dailysudoku.com

[Marty R.]

This puzzle is rated "Evil" by the site I got it from, but I usually solve them; the rating sounds much harder than the actual puzzle is, since I solve the majority of them. But this one I have tried at least six times. Every time when it looks like I'm nearing the end, I'm backed into a corner with a duplicate number.

That normally means I've made some sort of mechanical error, and I usually solve it with one or two more tries. But six times is unreal! When a puzzle is too difficult for me, the usual scenario is that I make some degree of progress, then reach an impasse and can't solve another cell.

I probably shouldn't embarrass myself by asking, but have you ever seen a published puzzle that was incorrect? I know the odds are very low, but having to erase everything and restart six times is unprecedented for me in my short Sudoku career.

[David Bryant]

Hi, Marty!

There are some invalid puzzles floating around on the web. But this isn't one of them. It has a unique solution, and doesn't require anything tougher than finding a couple of triplets. dcb

[keith]

Marty,

The puzzle is valid, and does not require heroic efforts.

Here is the solution as given by Sudoku Susser:

* The puzzle seems to be in good shape. All solved squares are correct, and the remaining possibilities in the unsolved squares are accurate.
* R5C1 is the only square in row 5 that can be <4>.
* R7C4 is the only square in row 7 that can be <9>.
* R8C5 is the only square in row 8 that can be <1>.
* R9C9 is the only square in block 9 that can be <2>.
From this deduction, the following moves are immediately forced:
R3C9 must be <6>.
* R9C6 is the only square in row 9 that can be <5>.
* R6C9 is the only square in column 9 that can be <5>.
* R8C8 is the only square in column 8 that can be <5>.
From this deduction, the following moves are immediately forced:
R8C1 must be <3>.
* R4C8 is the only square in column 8 that can be <6>.
* Intersection of row 1 with block 2. The value <7> only appears in one or more of squares R1C4, R1C5 and R1C6 of row 1. These squares are the ones that intersect with block 2. Thus, the other (non-intersecting) squares of block 2 cannot contain this value.
R2C5 - removing <7> from <2479> leaving <249>.
R2C6 - removing <7> from <167> leaving <16>.
* Intersection of row 3 with block 3. The value <9> only appears in one or more of squares R3C7, R3C8 and R3C9 of row 3. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.
R1C8 - removing <9> from <1239> leaving <123>.
R2C7 - removing <9> from <13479> leaving <1347>.
R2C8 - removing <9> from <12349> leaving <1234>.
* Intersection of column 5 with block 5. The value <8> only appears in one or more of squares R4C5, R5C5 and R6C5 of column 5. These squares are the ones that intersect with block 5. Thus, the other (non-intersecting) squares of block 5 cannot contain this value.
R4C6 - removing <8> from <378> leaving <37>.
R6C4 - removing <8> from <2378> leaving <237>.
* Intersection of column 8 with block 3. The values <24> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain these values.
R2C7 - removing <4> from <1347> leaving <137>.
R3C7 - removing <4> from <149> leaving <19>.
* Intersection of block 9 with column 7. The values <346> only appears in one or more of squares R7C7, R8C7 and R9C7 of block 9. These squares are the ones that intersect with column 7. Thus, the other (non-intersecting) squares of column 7 cannot contain these values.
R2C7 - removing <3> from <137> leaving <17>.
R4C7 - removing <3> from <3789> leaving <789>.
R6C7 - removing <3> from <13789> leaving <1789>.
* A set of 3 squares form a comprehensive hidden triplet. R1C3, R1C6 and R1C8 each contain one or more of the possibilities <136>. No other squares in row 1 have those possibilities. Since the 3 squares are the only possible locations for 3 possible values, any additional possibilities these squares have (if any) can be eliminated. These squares now become a comprehensive naked triplet.
R1C3 - removing <2> from <1236> leaving <136>.
R1C6 - removing <7> from <167> leaving <16>.
R1C8 - removing <2> from <123> leaving <13>.
* R4C6 is the only square in column 6 that can be <7>.
* R7C6 is the only square in column 6 that can be <3>.
From this deduction, the following moves are immediately forced:
R7C7 must be <4>.
R8C7 must be <6>.
R9C7 must be <3>.
* R7C2 is the only square in row 7 that can be <8>.
From this deduction, the following moves are immediately forced:
R8C2 must be <7>.
R8C3 must be <4>.
R9C2 must be <6>.
R8C4 must be <8>.
* R3C6 is the only square in row 3 that can be <8>.
* R5C9 is the only square in row 5 that can be <7>.
From this deduction, the following moves are immediately forced:
R2C9 must be <3>.
R1C8 must be <1>.
R1C6 must be <6>.
R5C8 must be <3>.
R2C7 must be <7>.
R3C7 must be <9>.
R4C7 must be <8>.
R4C5 must be <2>.
R6C7 must be <1>.
R5C2 must be <1>.
R6C8 must be <9>.
R1C3 must be <3>.
R2C6 must be <1>.
R6C5 must be <8>.
R6C4 must be <3>.
R6C2 must be <2>.
R4C3 must be <5>.
R4C1 must be <9>.
R7C3 must be <2>.
R6C3 must be <7>.
R2C2 must be <9>.
R7C1 must be <5>.
R2C3 must be <6>.
R3C3 must be <1>.
R2C5 must be <4>.
R4C2 must be <3>.
R1C1 must be <2>.
R2C8 must be <2>.
R9C5 must be <7>.
R3C4 must be <2>.
R3C8 must be <4>.
R1C4 must be <7>.
R9C4 must be <4>.
R1C5 must be <9>.

Best wishes,

Keith

[Marty R.]

Thanks David and Keith. Deep down I really knew that the odds of this being an invalid puzzle were extremely low, but as I mentioned, having to erase and restart six times is pretty unusual for me. I guess I'll go for seven!!