Question 4
Rocío must write in a line 100 distinct integers chosen from $1$ to $199$ in such a way that every number, from the second one up to the second-to-last one, is greater than at least one of its two neighbours. Then she computes the sum of the numbers in the even positions, which we denote $P$, and the sum of the numbers in the odd positions, which we denote $I$. Determine the largest possible value of $P - I$ that Rocío can obtain.