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An Impossible Sounding Puzzle with an Elegant Solution

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Subject: An Impossible Sounding Puzzle with an Elegant Solution
From: glennrho...@gmail.com (Glenn Rhoads)
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by: Glenn Rhoads - Mon, 21 Nov 2022 04:03 UTC

Two people are being held prisoner by a king. The king brings the pair into a room and explains that their fate depends on the following task to be given tomorrow. The floor of the room is tiled by 64 identical squares in an 8x8 pattern. The king will place a penny on each square tile. You will not know ahead of time which pennies have heads facing up and which have tails facing up. The king may use any procedure to determine which are heads and which are tails, including flipping some or all of the coins randomly. Tomorrow the king will bring one prisoner into the room. The king will point to some square saying that this is the magic square. The person in the room picks exactly one penny and flips it over (changes heads to tails or tails to heads). The person can pick any penny they like. The person exits the room on the opposite side from which they entered. The second person enters the room and gets to point at any square of their choosing and claim that this is the magic square. If he is right, they both go free, otherwise they will both be executed. The room has been constructed so that the two prisoners cannot communicate in any way during this procedure. But until tomorrow, they are held together in the same jail cell so that they can devise a strategy to maximize their chances of escape.

What strategy maximizes their chance of being set free? As hard as it is to initially believe, the prisoners can always escape! Describe such a strategy.

Re: An Impossible Sounding Puzzle with an Elegant Solution

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From: anton....@g{oogle}mail.com (Anton Shepelev)
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Subject: Re: An Impossible Sounding Puzzle with an Elegant Solution
Date: Tue, 22 Nov 2022 13:03:09 +0300
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by: Anton Shepelev - Tue, 22 Nov 2022 10:03 UTC

Glenn Rhoads:

> Two people are being held prisoner by a king. The king
> brings the pair into a room and explains that their fate
> depends on the following task to be given tomorrow. The
> floor of the room is tiled by 64 identical squares in an
> 8x8 pattern.
> [...]

The subject mentions "An Impossible Sounding Puzzle," so
that I thought it contained a puzzle that cannot be
pronounced. This puzzle is, in fact, *very* good, and I
used to act it live on several persons with a smaller board.
A colleage and I were the prisoners that left the dungeons
of several surprised kings.

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From: rich...@cogsci.ed.ac.uk (Richard Tobin)
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Subject: Re: An Impossible Sounding Puzzle with an Elegant Solution
Date: Tue, 22 Nov 2022 16:11:16 +0000 (UTC)
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by: Richard Tobin - Tue, 22 Nov 2022 16:11 UTC

Subject	Author
An Impossible Sounding Puzzle with an Elegant Solution	Glenn Rhoads
Re: An Impossible Sounding Puzzle with an Elegant Solution	Anton Shepelev
Re: An Impossible Sounding Puzzle with an Elegant Solution	Richard Tobin