Return to Answer

By modifying the connectivity rule, I was able to find many solutions.
This was to allow connectivity to wrap at the edges – a toroidal board.
Here is one of them.

The methodolgy was to write a C program:
Step 1: make a list of 122 blocks size 3x3 containing 4 'even' cells.
Step 2: permute those blocks to make a list of 103974 strips size 3x9.
Step 3: permute those strips to make a 9x9 grid.
Each step excluded perms with isolated cells or 2x2 blocks with the known neighbours, and impossible row or column counts of 'even' cells.
Step 4: check that all these 'even' cells connect.
Step 5: fill in the sudoku grid with odd and even numbers.
The first solution fell out in less than a minute.

The modified rule also applies to 2x2 blocks – there are none which connect via edges.

By modifying the connectivity rule, I was able to find many solutions.
This was to allow connectivity to wrap at the edges – a toroidal board.
Here is one of them.

The methodolgy was to write a C program:
Step 1: make a list of 118 blocks size 3x3 containing 4 'even' cells.
Step 2: permute those blocks to make a list of 103974 strips size 3x9.
Step 3: permute those strips to make a 9x9 grid.
Each step excluded perms with isolated cells or 2x2 blocks with the known neighbours, and impossible row or column counts of 'even' cells.
Step 4: check that all these 'even' cells connect.
Step 5: fill in the sudoku grid with odd and even numbers.
The first solution fell out in less than a minute.

The modified rule also applies to 2x2 blocks – there are none which connect via edges.

By modifying the connectivity rule, I was able to find many solutions.
This was to allow connectivity to wrap at the edges – a toroidal board.
Here is one of them.

The methodolgy was to write a C program:
Step 1: make a list of 122 blocks size 3x3 containing 4 'even' cells.
Step 2: permute those blocks to make a list of 103974 strips size 3x9.
Step 3: permute those strips to make a 9x9 grid.
Each step excluded perms with isolated cells or 2x2 blocks with the known neighbours, and impossible row or column counts of 'even' cells.
Step 4: check that all these 'even' cells connect.
Step 5: fill in the sudoku grid with odd and even numbers.
The first solution fell out in less than a minute.

The modified rule also applies to 2x2 blocks – there are none which connect via edges.

By modifying the connectivity rule, I was able to find many solutions.
This was to allow connectivity to wrap at the edges – a toroidal board.
Here is one of them.

The methodolgy was to write a C program:
Step 1: make a list of 122 blocks size 3x3 containing 4 'even' cells.
Step 2: permute those blocks to make a list of 103974 strips size 3x9.
Step 3: permute those strips to make a 9x9 grid.
Each step excluded perms with isolated cells or 2x2 blocks with the known neighbours, and impossible row or column counts of 'even' cells.
Step 4: check that all these 'even' cells connect.
Step 5: fill in the sudoku grid with odd and even numbers.
The first solution fell out in less than a minute.

The modified rule also applies to 2x2 blocks – there are none which connect via edges.

By modifying the connectivity rule, I was able to find many solutions.
This was to allow connectivity to wrap at the edges – a toroidal board.
Here is one of them.

The modified rule also applies to 2x2 blocks – there are none which connect via edges.

By modifying the connectivity rule, I was able to find many solutions.
This was to allow connectivity to wrap at the edges – a toroidal board.
Here is one of them.

The methodolgy was to write a C program:
Step 1: make a list of 122 blocks size 3x3 containing 4 'even' cells.
Step 2: permute those blocks to make a list of 103974 strips size 3x9.
Step 3: permute those strips to make a 9x9 grid.
Each step excluded perms with isolated cells or 2x2 blocks with the known neighbours, and impossible row or column counts of 'even' cells.
Step 4: check that all these 'even' cells connect.
Step 5: fill in the sudoku grid with odd and even numbers.
The first solution fell out in less than a minute.

The modified rule also applies to 2x2 blocks – there are none which connect via edges.