:your friends’ daughter madison has recently learned to spell some simple words. to encourage this, her parents got her a colorful set of refrigerator magnets featuring the letters of the alphabet (some number of copies of the letter a, some number of copies of letter b, and so on). the last time you saw her, the two of you spent some time arranging the magnets to spell out words that she knows. somehow with you and madison, things always end up getting more elaborate than originally planned, and soon the two of you were trying to spell out words so as to use up all magnets in the full set – that is, picking words that she knows how to spell, so that once they were all spelled out, each magnet was participating in the spelling of exactly one of the words. (multiple copies of words are okay here.) this turned out to be pretty difficult, and it was only later that you realized a plausible reason for this. suppose we consider a general version of the problem "using up all the refrigerator magnets", where we replace the english alphabet by an arbitrary collection of symbols, and we model madison’s vocabulary as an arbitrary set of strings over this collection of symbols. prove that determining if the collection of symbols can be used up to form strings from the vocabulary set is an np-complete problem.