Alok and Bhanu play the following coins in a circle game. 99 coins are arranged in a circle with each coin touching two other coin. Two of the coins are special and the rest are ordinary. Alok starts and the players take turns removing an ordinary coin of their choice from the circle and bringing the other coins closer until they again form a (smaller) circle. The goal is to bring the special coins adjacent
to each other and the first player to do so wins the game. Initially the special coins are separated by two ordinary coins O1 and O2. Which of the following is true ?

a) In order to win, Alok should remove O1 on his first turn.
b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.
c) In order to win, Alok should remove O2 on his first turn.
d) Alok has no winning strategy.

• removing different coins then o1 and 02 is correct
  bec lets consider that the series of coins in circle is
  .......sp o1 o2 sp..... in circular form
  now there are 95 other coins denoted by.......
  if for 1 st turn if alok remove other than o1 or 02 we are left wit 94 coins
  again bhanu has 2choices either(o1 or o2) or coins within 94
  if he removes a coin from 94..
  alok and bhanu continues...
  when there are only 5 coins its alok s turn and if he removes the 5 th coin
  then alok wins....
• 14 years agoHelpfull: Yes(38) No(5)
• In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.
  
  Reason:
  o1 and o2 shud be removed as late as possible becoz who ever removes it gives the oppurtunity for the other one to remove the other one on the 2nd chance
  
• 14 years agoHelpfull: Yes(37) No(2)
• b) remove coins different from o1 and o2
• 14 years agoHelpfull: Yes(29) No(0)
• alok has no winning strategy
  
• 14 years agoHelpfull: Yes(11) No(48)
• ans:remove diff from o1&o2
  there is 99 coin
  2 special00+2 o1&o2
  99-4=95
  if alok & bhanu keep removing coin other than these 4 coin after 47 turn alok turn is there now he remove one coin left other than these 4,so now bhanu must have to remove o1 or o2, after that alok remove left one n win.
• 13 years agoHelpfull: Yes(10) No(0)
• In order to win, Alok should remove one coin different from o1 and o2 in his first turn. and in every turn unless Bhanu (Have to) remove a coin from o1 or o2.
  This is a 100% winning Case and Alok will always win by by this strategy. By this strategy Bhanu will always face removing coin from an even no. of coins( e.g. 94,92,90....2) so in the end he will face the situation that if he removes any coin, Alok will win by removing adjacent coin. so the answer is b)
• 13 years agoHelpfull: Yes(6) No(1)
• in order to win alok should remove one of the coins different from 01 and 02 on his first turn
  because suppose the series ......g1c01c02g2..... so if in first move if alok remove c01 then in next turn bhanu will remove c02 and bhanu winns.
• 13 years agoHelpfull: Yes(3) No(0)
• Ans is B
  alok should remove coin other than o1,o2..
  there are 95 other coins.
  if for first turn if alok remove other than o1 or o2 we are left wit 94 coins
  again bhanu has 2 choices either(o1 or o2) or coins within 94
  if he removes a coin from 94..
  alok and bhanu continues...
  when there are only 5 ordinary coins its alok's turn and if he removes the 5 th coin(o3 or o4 or o5)not the o1 or o2
  then bhanu will have no choice and Alok will win.
• 13 years agoHelpfull: Yes(2) No(1)
• alok has no winning strategy
  as their are 96 coins or 2 (o1 and o2) coins are between special coin and both are even so alok removes whichever coin bhanu will always win
• 14 years agoHelpfull: Yes(1) No(19)
• alok should remove one of the coins different from o1 and o2 on his first turn
• 8 years agoHelpfull: Yes(0) No(0)
• In the given case, Out of 99 coins two are special coins and rest 97 are ordinary coins.
  Let special coins are denoted by S1 and S2 and given two ordinary coins O1 and O2 are between S1 & S2 in one direction of circle and rest O3 to O97 are on other direction between S1 and S2 on the circle as shown below:
  https://storage.googleapis.com/tb-img/production/15/08/Solution%20Placement%20-%208%20%281%29.PNG
  
  So there is "short" gap of 2, consisting of O1, O2 and a "long" gap of 95.
  
  Now Given the goal is to bring the special coins adjacent to each other and the first player to do so wins the game.
  
  Firstly if Alok remove O1 or O2 on his first turn then Bhanu will automatically remove the O2 or O1 resp. and thus Bhanu wins the game so Alok should not remove O1 or O2 on his 1st turn
  
  Secondly Alok should remove coin any from O3 to O97, making that gap equal to 94 then two cases arise
  
  1. If Bhanu picks any of O1 or O2 then Alok will remove the O2 or O1 resp. and thus win the game.
  
  2. If the Bhanu picks from the O3 to O97, he is just prolonging the game. He'll make
  an even gap odd, and Alok will respond by evening it up again. If Bhanu keeps it up
  then ultimately the "long" gap get down to 3 coins. Then Alok will take one of them, leaving 2 gaps of 2 coins. When Bhanu takes one of the remaining coins, a gap of 1 coin is created, and Alok wins by taking that coin.
  
  Hence in both cases Alok wins so Alok should remove one of the coins different from O1 and O2 on his first turn.
• 6 years agoHelpfull: Yes(0) No(0)