Logic problems include numerical puzzles like sudoku, spatial puzzles like nonograms, and language-based problems such as "knights and knaves" and "lateral reasoning." All of these puzzles present the problem solver with a situation and a set of rules, and require logical deduction.
Knights and knaves puzzles always follow a similar format. Typically, the problem solver is presented with two individuals, one knight who always tells the truth and one knave who always lies, and must determine which is which. The answer is deduced from a statement that one individual makes. For example, you meet Bob and Carl. Bob says "Neither of us are knaves." In this case, Bob is the knave, because his statement contradicts the rules of the puzzle and therefore must be a lie. This is an easy example, but there are hundreds of other knights and knaves puzzles, plus variations which include three individuals or allow the problem solver to ask one individual a single yes/no question.
Another type of logic puzzle is called a lateral thinking puzzle. These puzzles require the ability to think "sideways," meaning to see past the literal or implied meanings of words and concepts. For example, the police respond to a tip saying that a murder suspect named Charles is playing poker in a certain house. The police enter the house and see a pilot, a carpenter, a fireman, and a mechanic playing poker. Without speaking, they immediately arrest the fireman. How did they know? The answer is that pilots, carpenters, and mechanics can be women, but a fireman is a man. Notice also that the problem did not use the term "firefighter." This problem requires us to ignore the implication that pilots, carpenters, and mechanics are men. As with the knights and knaves puzzle, there are countless lateral thinking puzzles.