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....
Please Explain Your Answer..

• (b)In order to win, Alice's first move should be a 1-move....
  reason:there are two possibility after 1- move by Alice:-
  1. when bob takes 0-move....then the coin config is same ..... but now alice can neither take 1-move nor 0-move.... so she has to take 2 or greater move(let it be 2 move)............
  now we have only one coin above the gold coin......now bob can neither take 1-move nor 0-move nor 2-move.... so she has to take 3 or greater move.......
  but the move greater then 2-move brings gold coin on top....makes alice win...
  
  2.now bob takes 2-move after alice's first move....... now thre is only one coin above the gold coin..... so Alice takes 0-move........now we have only one coin above the gold coin......now bob can neither take 1-move nor 0-move nor 2-move.... so she has to take 3 or greater move.......
  but the move greater then 2-move brings gold coin on top....makes alice win...
  
• 13 years agoHelpfull: Yes(18) No(3)
• In order to win alice's first move should be a 1-move
  BECAUSE:
  if alice's first move is 1.the there are 2 coins above the gold coin.The there are two chances that Bob may choose 0 move or 2 move.
  i>If he choose 0 move then there are 2 coins above the gold one.
  Then bob's choice is 2 move. then there are 1 coin above gold and Bob's move must be 3 or greater. So, when alice turns come then the gold is above.So alice win the game.
  ii> Similarly, if bob' choice is 2 then also Alice win the the game.
• 13 years agoHelpfull: Yes(16) No(6)
• no winning strategy
  
• 14 years agoHelpfull: Yes(6) No(5)
• first move must be 1 move
  Already solved repeated question
• 14 years agoHelpfull: Yes(5) No(9)
• In order to win, Alice's first move should be a 1-move
• 14 years agoHelpfull: Yes(3) No(7)
• Alice has no winning strategy
• 13 years agoHelpfull: Yes(2) No(1)
• for this question there is no trick or any explanation.
  just mug up the answer is that option in which Alice will make first move as 1 or any option having first 1 move.
• 14 years agoHelpfull: Yes(1) No(5)
• in order to win aliace first move should be 0.
• 13 years agoHelpfull: Yes(1) No(10)
• In order to win, Alice's first move should be a 0-move.
  Since It is Way to Win 0-move by Alice 1-move by Bob 2-move by Alice Make Third Coin top
  The Answer is Alice First move should be 0-move
  
• 13 years agoHelpfull: Yes(1) No(6)
• the answer should be in order to win alice's first move can be a 0-move or a 1-move
• 13 years agoHelpfull: Yes(1) No(2)
• for this question the answer is alice has no winning stratergy
  
• 13 years agoHelpfull: Yes(1) No(1)
• In order to win Alice first move should be 0-move
• 13 years agoHelpfull: Yes(0) No(4)
• alice move must be 1 move
• 13 years agoHelpfull: Yes(0) No(2)
• Alice has no winning strategy.
• 13 years agoHelpfull: Yes(0) No(2)
• !! answer would be first one....................
  to win alice.alice,s first move should b one-move
  coz
  in case of first 0 move,opposote one can,nt be move 0 den he wil move one...........den next time alice will move first d,got golden coin on upper surface.....
  if alice move z 1 den opposite can,t be move 1 den he will 0.....den alise has to move o and opposite wil move 1 ,den he wil get coin....
• 13 years agoHelpfull: Yes(0) No(0)