I would really appreciate some help because I spent more than hours finding another number. It is supposed to be a very hard one but I started well and according to the key, my numbers are correct. Do not mind the grey box, I used some online tool to re-create the puzzle. Thanks in advance
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4 Answers
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For a logically complete version of Jens's answer (showing that the solution is unique as well as that it exists), try
putting a 9 in the top left corner of the bottom right 3x3 box.
That leads to
which is impossible. So, by contradiction, that cell must be
2, and the complete Sudoku follows.
answered Jan 3, 2020 at 16:32
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In the lower right 3x3 square, try putting a
2 in the top left corner. The rest falls into place.
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2$\begingroup$ Thanks but how did you know? Should this not be always deterministic somehow?? $\endgroup$– John VJan 3, 2020 at 15:51
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$\begingroup$ Sometimes you need to guess. In this case it was either 2 or 9. My first try worked. $\endgroup$– JensJan 3, 2020 at 15:55
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$\begingroup$ In the bottom squares, the unknown numbers are 29 in both the middle square and the right hand square. In the second row from the top, the unknown numbers are 79 in the same columns as the 29s at the bottom. Therefore you know that guessing a 2 or a 9 in the bottom squares is going to fix the values of 6 squares and eliminate a lot of possibilities elsewhere. So try it and see what happens! $\endgroup$ Jan 4, 2020 at 0:06
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placing a 2 in the top right 3x3 square, in its top left corner, will lead to a contradiction of two 2's in the same column (the one you placed, and another in the bottom right 3x3 box)
thus
the only number that can go in that specific tile is a 5
the solution then becomes
912|867|534 543|219|678 678|435|921 ---+---+--- 456|723|189 781|954|362 329|186|457 ---+---+--- 867|591|243 295|348|716 134|672|895
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$\begingroup$ Sorry I do not follow - there are no 2s so far. I could place the other two (in the bottom square) to the bottom middle box. $\endgroup$– John VJan 3, 2020 at 18:13
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Look at the middle three squares. The unknown numbers are
. . . | 17 23 237 | 13 . .
37 . 12 | . . . | 13 . 27
37 12 . | 178 238 . | . . 27
If you guess any single number in the middle row, that fixes almost everything else in these squares: either
. . . | 1 2 7 | 3 . .
3 . 2 | . . . | 1 . 7
7 1 . | 8 3 . | . . 2
or
. . . | 7 23 23 | 1 . .
7 . 1 | . . . | 3 . 2
3 2 . | 1 8 . | . . 7
and it soon becomes clear which option solves the whole puzzle.
