Problem of the Week 1172
Consider all strings of length 11 that can be made from 10 "!"s and one "x." For example,
How many different functions can be described by such a string (using different parenthetizations), where these three functions are in play?
It turns out one can find a closed form here even with the 11 replaced by n. We are concerned here only with the abstract functions, not with any possible coincidences of values. So the actual functions used are not really relevant; for example,
I know the answer to this question, but have not thought about extensions, with
Source: Inspired by a student here at Macalester who told me about the !x notation for derangements, which was new to me.
© Copyright 2013 Stan Wagon. Reproduced with permission.