A 2 × 3 board of boxes, 6 still on the table

A Dots and Boxes position drawn as dots and lines, and — where the figure asks for it — the same position as a strings-and-coins graph: one coin per box, one string per line, and the border lines running to the ground. Lines already played are solid, lines still available are dashed, and a box with no strings left has been pocketed. The footer carries the exact net score the solver computes from here and the normal-play verdict on the same position.

1 essay calls boxes-board. The drawing above is what it returns with no arguments at all; every call below passes it something, because a placement that passes nothing draws whichever member of the family the generator happens to default to rather than the one its essay argues about.