Readers familiar with numbers and their patterns will most likely know of the game-playing exercise where one is invited to spot the next number in a sequence, only to find that after giving an answer there can be a multiplicity of possibilities, each of which is valid according to its own rule of sequence construction. This is an instance of partial sequence matching and the purpose of this note is to show how a simple method of constructing a partial sequence match can be achieved. It requires only a knowledge of polynomials and matrix algebra, which are topics within the grasp of an undergraduate, and will be instanced against the backdrop of some wellknown sequences.