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On May 07, Eric Roode wrote:
> This is the puzzle that I started to tell last night, but didn't have
> time for (as we left the restaurant).
>
> There are four coins on a sheet of paper on the table, arranged in a
> diamond. Call them North, South, East, and West. You are
> blindfolded. You don't know which coins are heads or tails. Your
> objective is to get the coins to all be the same way (ie, all heads or
> all tails). On each turn, you may call out one or more directions
> ("East, North" for example), and your friend will flip those coins
> over. The game ends when all coins face the same way. (Your friend
> will tell you when the game is over). Also, after any of your moves,
> your so-called friend may rotate the paper 90 degrees either way, or
> 180 degrees, thus redefining what north, south, east, west are. You
> don't get to know whether the friend rotated the playing field, and at
> no point do you get any information about which coins are heads or
> tails.
>
> What's your strategy for flipping the coins?
>
> Surprisingly, there is enough information to consistently win the
> game, in a fairly small number of moves.
At the risk of sounding dense, I don't see how it's possible. There's
no scenario where I'm guaranteed to know how to win in one move, and I don't
even see how I can know whether I've got a 1/3 or 2/2 layout.
The best I can see is that I'll win eventually if I flip one coin (or
equivalently, three coins) at random each time, but I can only present a
statistical likelihood of when I'll actually win -- it could take a really
long time.
Hint, please?
- Kurt
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