14.5. 14 ** A storybook contains 30 stories, with lengths of $1, 2, \cdots, 30$ pages respectively. Starting from the first page of the book, stories are published, and each subsequent story begins on a new page. Question: What is the maximum number of stories that can start on an odd-numbered page?
The maximum number of stories that can start on an odd-numbered page is 23. Because for every story with an odd number of pages, regardless of whether its starting page is odd or even, the starting page of the story immediately following it will always have a different parity. There are 15 stories with an odd number of pages, so the parity must change at least 14 times, meaning at least 7 stories start on an even-numbered page. Therefore, the maximum number of stories that can start on an odd-numbered page is $30-7=23$. For example, arranging the stories in the order of lengths $2,4,6, \cdots, 30,1,3, \cdots, 29$ results in exactly 23 stories starting on an odd-numbered page.