudoku: CLICK TO LOADSolution count says 1 solution but it actually has two solutions.

## Wednesday 13-Aug-2014

## ... by: Claude, Europe

I cannot find your app in the store, correct ?

Thanks for your answer

Hopefully all apps will be back up either later today or next week if I have to wire money.

## Wednesday 13-Aug-2014

## ... by: Mina, X

## Sunday 10-Aug-2014

## ... by: Sundeep, India

Thanks to this wonderful site, I am learning more tricks.

One small modification I would suggest (as I made that mistake) - could you make the link in (See Strategy Overview documentation) below the solver open in new tab/window by default? Or some other workaround - my issue was that manual edits (possible numbers inside unfilled squares) disappeared when I accidentally clicked the link and came back to the page.

Cheers!

## Wednesday 6-Aug-2014

## ... by: 35436363, europe

Load Sudoku: CLICK TO LOADKakuro won't work in any of the other solvers...