# Nested sudoku in entrance exam

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?

• 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.
– smci
Commented Jun 4, 2017 at 23:59
• @smci why 2x2? There is no 2x2 constraint Commented Jun 5, 2017 at 2:44
• Counter-intuitively, the red boxes actually make it easier rather than harder Commented Jun 5, 2017 at 2:45
• @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..."
– smci
Commented Jun 5, 2017 at 3:20
• @smci these are commonly known as windoku or hyper sudoku. Commented Jun 5, 2017 at 22:36

## 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.

• 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.

• 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.

• 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.

• 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.

• 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.

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