A gaming machine is controlled by a processor in response to a wager and comprises a puzzle feature optionally triggered by a start-feature outcome of a basic game. The puzzle feature includes a plurality of arrangements of randomly-selected puzzle elements for generating respective payouts. At least one of the puzzle elements of each arrangement being shared by another one of the arrangements and contributing to the payouts generated by the respective arrangements that share the one of the puzzle elements. The puzzle elements may, for example, be letters, symbols, pictures, shaped puzzle pieces, or playing cards.