Knights and Knaves

A Knights and Knaves puzzle, also called Liars and Truthtellers, is a type of deduction logic puzzle where solvers are presented with a set of people who either always tell the truth or always lie, and solvers have to determine which are which. Commonly used as a way of teaching Boolean logic, these puzzles have existed formally since at least the 1930s, and have had several variations in name, goal, and exact nature of the people involved.

Most K&K puzzles involve either identifying which people are knights/knaves, figuring out the answer to a particular question, or both (if doing the former is required to accomplish the latter). The most famous example is of two guards standing at a split in a road, where one path is safe to travel on. Between the two guards, one always lies, and one always tells the truth, and together they will only answer one question. The goal is then to both figure out who is who, and which road is safe, based on the answer to a single question.

Background
The most common name for this puzzle type, 'Knights and Knaves', comes from Raymond Smullyan's  'What is the Name of this Book? ', which collected various types of logic and deduction puzzles.

Played Straight

 * Paranoia (MITMH 2003) - A relatively straightforward liars and truthtellers. Involves taking three statements from each person and ordering them based on them.
 * Diplomatic Victory (MITMH 2014) - A puzzle about true and false statements. The only twist is the subject matter (the game Diplomacy) informs whether the statements were true or not.

Notable Twists

 * True and False (MITMH 2002) - What appears to be a simple true/false statements puzzle, but complicated by the fact that there are two possible assignments of truthfulness to the set. Each one extracts to a different answer, with the true answer needing both halves.
 * The Sexaholics of Truthteller Planet (MITMH 2009) - A Knights and Knaves puzzle, but with the ability for each to switch to the other overnight due to a mysterious disease passing through the planet. Solvers have to determine who is infected, and track the changes in truthfulness each day.
 * Murder at the Asylum (MITMH 2018) - Has the traditional truthtellers and liars, but adds an additional 'alternator', who will lie and tell the truth with alternating statements. In addition, each person is assigned a status in the murder (innocent, accomplice, or murderer), and a sanity (sane, delusional, and partial), the latter of which affects what people believe are true, rather than how they make their statements. In the end, solvers need to determine the status of all the residents in all three categories.