The difficult Sudoku in last Friday's Metro looked like this:
I completed it as far as I could as follows (my entries are the underlined numbers). The four missing numbers are two 1's and two 9's but there appear to be two different ways of placing them. Is this accident or design? Is one answer right and another one wrong?
Every little irritant helps
3 hours ago
16 comments:
Sixth column has two 2's in it.
I've always been mildly curious about these puzzles (not curious enough to learn how to do them, but mildly curious) and I always wondered how one could prove that the solution to a puzzle offered is unique and what conditions the puzzle has to satisfy to make it so.
I think we need to speak to someone with a rather higher level of mathematical sophistication than I have.
Its a mind game and I am out of it.
And the fifth column has two 6s.
Is it a joke of some kind? Because I'm not getting it.
I don't know if it is mathematically possible for a Sudoku to have more than one solution, but if your solution meets the rules then it is right. No solution is any "righter" than another.
But there are still two 2's in column six, so your original question is moot.
"your original question is moot": only in the American sense. In the British sense it's the very opposite of "moot".
And why is the Word Verification "boati"?
I think I've messed up badly here. Apologies.
In some grids it is possible to have several correct solutions Mark - contrast this with huge permutations of incorrect ones.
For Suduku to have a solution there has to be at least one of every symbol at the start.
Bottom 3 lines:
875396214
391284657
624571398
Anon, I don't think that works either - we'd have two 9's in the fifth column.
It is your day for another blush, Mark. Look at the full grid:
759412836
468953172
213768549
986137425
532649781
147825963
875396214
391284657
624571398
Thanks MTG, rub it in, why don't you?
ACO - no it doesn't !
consider the case where every number is completed with the exception of all the nines - it would be trivial to complete it
there are feasible Sudokus regularly published that start without any instances of one number
it's matrix algebra with one more degree of freedom than you think
but you do at least need 8 out of 9 to be represented at the start in order for their to be an unique solution
Mark - notwithstanding you cocked up this particular solution (& I admire you for leaving the post up!) your general question is fair, and the answer is: there are often non-unique solutions, along the lines that (if it had been correct) your initial case demonstrated
(i.e. a potential switch-around within two pairings, either of which represent a solution)
Sudoku addicts experience most errors on easy grids, Mark. I echo admiration for leaving the post up.
ND, MTG, I think the only thing I can salvage from this is my humility :)
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