What is the difference between "Intent" and "Problem" for Design Patterns?

I pulled this information from Design Patterns Explained: A New Perspective on Object-Oriented Design
According to this book, There are a few key features to a design pattern:
Name: It's name
Intent: The purpose of the pattern
Problem: The problem that the pattern is trying to solve
Solution: How the pattern provides a solution to the problem in the context it shows up.
...
There are a few others, but I'm mainly concerned with the difference between Intent and Problem here. I don't really get how the "Intent"(the purpose) of every design pattern isn't to just solve the "Problem".