Clear the board in groups of three. Every deal is solvable — but the order you clear it in decides whether you strand yourself.
Every card has four attributes: how many shapes it shows, which shape, how it's shaded, and what colour it is. Each attribute has three possible values.
Pick three cards. They form a valid triad only if, for every attribute separately, the three cards are either all the same or all different — never exactly two matching and one different.