Rubaanov I.S.

On the table, there are 7 cards with digits from 0 to 6. Two players take turns picking one card each. The player who first forms a natural number divisible by 17 from their cards wins. Who will win with correct play - the starting player or their opponent?
Let's denote the players as $A$ (the starter) and $B$ (the opponent). We will outline a strategy that guarantees $A$ a win. Suppose $A$ takes the digit 3 on the first move; then $B$ is forced to take 4 (otherwise, $A$ will take 4 on the second move and win by forming the number 34). Note that in this case, $B$ cannot win on their second move, because the only two-digit number containing 4 and divisible by 17 is 34. Next, $A$ will take 1, threatening to form the number 51 or 136 on the next move. As shown above, $B$ cannot win immediately. $B$ also cannot counter both threats simultaneously, so $A$ will win on the next move.

## Answer

The starter.

