Re^3: decomposing binary matrices

[BrowserUk]

Hm. Sorry to have wasted your time. I'd picked up on this bit of the OP

... since A and E are restricted to only two values between them, they must consume those two values;

... and hung my hat on it, but that obviously doesn't apply in the same way to the two examples above.

Question: Would this example also decompose into the (same?) two groups as the above?

my @grid = (
    [ 0, 1, 0, 1, 0, 0, ],
    [ 0, 0, 0, 1, 1, 0, ],
    [ 0, 1, 0, 0, 1, 0, ],
    [ 1, 0, 0, 0, 0, 1, ],
    [ 1, 0, 1, 0, 0, 0, ],
    [ 1, 0, 0, 0, 0, 1, ],
);

[hv]

Yes: labelling the columns A..F and the rows 1..6, we know variables {B, D, E} must consume values {1, 2, 3} between them, and likewise {A, C, F} must consume {4, 5, 6}. In this example, however, the latter can be further decomposed: C can only be 5, so {A, F] are left with {4, 6}.

Hugo