Question 145
Alberto and Barbara are sitting next to each other in front of a table on which they have arranged in a row, from left to right, 15 chocolates. Some of the chocolates are milk chocolates, the others are dark chocolates. Taking turns, starting with Alberto, they play the following game: during his or her turn, each of the two must eat a strictly positive number of consecutive chocolates, always starting from the leftmost one among those remaining, and in such a way that the number of eaten chocolates of the same type as the first one is odd (for example, if at some turn the sequence of remaining chocolates is LLFLF, where L stands for milk and $F$ for dark, the player whose turn it is may eat the first chocolate from the left, the first 4 from the left, or all 5 chocolates).
Whoever eats the last chocolate wins.
Among the $2^{15}$ possible initial sequences of chocolate flavors, how many are those for which Barbara has a winning strategy?
Whoever eats the last chocolate wins.
Among the $2^{15}$ possible initial sequences of chocolate flavors, how many are those for which Barbara has a winning strategy?