Statue Park

Shade cells so the shaded groups are exactly the bag of shapes below — each one used once, rotated and reflected however you like. The unshaded cells, the park, must stay in one piece. A black circle is part of a statue; a white circle is park. Click a cell to cycle shaded → park → blank; right-click cycles the other way.

Size Hint level

The rule that isn't a rule

Every write-up of Statue Park lists "two pieces may not touch" among the rules. It isn't one. A maximal connected group of shaded cells is never orthogonally adjacent to another maximal group — that is what maximal means. So if you take the answer to be a set of shaded cells rather than an assignment of placements to pieces, the non-touching rule is free, and the identity of each piece becomes unobservable.

That has a measurable consequence, and this repository measures it. Enumerate answers the way the rulebook is written — hand every bank piece a labelled placement — and you get a bigger number than the shading model, by exactly ∏ m_t!, the number of ways to permute equal pieces. Three copies of the same tetromino on 5×5: 16 shadings, 96 labelled placements, ratio 6 = 3!. The two engines in the repo share no code, and the factor comes out on the nose every time.

Both colours of circle always suffice — the question is which is cheaper

Two answers to the same bank shade the same number of cells, because the bank fixes the total. So if two answers differ, there is a cell shaded in the first and not the second and a cell shaded in the second and not the first. A black circle can always kill the impostor, and so can a white one: a black-only clue set and a white-only clue set both always exist. That turns a qualitative question into a price comparison, and the price is not what the rulebook's emphasis suggests.

Five rungs, and the one that costs nothing until it doesn't

clue is the circles plus the head count. place filters the catalogue of legal placements — a placement dies when one of its cells is known park, or when a cell touching it is known shaded. fit is the rung that makes this puzzle itself: a shaded cell has to be part of one piece, so a neighbour that no surviving placement joins to it must be park. white is the topology of the complement, including the cut vertices that would strand part of the park. probe is singleton consistency on top.