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  • 2 players A & B are playing a game involving a number n
  • Player A makes the first move & both players play alternately.
  • In each move the player takes the number n,chooses a number i such that 2^i < n and replaces n with k = n - 2^i iff the number of 1s in the binary representation of k is greater than or equal to the number of 1s in the binary representation of n
  • Game ends when no player can make a move, ie there does not exist such an i

For example:

n = 13 = b1101 

Only possible i=1

k = n - 2^i = 11 = b1011 

Again,only possible i = 2

k = n - 2^i = 7 = b111 

Since Player A cant make any more moves, Player B wins

I've deduced that at any step,we can only choose an i,such that there is a 0 at the corresponding position in the binary representation of n.

For Example: if n=1010010,then i can only be {0,2,3,5}.

But I cant move any further.A minimax algorithm isnt exactly striking me.I would appreciate any help.Thanks in advance

1 Answers 1