Question 58
In a garden, there are 2023 rose bushes planted in a row. Each bush contains either red or blue roses. Vicky is taking a walk and wants to pick some of the flowers. She starts at a bush of her choice, and picks a rose from it to add to her basket. She then continues walking down the row and picks a single flower from each bush she visits. Vicky can skip some bushes, but she cannot skip two adjacent bushes. She can leave the garden at any point. Let $r$ and $b$ be the number of red and blue roses she picked, respectively. Determine the maximal value of $|r-b|$ Vicky can achieve, irrespective of the configuration of bushes.