Prolog to the rescue!

use Language::Prolog::Yaswi qw(:load :query);
use Language::Prolog::Sugar vars => [qw(A B C D E F)],
                            functors => [qw(problem)];

swi_inline <<EOP;

:- use_module(library(clpfd)).

problem(Vars) :-
    Vars = [A, B, C, D, E, F],
    Vars ins 0..1,
    A + E #=< 1,
    A + B #=< 1,
    C + E #=< 1,
    D + F #=< 1,
    B + D #=< 1,
    A + C + E #>= 1,
    B + D #>= 1,
    E + F #>=  1,
    D + F #= 1,
    A + E #=< 1,
    C + D #=< 1,
    A + B + C + D + E + F #= 3,
    label(Vars).

EOP

swi_set_query(problem([A, B, C, D, E, F]));
while (swi_next) {
    my @r = swi_vars(A, B, C, D, E, F);
    print join(', ', @r), "\n";
}

# prints:
# 0, 1, 0, 0, 1, 1
# 0, 1, 1, 0, 0, 1
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update: Language::Prolog::Yaswi 0.18 required!