On each move, a player may subtract 1 from the integer, or halve it, rounding up if necessary. The person who first reaches 0 is the winner.

Alice goes first: she makes her choice of move on the starting value.

For example, starting at 15 a legal game (if not particularly well played) could be:

Alice .......................................15 → 8

Bob ......................................... 8 → 7

Alice ....................................... 7 → 4

Bob ......................................... 4 → 2

Alice ....................................... 2 → 1

Bob ......................................... 1 → 0 Bob wins.

For which values of n is there a winning strategy for Alice?

## No comments:

## Post a Comment