The jailer will then bring your friend into the room. If you attempt to leave other messages behind, or clues for your friend … yes, you guessed it, instant death! This is the only change you are allowed to make to the jailers initial layout. If the coin you select is a head, it will flip to a tail. A single coin, but it can be any coin, you have full choice. The jailer will then allow you to turn over one coin on the board. Once all the coins have been laid out, the jailer will point to one of the squares on the board and say: “This one!” He is indicating the magic square. If you attempt to coerce, suggest, or persuade the jailer in any way, instant death. If you attempt to interfere with the placing of the coins, it is instant death for you. He may elect to look and choose to make a pattern himself, he may toss them placing them the way they land, he might look at them as he places them, he might not …). Some coins will be heads, and some tails (or maybe they will be all heads, or all tails you have no idea. He will place the coins randomly on the board. The jailer will take the coins, one-by-one, and place a coin on each square on the board. In the cell will be a chessboard and a jar containing 64 coins. The jailer will take you into a private cell. If you complete the challenge you are both free to go. What is the upper bound for n, if m coins are allowed to flip? I want to know does this puzzle works perfectly for every n × n chess board? Is there a upper bound to n?
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