The term 'cut a groove into' can be broken down into three crossword solutions: NICK (4 letters), DADOED (6 letters), and RABBET (6 letters). NICK is a type of cut made with a chisel, which is used to create a groove in wood. DADOED is a type of joint that is created by cutting a groove into two pieces of wood, which are then joined together. RABBET is a type of joint that is created by cutting a groove into the edge of one piece of wood, which is then joined to another piece of wood. All three of these solutions refer to the same process of cutting a groove into a material, such as wood, in order to join two pieces together.