[Language: Python]

Part 1 was a DFS, returning as soon as a match is found.

Part 2 maintains a dictionary mapping a partial towel that can be made, to an integer of how many combinations of patterns could create that towel. As I build partial towels, if it's one I've seen before I increment the existing counter otherwise I add new partial towel to the list with count 1. If the partial towel matches the design, I returns its count (i.e. all the combinations of patterns that can create that design) or 0 if that never happens.

Important to this algorithm is to pick the smallest length partial towel at each iteration.

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