Solution to "PH! IN TSA A WMF!"


I was right. My friend was wrong. The problem can be written using only acronyms in more than seventeen trillion ways. In fact, it can be written in exactly 17,592,186,044,416 ways.

This problem isn't too bad. There are a couple ways to approach it. Here is the simplest I can think of, and you may kick yourself if you didn't see it.

First of all, we know we have to replace every word with its first letter capitalized. Starting with the first letter, we can choose to write it by itself or with a space immediately to its right, for a total of two choices. This goes for any letter which is not directly followed by a punctuation mark. And since punctuation must be preserved, any letter attached to a punctuation mark cannot have a space to its right. So basically, each word with no punctuation attached to it can be written in two different ways--with or without a space to its right. Counting the words free from punctuation, there are 44, which gives us a total of 2^{44}=17,592,186,044,416 ways to write the problem using only acronyms. That is, about 17.6 trillion ways.