In a first aspect of the invention, the three-way ring puzzle has a rectangular housing with a first and second opposite sides. A first series of stems extends from the first side, and a second series of stems extends from the second side. Each stem has an eyelet on its extremity outside the housing and a wire loop is loosely mounted in this eyelet. Each of the stems in the first series aligns with and is joined inside the housing to one of the stems in the second series. A first and second elongated wire bands are respectively mounted in the wire loops on the first and the second series of stems. In another aspect of the present invention, the housing has a cylindrical shape, the stems extend diametrically through the housing and each of the elongated wire bands has a curved shape.