How to solve this? [Game theory]

Revision en3, by remidinishanth, 2018-01-13 09:54:53

Hello,

Can someone explain the logic [and formal proof why this logic works] to solve this problem?

Consider a heap of N objects. Two players take turns playing the following game:

At his very first move, the first player removes from the heap between 1 and N-1 objects After that, at each step the player to move can remove any number of objects between 1 and the number of objects removed by the other player at the previous move When the heap becomes empty, the player to move loses the game.

[UPD.]

I know that removing the number of objects from Last on bit works. The Last on-bit, I mean the below.

int k=0;
while( n % (1<<(k+1)) == 0)
k++;
printf("%d",(1<<k));
fflush(stdout);
n -= (1<<k);


I need a formal proof/Argument that why is this working. Or why this is guaranteed to work?

Thank you.

#### History

Revisions

Rev. Lang. By When Δ Comment
en4 remidinishanth 2018-01-13 09:55:39 24
en3 remidinishanth 2018-01-13 09:54:53 374 Tiny change: 'he Last on bit I mean th' -> 'he Last on-bit, I mean th'
en2 remidinishanth 2018-01-13 09:35:03 40 Tiny change: 'the logic to solve ' -> 'the logic [and formal proof why this logic works] to solve '
en1 remidinishanth 2018-01-13 07:37:38 640 Initial revision (published)