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“Information made with a computer that absolutely requires a computer to run as intended.”
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“A system of rules which the user interacts with, by applying reversible actions on the system, trying to solve a deductive logic problem defined by the rules.”
A puzzle can be solved simply by studying the initial setup, learning the rules and exhausting all possible logical operations based on the initial state. A human user cannot do this due to our limited mental faculties, which is where the challenge lies. We have to experiment with the available actions to find shortcuts and new connections between rules, which allow us, in the end, to solve the problem.
This is why reversibility is a key part of puzzles. A non-reversible puzzle is impossible to solve the human way. Some puzzles have non-reversible actions, but can be reset completely if the user gets stuck or just wants to try again from the start. This is one form of reversibility and doesn’t change the puzzle itself. It can make the user experience more annoying though.