Question 29
Answer format: Round a noninteger answer to the nearest integer. If the calculated answer has more than five digits, give its last five digits.
Two players alternately place marbles into a row of 10 squares. A move fills 1 to 5 empty squares consecutively from the left. The player who fills the last square loses. Example: A begins; the successive moves are A:2, B:3, A:2, B:2, then A must fill the last square and loses. A winning strategy allows the first player to win. If the row instead has 30 squares, how many marbles should the first player place on the first move to guarantee a win?
Two players alternately place marbles into a row of 10 squares. A move fills 1 to 5 empty squares consecutively from the left. The player who fills the last square loses. Example: A begins; the successive moves are A:2, B:3, A:2, B:2, then A must fill the last square and loses. A winning strategy allows the first player to win. If the row instead has 30 squares, how many marbles should the first player place on the first move to guarantee a win?