5. There are 1993 matches on the table. Two children, A and B, take turns to pick up 1, 2, or 3 matches each time. The one who picks up the last match wins. If A goes first, which child will win? How should he play this game?
5. Player A can win. Note that as long as the number of matches left after Player A's turn is a multiple of 4. Since 1993 is a number of the form $4k+1$. Player A takes 1 match first, leaving 1992 matches, which is a multiple of 4. Thereafter, when Player B takes 1, 2, or 3 matches, Player A takes 3, 2, or 1 matches respectively, thus keeping the total number of matches taken by both to 4. Player A will then win.