James Thurber once wrote about a word game called "ghost". Two or more people could play. The first person would propose a letter, such as "W", signifying that they were thinking of a word with a "W" in it. The next person would add a letter to the beginning or end, announcing for example, "OW", indicating that he could produce a word with those consecutive letters; perhaps he is thinking of "throw". The next player says "OWD". The fourth player can't think of a word with "OWD" in it, and assumes the third player was bluffing, and challenges. The third player says "Showdown", and wins a point, while the fourth loses one.
The game may go back to Lewis Carroll, who wrote about a similar puzzle called "Mischmasch".
The game of Ghost is dynamic; you start a word, but your opponent tacks on a letter you weren't prepared for, and then you think of a word that might be his word, and you tack on another letter, but that's not what he was thinking of, and he's wondering if you're bluffing, and so on.
If we're willing to give up the dynamic nature of the original game, we can make a solitaire version of the puzzle. I'll give you a set of letters that constitute the "middle" of some word, and you have to come up with such a word. For instance, if I say "CTU", you can respond with "piCTUre". In some cases, there might be several possible answers.
I give up, show me the solution.