5. 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? (I. Rubanov)
Answer. Beginner. Solution. Let the players be A (the beginner) and B (his opponent). We will present a strategy that allows A to win guaranteed. Suppose he takes the digit 3 on his first move; then B is forced to take 4 (otherwise, A will take it on his second move and win, forming the number 34). Note that in this case, B cannot win on his second move, as the only two-digit number containing 4 and divisible by 17 is 34. Next, A takes 1, then B must take 5 (indeed, otherwise, he will not win with this move, and A will take 5 on the next move and form 51). Then, A takes 6 on his next move and wins, forming the number 136. There are other winning strategies for A as well.

Criteria. Only the correct answer - 0 points. A strategy is presented that does not work in at least one variant of the opponent's move - 0 points.