chiark / gitweb /
Dominosa: further forms of set analysis.
I realised that even with the extra case for a double domino
potentially using two squares in a set, I'd missed two tricks.
Firstly, if the double domino is _required_ to use two of the squares,
you can rule out any placement in which it only uses one. But I was
only ruling out those in which it used _none_.
Secondly, if you have the same number of squares as dominoes, so that
the double domino _can_ but _need not_ use two of the squares, then I
previously thought there was no deduction you could make at all. But
there is! In that situation, the double does have to use _one_ of the
squares, or else there would be only the n-1 heterogeneous dominoes to
go round the n squares. So you can still rule out placements for the
double which fail to overlap any square in the set, even if you can't
(yet) do anything about the other dominoes involved.