Hrpa

Mirko and Slavko’s favourite pastime is competing against each other in mathematical games. This time
they took a heap of N pebbles and settled on the following rules:

1. Mirko is the first to play, then Slavko, then Mirko again, then Slavko and so on;
2. Mirko can take any number of pebbles (between 1 and N, inclusive) from the heap during his
first move;
3. In each of the following turns the current player must take at least 1 pebble and is allowed to
take at most double the amount of pebbles taken during the previous turn by the other
player; naturally, one cannot take more pebbles than the remaining amount in the heap;
4. The player who takes the last pebble is the winner.

Both Mirko and Slavko play optimally (if it is possible for one player to beat the other, that player will
always win). We need to find the minimum number of pebbles that Mirko must take during his first
turn such that he is guaranteed to win the game.