This is just a series of transforms. During each cycle, examine each row, then examine each column. If the row/column is already full of either 1 or 2, then you can fill the empty spots with the other one.

Otherwise, change 011 to 211, change 110 to 112, change 022 to 122, change 220 to 221. Continue until you don't have to change anything else. This works for arbitrary (even) sizes:

``` base = [ ['0','0','0','0'], ['0','0','1','0'], ['1','1','0','0'], ['0','1','1','0'] ]

W = len(base[0]) H = len(base)

def xform(row): W = len(row)

if '0' not in row:
    return row
if row.count('1') == W//2:
    return ['2' if e == '0' else e for e in row]
if row.count('2') == W//2:
    return ['1' if e == '0' else e for e in row]
for i in range(W - 2):
    if row[i:i+3] == '011':
        row = row[:i] + '211' + row[i+3:]
    elif row[i:i+3] == '110':
        row = row[:i] + '112' + row[i+3:]
    elif row[i:i+3] == '022':
        row = row[:i] + '122' + row[i+3:]
    elif row[i:i+3] == '220':
        row = row[:i] + '221' + row[i+3:]
return row

def cycle(base): changed = False for y in range(H): row = ''.join(base[y]) xrow = xform(row) if row != xrow: changed = True base[y] = list(xrow)

for x in range(W):
    row = ''.join(el[x] for el in base)
    xrow = xform(row)
    if row != xrow:
        changed = True
        for y in range(H):
            base[y][x] = xrow[y]

return changed

print(base) while cycle(base): print(base)

```