## Task A-1.5.

There are 42 pebbles on the table. Two players take turns making moves. In each move, a player must take at least one pebble, but no more than half of the remaining pebbles. The player who leaves only one pebble on the table after their move wins.

Which player can definitely win?
## First Solution.

The first player can win with the following strategy: leave the opponent with 31, 15, 7, 3, and 1 stones in sequence.

In the first move, take 11 stones. Then the second player must take between 1 and 15 stones, leaving between 16 and 30 stones on the table. No matter how many are left, the first player can take enough to leave 15 stones on the table after their move.

When there are 15 stones on the table, the second player must take between 1 and 7 stones, leaving between 8 and 14 stones on the table. No matter how many are left, the first player can take enough to leave 7 stones on the table after their move.

When there are 7 stones on the table, the second player must take between 1 and 3 stones, leaving between 4 and 6 stones on the table. No matter how many are left, the first player can take enough to leave 3 stones on the table after their move.

When there are 3 stones on the table, the second player can only take exactly 1 stone, leaving 2 stones on the table. The first player then takes 1 stone, leaving one on the table and thus wins.