Next Level Odd-One-Out Puzzles

A commonly occurring task in intelligence tests or recreational riddles is to “find the odd one out”, that is, to determine a unique element of a set of objects that is somehow special. It is somewhat arbitrary what exactly the relevant feature is that makes one object different. But once that is settled, the answer becomes obvious. Not so with a puzzle popularized by Tanya Khovanova to express her dislike for this type of puzzle. Here, it is a more complicated relation between the objects and the features that determines the odd object, because there is only one object that does not have a unique feature expression. This puzzle inspired me to look for even more complicated relations between objects, features and feature expressions that appear to be even more symmetric, but actually still single out a “special object”. This paper provides useful definitions, a theoretical basis, solution algorithms, and several examples for this kind of puzzle.