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My university (Keio university in Japan) set this question in 2013's entrance exam. The red boxes include numbers from 1 to 9.

What's the solution for this sudoku?

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  • $\begingroup$ Please change the title as per my suggestion to "Overlapping-constraint 3x3;2x2 sudoku..." It's more explicit and clear. Otherwise it just sounds like yet another 3x3 sudoku question, which it isn't. The point is the 2x2 constraints overlap, but on a different grid. $\endgroup$
    – smci
    Jun 4, 2017 at 23:59
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    $\begingroup$ @smci why 2x2? There is no 2x2 constraint $\endgroup$
    – Kevin
    Jun 5, 2017 at 2:44
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    $\begingroup$ Counter-intuitively, the red boxes actually make it easier rather than harder $\endgroup$
    – Kevin
    Jun 5, 2017 at 2:45
  • $\begingroup$ @Kwvin: there is a 2x2 constraint; it's the red boxes; they are conceptually a separate 2x2 grid, (but partially overlapping with the 3x3 grid). That's why I said "Overlapping-constraint 3x3;2x2 sudoku..." $\endgroup$
    – smci
    Jun 5, 2017 at 3:20
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    $\begingroup$ @smci these are commonly known as windoku or hyper sudoku. $\endgroup$
    – paramesis
    Jun 5, 2017 at 22:36

1 Answer 1

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Final solution

Ta-da!

Step-by-step explanation

  • In the upper right red square, there's only one possible position for 7.
  • In the lower right red square, there's only one possible position for 5.
  • In the seventh row, there's only one possible position for 7.
  • In the eighth row, there's only one possible position for 6.
  • In the second row, there's only one possible position for 3.

first steps

  • In the eighth column, there's only one possible position for 3.
  • In the bottom middle 3x3 box, there's only one possible position for 3.
  • In the seventh row, there's only one possible position for 5, then only one for 4, then only 3 is left.
  • In the lower right red square, there's only one possible position for 2, then only 1 is left.
  • Now only 1 is left in the bottom right 3x3 box.

next steps

  • In the eighth row, there's only one possible position for 7, then only one for 8, then only 4 is left.
  • Now only 2 is left in the bottom left 3x3 box.
  • In the first column, there's only one possible position for 5, then only one for 1, then only 6 is left.
  • In the top left 3x3 box, there's only one possible position for 7.

filling in bottom and left

  • In the lower left red square, there's only one possible position for 6, then only 4 is left.
  • In the second column, there's only one possible position for 1, then only one for 2, then only 5 is left.
  • In the middle left 3x3 box, there's only one possible position for 3, then only 6 is left.
  • In the sixth row, there's only one possible position for 2, then only 8 is left.

getting there ...

  • In the ninth column, there's only one possible position for 7, then only 8 is left.
  • In the fifth row, there's only one possible position for 6.
  • In the seventh column, there's only one possible position for 1, then only 8 is left.
  • Now only 2 is left in the top right 3x3 box.

more and more

  • In the upper left red square, there's only one possible position for 8, then only one for 5, then only 4 is left.
  • Now only 4 is left in the third row.
  • In the upper right red square, there's only one possible position for 2, then only one for 1, then only 3 is left.
  • Now only 4 is left in the fourth row and in the eighth column.
  • Now only 1 is left in the fifth row, and only 7 in the second row.

Now we're basically done

And from there it's easy to get the final solution.

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