Induction Puzzles or Logical Puzzles:

               Induction Puzzles are logic puzzles. In most cases, the puzzle's scenario will involve several participants with reasoning capability (typically people) and the solution to the puzzle will be based on identifying what would happen in an obvious case, and then repeating the reasoning that: "as soon as one of the participants realizes that the obvious case has not happened, they can eliminate it from their reasoning, so creating a new obvious case".

               Typical tell-tale features of these puzzles include any puzzle in which each participant has a given piece of information about all other participants but not themselves. Also, usually some kind of hint is given to suggest that the participants can trust each others intelligence.

               Examples :
                            1. Prisoners and hats puzzle.
                            2. 100 Prisoners in Solitary cells
               Reference :

Dissection Puzzles

                  A dissection puzzle, also called a transformation puzzle, is a tiling puzzle where a solver is given a set of pieces that can be assembled in different ways to produce two or more distinct geometric shapes. The creation of new dissection puzzles is also considered to be a type of dissection puzzle. Puzzles may include various restraints, such as hinged pieces, pieces that can fold, or pieces that can twist. Creators of new dissection puzzles emphasize using a minimum number of pieces, or creating novel situations, such as ensuring that every piece connects to another with a hinge.

                 Examples :
                               1. Stick Matches Image Puzzle
                 Reference :

Lateral Thinking Puzzles

            Lateral thinking puzzles are often strange situations which require an explanation. They are solved through a dialogue between the quiz master who sets the puzzle and the solver or solvers who try to figure out the answer. The puzzles as stated generally do not contain sufficient information for the solver to uncover the solution. So a key part of the process is the asking of questions. The questions can receive one of only three possible answers - yes, no or irrelevant. 

When one line of enquiry reaches an end then another approach is needed, often from a completely new direction. This is where the lateral thinking comes in. 

Some people find it frustrating that for any puzzle it is possible to construct various answers which fit the initial statement of the puzzle. However, for a good lateral thinking puzzle, the proper answer will be the best in the sense of the most apt and satisfying. When you hear the right answer to a good puzzle of this type you should want to kick yourself for not working it out! 

This kind of puzzle teaches you to check your assumptions about any situation. You need to be open-minded, flexible and creative in your questioning and able to put lots of different clues and pieces of information together. Once you reach a viable solution you keep going in order to refine it or replace it with a better solution. This is lateral thinking!