(t;d):(", "\*:;2_)@\:0:"i/19.in"       / towels, designs
s:{y~*|(#y)':x}                        / is y a suffix of x
p:(0/(,1){x,+/x(#y)-#'s/:[y]#t}/,\)'d  / number of ways to make each design
+/~~p                                  / part 1: number of creatable designs
+/p                                    / part 2: number of different ways to make each design

Basically stole this solution from shadow, as per usual :P

~/aoc24k/19.html