2
$\begingroup$

Sudoku is played on a 9x9 grid where you place the digits 1 through 9 in individual grid cells.

The constraints are that every column must have all digits 1-9 and so must every row. On top of that, the 9x9 grid is broken up into a 3x3 grid of areas that each 3x3, which must also have all digits 1-9.

I'm wondering, if you add the requirement that ANY 3x3 section must contain all digits 1-9, is that solvable, or do the constraints make it impossible to arrange numbers to satisfy them?

$\endgroup$
2
$\begingroup$

That would be impossible:

Say you have a $1$ in the top left corner (row $1$, column $1$). Then given that it needs to occur in the box whose top left corner is $(2,1)$, and given that it cannot occur twice in the box whose top left corner is $(1,1)$, and finally given that it cannot occur in $(4,1)$ (for it cannot occur twice in column $1$), it will have to occur in either $(4,2)$ or $(4,3)$. Likewise, by considering row $1$ and the box whose top left corner is $(1,2)$ you need a $1$ in $(2,4)$ or $(3,4)$. Hence it is twice in the box whose top left corner is $(2,2)$.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ @AlanWolfe: you need to define what the requirement are for other sized grids. It seems obvious to me what the requirements are for a grid that is $n^2$ on a side, but $3 \times 3$ doesn't fit the pattern. For a $16 \times 16$ grid, I would expect it to be divided into $4 \times 4$ squares, each with the numbers $1$ through $16$. $\endgroup$ – Ross Millikan Dec 10 '17 at 3:41
  • $\begingroup$ Deleted after realizing the question was nonsense. Thanks! $\endgroup$ – Alan Wolfe Dec 10 '17 at 4:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.