They are puzzles. Some of them have 36 pieces while some only have 9 pieces. Some wuzzle pieces are sold in packs. Most cost wooz.
Introduced on May 7th, 2013, wuzzles were quite popular among Woozens.
Wuzzles are little puzzle games that let you build great new items for your Woozen once you have collected all the pieces. Each Wuzzle consists of a Wuzzle Board and multiple Wuzzle Pieces. Once you have correctly placed all the Pieces on the Board you will receive your prize, whatever item is shown on the Wuzzle.
To play a Wuzzle, all you have to do is click on the “Play” button that appears when you select a Wuzzle Piece or Board in your inventory. Once the Wuzzle is open, just click and drag the Pieces to the correct location on the Board. When you have finished placing all the pieces correctly, you will receive your reward and the Pieces and Board for that Wuzzle will disappear from your inventory. You can quit the Wuzzle at any time without having completed it and the pieces will be saved where you left them until you are ready to keep playing.
Their are also different rarities of wuzzles, including: common, uncommon, rare, very rare, extremely rare, and insanely rare. The higher the rarity the better the prize.