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.

• Ans is Option b..We have 99 coins including 2 special coins.initially special coins are separated by O1 and O2.If Alok remove one of the other 95 coins then bhanu also remove one of the 94 coins.After they remove 47 coins each the remaining coins are 5.In these 5 coins every special coins is separated by two ordinary coins.After this Alok removes one ordinary coin then the two special coins will come together and Alok wins the game.
• 14 years agoHelpfull: Yes(27) No(2)
• option B is cirrect.
  If Alok removes coin either from O1 or O2, then there will be only 1 ordinary coin b/w special coins.Then obviously Bhanu will remove that coin in his turn and wins.
  So Alok should not touch O1 and O2 in his first turn.
• 14 years agoHelpfull: Yes(19) No(2)
• b) In order to win, Alok should remove one of the coins different from O1 and O2 on his first turn.
• 14 years agoHelpfull: Yes(9) No(0)