Sudoku puzzle with exactly 3 solutions While published sudoku puzzles typically have a unique solution, one can easily conceive of a sudoku puzzle with two solutions. However, is it possible to construct a sudoku puzzle with exactly 3 different solutions?
Inspired by https://puzzling.stackexchange.com/a/6.

You could use this as a model (this works for $4 \times 4$ but needs to be adapted for $9\times 9$):
$\begin{array}{cccc}
1 & 2 &   &   \\
3 & 4 & 1 & 2 \\
  & 1 &   &    \\
  & 3 &   & 1 \end{array} $
With solutions
$\begin{array}{cccc}
1 & 2 & 3  & 4  \\
3 & 4 & 1 & 2 \\
2/4 & 1 &  4/2 &  3  \\
 4/2 & 3 &  2/4 & 1 \end{array} $
and
$\begin{array}{cccc}
1 & 2 & 4  & 3  \\
3 & 4 & 1 & 2 \\
2  & 1 & 3  & 4   \\
4  & 3 &  2 & 1 \end{array} $
