Hi all, Here's the conversation so far - my reply is at the bottom of the email so you can read through to get the context, and then my reply: On Wed, Apr 15, 2015 at 12:55 PM, Veit Elser <ve10@cornell.edu> wrote:

There's a growing class of puzzles I call Mensa Correctional Facility puzzles. In these puzzles there is always a warden who challenges prisoners with math/logic puzzles and grants them freedom when they succeed in solving them. Does anyone know the origins of the following one:

In this puzzle the warden challenges a pair of Mensa inmates. The first inmate is shown to the warden's room and the warden proceeds to place identical coins, each one either heads up or tails up, onto the 64 squares of a checkerboard. He then points to one of the coins and declares it to be the "freedom coin". The inmate watching this is then invited to flip one of the coins to help his partner identify the freedom coin. Then, without allowing the inmates to communicate the second inmate is lead into the room, shown the coins, and after a little head scratching points to the freedom coin -- he is, after all, a Mensa inmate -- and the prisoners are set free.

How did they do it?

On Wed, Apr 15, 2015 at 1:04 PM, Mike Stay <metaweta@gmail.com> wrote:

I first heard it last year from a coworker who likes such puzzles, but the setup was slightly different: the warden allows the two to agree on a strategy in his presence first; then one of them leaves; then the warden is free to place the coins in whatever way he pleases and choose any coin as the freedom coin. Then the other prisoner leaves, the first one comes back, and has to make his choice.

Thane Plambeck <tplambeck@gmail.com> replied:

This puzzle, and related ones, seem to be coming up a lot. It was performed (with 16 replacing 64) at a recreational math conference I recently attended in Portugal earlier this year. I was also told about it at the last Gathering 4 Gardner in Atlanta (spring 2014). The person who showed it to me first was Colin Wright I think (cc'ed), who might be able to say where he heard about it (if he didn't make it up himself).

I certainly didn't make it up. I was presented this as a puzzle based on labelling the vertices of a 64 dimensional cube, and then re-interpreted it back to the original form of deducing a number from a coin configuration. Not sure when I heard it first, but it was probably mid 2013 or so. I can perform it with 64 squares, it it takes my accomplices too long to learn the decoding, unless they've done this sort of thing before. I wrote up my "performance" from Lisbon here: http://www.solipsys.co.uk/FlippingPuzzle/AnotherFlippingPuzzle.html That includes all the relevant references I could find. The earliest reference I could find was "Two applications of a Hamming code" by Andy Liu in Mathematics Magazine, January 2009. You can find that here: http://www.ingentaconnect.com/content/maa/cmj/2009/00000040/00000001/art0000... Hope that helps! Best regards, Colin -- If you never go off at a tangent, you will forever run in circles.