= Solution
A flattened Boolean <array> stores the whole board in $N^2$ entries, with cell $(x,y)$ at position `y*N + x`. For the pictured board, its bottom-to-top rows are \b[`111111 | 111100 | 111100 | 110000 | 000000 | 000000`].
A column-height <array> uses only $N$ entries: column $x$ contains exactly the cells below height $h(x)$. The pictured board is \b[$h=(4,4,3,3,1,1)$], with 16 occupied cells. The alternatives are essentially different because the first stores every cell and the second encodes the boundary of an <order ideal>.
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