Question 5
Peter and Andrey play the game on the $n \times 1$ board, making moves alternate. Peter starts, and on his turn he places «+» to any empty cell. Andrey on his turn places «-» to any empty cell. The game is finished when all cells are filled. Peter's prize equals to the greatest number $k$ such that for each $\ell$ from 1 to $k$ there are $\ell$ successive cells, the amount of pluses on which is greater than the amount of minuses.
Find the maximal prize which Peter can guarantee for himself.
Find the maximal prize which Peter can guarantee for himself.