Odd-One-Out

Odd-One-Out, also called Odd Man Out is a puzzle type and extraction method involving sets of things with a common property, and selecting the one item within that set that does not share that property.

Background
The odd-one-out problem is a common question featured in IQ tests, often found alongside analogy questions. Often, test-takers would be presented with a series of shapes or abstract images and asked to select the one option that doesn't share a particular characteristic with the other entries. Variations on this type of question included items presented in a sequence, wherein one member of the sequence does not properly continue it (which is commonly done with mathematical sequences), and words rather than shapes/numbers, where the goal is to either find an intended connection between all but one of the words or come up with some kind of connection that would exclude one of the entries (with the latter commonly being found on creativity tests). Another rather famous case of odd-one-out problems being used outside of puzzles is on the children's TV show Sesame Street. A common segment/song from the show is 'One Of These Things', which told viewers that 'One of these things is not like the other, one of these things just doesn't belong ' and asked them to pick out one out of four things that either was not identical or did not fit with the category established by the others. Usually the difference was quite obvious, like a number '2' among three of the letter 'W', but sometimes it covered categories of items, like having a selection of vegetables and a single piece of meat. Either way, the purpose was to teach kids the concept of "differences", and the song accompanying the segments ingrained itself in many a child throughout its run. This segment first appeared in the first ever episode, and continued to be a regular occurrence at least until 2019. It also had a variation called "Three Of These Things" which asked the inverse question, attempting to teach the concept of "sameness".

As an entire puzzle
Odd-one-out puzzles can theoretically have anything as their subject. Most commonly, they're done with words, but they can also be reasonably done with numbers, music, images, or physical objects. It's also common to use non-words to represent particular words, such as in 2016's Road Trip puzzle (where car models had to be ID'd to get the words used in the comparison), but this method often results in extra constraints on possible words, leading to less interesting sets.

When it comes to the connections between the non-odd things, it can also vary quite a bit, but certain types tend to work better with particular subjects. When a puzzle uses only words as a subject, there is a lot fewer unique connections to work with. Often, writers will use anagrams, hidden themed substrings, and qualities of the words themselves rather than focusing on definitions. Conversely, if a puzzle uses non-words to represent word-based sets, definition-based sets are more common, along with other sets that would be immediately obvious if the words were given right away (like an identical substring). If the subject is some sort of media (book titles, music tracks, etc.), the connections can start to be more trivia-based, or otherwise make use of facts about the thing itself rather than creative interpretation.

Additionally, puzzles may take on the same pattern-based problems used in IQ tests, asking solvers to identify the "wrong" item in a sequence, sometimes adding the extra request of "correcting" the sequence by changing something about the odd-one-out.

As an extraction
Odd-one-out extractions are less common that full puzzles, primarily because they lack the pretense that makes the full puzzles work. A writer can't spring an odd-one-out final clue phrase, for example, and simply list off several things and expect a solver to guess one as the final answer. It can be done well, though, and that depends heavily on the type of puzzle it's being used as an extraction for. In particular, word-heavy puzzles with lots of individual words and phrases present are the best candidates for an odd-one-out extraction, since they have both the opportunity to tie it into a theme or clue it elsewhere, and have a lot of fodder to work with. On the flip side, puzzles that rely heavily on visual elements, logic puzzles, and puzzles with a lot going on already will struggle to make an odd-one-out extraction work, either due to a lack of precedent, a lack of material, or a lack of clarity.

Played Straight

 * Odd Man Out (MITMH 2005) - A relatively straightforward word-based odd-one-out puzzle..
 * Recover The Pokemon Core Memory (MITMH 2018) - Five color-coded groups of words.

Notable Twists

 * Unprecedented Discovery (MITMH 2003) - On top of each group of words having an odd-one out, each connection has to be identified since.
 * Fourth Place (Puzzled Pint February 2016) - An unsorted set of words/phrases that can be grouped into sets of four based on a particular connection..
 * Worst Crossword Ever (Huntinality 2022) - As a visual extraction method..