Worked examples
A chain banks when its total divides evenly by the key and every tile is linked to the rest.
Three linked tiles totalling 14; the remainder is 0, so every tile turns green and the chain banks.
Four linked tiles totalling 20; one tile in the chain touches at a corner, which counts. But the remainder isn't 0, so the tiles stay gold and nothing banks.
Both tiles divide by the key, but they don't touch, so it's a broken chain: the tiles stay pale and earn nothing.