Alice and Bob play the following coins-on-a-stack game. 20 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 by 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 (0 = i = 20). We will call this an 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 gold coin happens to be on top when it's a player's turn then the player wins the game.


Initially, the gold coinis the third coin from the top. Then
Alice has no winning strategy.
In order to win, Alice's first move should be a 1-move.
In order to win, Alice's first move can be a 0-move or a 1-move.
In order to win, Alice's first move should be a 0-move.

• in order to alice first move should be 1-move
• 14 years agoHelpfull: Yes(67) No(9)
• BAL CHAL GULO AKTAO O THIK KORE ANSWER DITE PARE NA
• 14 years agoHelpfull: Yes(58) No(21)
• d) Alice has no winning strategy
  Case 1:suppose Alice starts with a 0 move. Now bob cleverly goes for a 2 move so that there is only one coin above the gold coin. Now irrespective of alice's move, Bob wins.
  Case 2:suppose alice stats with a 1 move it barely makes any difference. Again Bob goes for a 2 move and he wins. So alice has no winning strategy at all.
  
• 13 years agoHelpfull: Yes(20) No(19)
• Alice has no winning strategy.
• 14 years agoHelpfull: Yes(8) No(31)
• please explain clearly
• 14 years agoHelpfull: Yes(5) No(4)
• plz give explanation
• 14 years agoHelpfull: Yes(4) No(3)
• Plz explain your answer
• 14 years agoHelpfull: Yes(3) No(5)
• plz gv explaination
• 14 years agoHelpfull: Yes(2) No(3)
• In order to win Alice’s first move should be a 1 move
• 13 years agoHelpfull: Yes(2) No(3)
• plzz give expalnation..
• 12 years agoHelpfull: Yes(2) No(0)
• alie shoud make a 1- move
  then bob could make either a 0-move or 2- move
  for 0-move alice will play a 2-move and
  for 2-move of bob alice will play a 0-move
  i any case turn will be of bob in which case he has to commit a 3- move and hence alice has the top coin in his turn
  
• 10 years agoHelpfull: Yes(2) No(0)