Induction puzzles are logic puzzles which are solved via the application of the principle of induction. In most cases, the puzzle's scenario will involve several participants with reasoning capability 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 realises that the obvious case has not happened, they can eliminate it from their reasoning, so creating a new obvious case".

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Note added at 2 hrs (2017-06-26 14:00:44 GMT)
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Google: Muddy Children, Other Logic Puzzles,
and Temporal Dynamic Epistemic Logic

Здесь она (или похожая) так называется:
https://ru.wikibooks.org/wiki/Эпистемическая_логика