Question 29
Answer-format rule printed in the source: round a non-integer answer to the nearest integer. If a calculated answer has more than five digits, write its last five digits.
Two players take turns filling a row of 10 small squares with marbles. On each turn, the player puts 1 to 5 marbles, one in each next empty square, continuously from the left. The player who fills the last square loses. Example: A starts and puts 2; B puts 3; A puts 2; B puts 2; A must fill the last square and loses. The source states that the starting player has a winning strategy. If the row instead has 20 squares, how many marbles should the first player put on the first turn to guarantee a win?
Two players take turns filling a row of 10 small squares with marbles. On each turn, the player puts 1 to 5 marbles, one in each next empty square, continuously from the left. The player who fills the last square loses. Example: A starts and puts 2; B puts 3; A puts 2; B puts 2; A must fill the last square and loses. The source states that the starting player has a winning strategy. If the row instead has 20 squares, how many marbles should the first player put on the first turn to guarantee a win?