Devise an algorithm for mentally multiplying the two numbers.

(II) Derive the 2-digit duodecimal analogue to (I) that utilizes a very very similar algorithm.

__Extra Challenge__: Generalize (I) and (II) to all positive integer bases less than 37.

**Clarification**: It may NOT be very facile to effect the mental multiplication in part (II), but with the algorithm, it would be fairly easy to derive the product very quickly by way of p&p.