Alice and Bob play the following coins-on-a-stack game. 100 coins are stacked one above the other. One of them is a special (gold) coin and the rest are ordinary coins. The goal is to bring the gold coin to the top of the repeatedly moving the topmost coin to another position in the stack. Alice starts and the players take turns. A turn consists of moving the coin on the top to a position I below the top coin (for some I between 0 and 100). We will call this as i-move (thus a 0-move implies doing nothing). The proviso is that an i-move cannot be repeated, for example once a player makes a 2-move, on subsequent turns neither player can make a 2-move. If the gol coin happen to be on the top when it’s a player’s turn then the player wins the game. Initially, the gold coin is the third coin from the top. Then

In order to win, Alice’s first move should be a 1-move.
Alice has no winning strategy.
In order to win, Alice’s first move can be a 0-moveor a 1-move.
In order to win, Alice’s first move should be a 0-move.

• if alice makes a 0 move, then Bob will definitely make a 2 move which will leave only one coin on top of the gold coin and alice will have to make a non zero move as she has taken 0 already thus bringing the gold coin on top and making bob win. So in order to win, Alice CANT make a zero move.
  
  now if alice makes a one move, then it will leave the stack in its initial position only.... now if bob makes a zero move, it would make alice win(as explained earlier) and if he makes a 2 move it will leave just one coin above the gold, then alice will definitely take a zero move leaving bob no other choice but to take a non zero move which would bring the gold coin on top and make alice win...
  so to win, alice must make a ONE move...
• 13 years agoHelpfull: Yes(40) No(6)
• Alice has no winning strategy,
  coz,if Alice make 0 move then Bob has to make either 1 or 2 move,then Bob has the chance to win.(as the gold coin is at the third position from top.)
  If Alice make 1 move,Bob has to make either 0 or 2 move,in that case,Alice will never win.
• 13 years agoHelpfull: Yes(6) No(12)
• sorry for last answer.its wrong.
  alice has to make a 1-move to win
  
• 13 years agoHelpfull: Yes(6) No(1)
• if alice does a 0 move,bob would do 2 move ensuring a win.
  so alice cannot start with a o-move.
  
  if alice does a 1 move,bob would do a 2move ensuring a win
  so alice cannot start with a 1-move.
  
  so no winning strategy.
  
• 13 years agoHelpfull: Yes(4) No(8)