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Retagged, minor clarification of problem, and typo corrected
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orthagonally Orthogonally connecting even sudoku digits avoiding squares

Is there a way to complete a sudoku where you have to make sure all even digits are orthagonallyorthogonally connected to all the others, while avoiding 2x2 squares of even digits? 

It is known to be possible without avoiding squares. Example withwhen 2x2 squares are permitted - see, for example, the following arrangement:

with squares

SoBut is it possible while avoiding 2x2 squares of even digits?

orthagonally connecting even sudoku digits avoiding squares

Is there a way to complete a sudoku where you have to make sure all even digits are orthagonally connected to all the others, while avoiding 2x2 squares of even digits? It is possible without avoiding squares. Example with squares:

with squares

So is it possible?

Orthogonally connecting even sudoku digits avoiding squares

Is there a way to complete a sudoku where you have to make sure all even digits are orthogonally connected to all the others, while avoiding 2x2 squares of even digits? 

It is known to be possible when 2x2 squares are permitted - see, for example, the following arrangement:

with squares

But is it possible while avoiding 2x2 squares of even digits?

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orthagonally connecting even sudoku digits avoiding squares

Is there a way to complete a sudoku where you have to make sure all even digits are orthagonally connected to all the others, while avoiding 2x2 squares of even digits? It is possible without avoiding squares. Example with squares:

with squares

So is it possible?