Maximal partial Room squares

A partial Room square of order n and side n-1 on an n-element set S is an (n-1) x (n-1) array F satisfying the following properties:
(1) every cell of F is either empty or contains an unordered pair of symbols from S,
(2) every symbol of S occurs at most once in each row and at most once in each column of F,
(3) every unordered pair of symbols of S occurs in at most one cell of F.
The number t of occupied cells in a partial Room square is its volume.

A maximal partial Room square is a partial Room square with the property that no further pair of elements of S can be placed into any unoccupied cell of F without violating the above conditions (1), (2) and (3).

Let M(n) = {t : there exists a maximal partial Room square of order n and volume t }.

M(10) ⊃ {24,25,...,45}
M(12) ⊃ {31,32,...,66}
M(14) ⊃ {43,44,...,91}


Downloadable files:
n=10 [8K]
n=12 [19K]
n=14 [35K]
t=n(n-1)/2-1 [13K]