They will use 1 flip to solve the chosen sub-board as per the original solution - except in the case that the solution is to flip the top-left coin of the chosen sub-board and it is already heads. The first individual will choose the first sub-board that the magic square is in, the chosen sub-board. These four sub-boards will be labelled A, B, C, and D, respectively. Let the board be $nÃn$ for any $n=2^k+j$ for $0I'll just give a quick outline for a proof of why 1 flip is not always sufficient. The jailer explains all these rules, to both you and your friend, beforehand and then gives you time to confer with each other to devise a strategy for which coin to flip. If he guesses incorrectly, you are both executed. If he guesses correctly, you are both pardoned, and instantly set free. Based on the configuration of the coins he will point to one square and say: âThis one!â Your friend will look at the board (no touching allowed), then examine the board of coins and decide which location he thinks is the magic square. 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: âThis one!â 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 â¦). 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 à n chess board? Is there a upper bound to n?
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |