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I was trying to understand the egg dropping puzzle. The problem objective is:

What strategy should you adopt to minimize the number egg drops it takes to find the solution?. (And what is the worst case for the number of drops it will take?)

I understand we want to minimize the egg drops, but what does this worst case number of drops infer to. This makes me more confuse. Can anyone explain its meaning.

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Imagine this as a game of two players: the experimenter vs. nature.

The egg breaking limit is not chosen in advance. Instead, the players together form statements about its possible values, all the way until only one value remains.

On each turn, the experimenter chooses the floor from which to drop the egg. After that, the nature chooses whether the egg actually breaks or not.

Of course, with some moves of the experimenter, nature can't choose because the previous statements already determine the outcome. However, note that a good strategy for the experimenter does not make such redundant moves.

With such formulation, the "worst case" here is equivalent to the game-theoretic "if nature plays optimally", and "minimizing the number of moves in the worst case" to "if both play optimally".

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  • $\begingroup$ still not able to get the clear picture. $\endgroup$ – Navjot Waraich Jul 8 '18 at 10:50
  • $\begingroup$ @JotWaraich Are you familiar with game theory? Consider the game tree of this game. The leaves are situations where the egg-breaking limit becomes known. The experimenter's objective is to minimize the number of moves, the nature's objective is to maximize it. $\endgroup$ – Gassa Jul 8 '18 at 11:01
  • $\begingroup$ your explanation is good but i think my knowledge is not up to the mark to understand it. Surely i have understood somewhat but not everything. Thanks mate for putting the effort. I really appreciate :) $\endgroup$ – Navjot Waraich Jul 8 '18 at 11:17

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