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Clash Royale CLAN TAG #URR8PPP up vote 3 down vote favorite I have a slight variation of the coin flipping problem. There is a line of $n$ coins on the table; some of them are heads up and the rest are tails up, in no particular order. The object of the puzzle is to remove all the coins by a sequence of moves. On each move, one can remove any head-up coin, after which its neighboring coin or coins, if any, must be turned over. Coins are considered “neighbors” if they are next to each other in the original line; if there is a gap between coins after some moves, the coins are no longer considered neighbors. Determine the property of the starting line that is necessary and sufficient for the puzzle to have a solution. For those lines that can be removed by the puzzle’s rules, design a method for doing so. mathematics logical-deduction coins share | improve this question edited 21 mins ago Glorfindel 11.6k 3 44 73 asked 1 hour ago