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## Discussion...

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## ... by: online spelling check

I was disappointed to discover that I had to shot. in my viewpoint, the sudoku world persons shouldn't application bamboozles that want guessing. Beside the previous bill's say, this tests the perplex as presented has further than individual answer, further is thus nether-persistent. transfer essays

## ... by: spelling check online

I was disappointed to locate that I had to infer. in my advice, the sudoku universe persons shouldn't utility confounds that exact guessing. Beside the previous bulletin's commentary, this verifys the baffle as presented has additional than unit resolution, besides is thus nether-persistent.
spelling check online

## ... by: eighsse

895 327 416
417 856 392
326 914 578

769 431 825
158 269 743
234 578 961

682 745 139
573 192 684
941 683 257

I wrote a Sudoku-solving program. It solved this one in 1.44 seconds :D

## ... by: Ngalo

Be warned, the aoplicatipn known as Google Goggles has been deemed highly malicious by countless downloaders. The aoplicatipn hardly functions as it should, and as is evident by my own expeirence and tons of the comments, this aoplicatipn cannot be uninstalled. If anyone knows a way to remove an app that is acting this way please respond to this, and to all users, don't think that just because an app is made by google that its safe, it still amazes me that they put their name on this trash

## ... by: JC Van Hay

The puzzle is solved by AS solver after the following Chain[8] :

(8=5)J5-[5J8=5D8 AND 5G6=(5-9)G9=9G46-9H5=9A5-9A2=9F2]-9D8F7=(9-8)D7=8B7 => 8J5=8B7 :=> -8B5;

A short path afterwards :

AIC[5](-6B4), AIC[5](-7A4), Chain[12](-47A2), AIC[4](-3H5,-9G6).

## ... by: fariande

Using my algorithm discussed previously in this site.

Load the puzzle in the Solver and turn off all strategies other than the basic 1-6 under Show Candidates. Then proceed as far as possible in the Solver. The Solver fills in the correct cell values for cells A8, E2, E5, G1 and H7 before it gets stuck.

We start with cell G9 having candidate values 5 and 9. Inserting the candidate value 5 in G9 and proceeding with the Solver yields a contradiction. Inserting the value 9 in G9 and proceeding with the Solver yields an inconclusive result. Nevertheless, the correct value for cell G9 must be 9 since we know it is not 5. Moreover, inserting 9 for G9 and proceeding with the Solver until it gets stuck we see that cell C4 has only the candidate values 3 and 9.

Next we add cell C4 having candidate values 3 and 9 to the mix and search for a valid starting path of the form (G9, C4). The only possible 2-tuple starting paths for (G9, C4) are (9,3) and (9,9). Inserting (9,3) for (G9, C4) and proceeding with the Solver yields a contradiction. Inserting (9,9) for (G9, C4) yields an inconclusive result. Nevertheless, we know that (G9, C4) = (9,9) since it is not (9,3). Moreover, inserting (9,9) for (G9, C4) and proceeding with the Solver until it gets stuck we see that cell A4 has the two candidate values 2 and 3.

Next we add cell A4 having candidate values 2 and 3 to the mix and search for a valid starting path of the form (G9, C4, A4). The only possible 3-tuple starting paths for (G9, C4, A4) are (9,9,2) and (9,9,3). Inserting (9,9,3) for (G9, C4, A4) yields the solution and we are done.

This solution is a rather simple application of the algorithm and does not show its real power. In weeks to come I am sure that more difficult applications of the algorithm will surface.

There are exactly nine 1-cell solution paths. They are A5=2, B3=7, B8=9, D5=3, D8=2, E4=2, E8=4, E9=3 and F7=9.

## ... by: fariande

I'm back! Some long-time readers might remember me from the early days of this forum when I solved the first 13 Stuart puzzles with the algorithm I will explain in a moment.

When I started solving sudokus in 2006, the game was simple. You used the basic strategies 1-6 in Stuart's Solver and that usually got the sudoku solved. In the event these basic strategies failed, you resorted to random guessing or some variation of Ariande's Thread to complete the solution.

Many sudoku solvers objected to Ariadne's Thread, saying it involved guessing and backtracking. Thus began a holy quest to obtain enough strategies so that any sudoku could be solved without the "guessing" that Ariadne's Thread appeared to require. This holy quest continues today.

I am old school and have not bought into this quest. I prefer to keep it simple by using only the basic strategies 1-6 and, when needed , use the algorithm described below. The algorithm is equivalent to Ariadne's Thread but avoids backtracking, has a very good bookkeeping scheme and makes efficient use of Stuart's Solver. Here is the algorithm.

A Sudoku Algorithm
This algorithm will solve any sudoku having a unique solution using only Stuart's Solver and the basic strategies 1-6 under Show Candidates.

Load the puzzle in the Solver and turn off all strategies other than the basic 1-6 under Show Candidates. (Also, save the puzzle since you will be reloading the puzzle many times when using the algorithm.) Then proceed as far as possible in the Solver. If the Solver gives a solution then we are done. If the Solver gives an inconclusive result ( i.e., it exhausts strategies 1-6 and gets stuck) then proceed with the steps below until the Solver gives a solution.
Step 1:
Pick an empty cell that looks promising, call it Cell 1, and use the Solver to check each candidate in Cell 1. For each candidate one of three things will result. Either the candidate leads to a contradiction (i.e.,the Solver gives the "error on the board" warning), the candidate results in a solution, or the candidate leads to an inconclusive result. If one of the candidates gives a solution then we are done. Otherwise, discard all candidates that lead to a contradiction from further consideration and retain only the candidates that give an inconclusive result.
Step 2:
Now add another promising empty cell, call it Cell 2, to the mix and search for a valid starting path of the form (Cell 1, Cell 2) using only the inconclusive possibilities from Cell 1 and the candidates for Cell 2. Use the Solver to check each possible 2-tuple and label each as either a contradiction, inconclusive, or a solution. If one of the candidate 2-tuples gives a solution then we are done.
Step k, k greater than 2:
Assuming that Step (k-1) did not yield a solution, add another promising empty cell, call it Cell k, to the mix and search for a valid starting path of the form (Cell 1, Cell 2, … , Cell k) using only the inconclusive (k-1)-tuples for a valid starting path for (Cell 1, …,Cell (k-1)) and the candidates for Cell k. Use the Solver to check each possible k-tuple and label each as either a contradiction, inconclusive, or a solution. If one of the candidate k-tuples gives a solution then we are done. Otherwise, discard all k-tuples that are contradictions and retain only the inconclusive k-tuples as the candidates for a valid starting path for (Cell 1, Cell 2, …, Cell k).

Eventually at some step the process will terminate when we find a solution.

Concluding remarks: After obtaining a solution using the above algorithm, I use that solution to find all 1-cell solution paths. If there are no 1-cell solution paths, then I try to find some 2-cell solution paths. It is extremely rare to find a sudoku with neither a 1-cell or 2-cell solution path. For example, of the first 13 Stuart Unsolvables, only Puzzle #4 failed to have a 1-cell solution path, and it had a 2-cell solution path.

## Archive

Each week a new 'unsolvable' will be published and the previous will be accessible here from this archive section. If you like very tough puzzles, these are for you.
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