$r,m$-colorings of knots are the solutions of systems of linear equations derived by associating to each crossing of the knot diagram under study the equation \[m \times \mbox{ under-arc }+ (1-m) \times \mbox{ over-arc } = \text{ emerging under-arc }. \]This is an invariant of the knot. We elaborate on this and work out calculations for the so-called Pretzel knots. To Bernardo, on his 4th birthday.