What is the difference between a problem statement and a design statement? Could you give an example of what the two could be for a single design brief?
A problem statement and a design statement are both important elements of a design brief, but they serve different purposes.

A problem statement defines the challenge that the design project aims to solve. It helps to identify the specific issues, constraints, or opportunities that the design team needs to address. The problem statement sets the foundation for the design project by defining the scope and boundaries of the project.

A design statement, on the other hand, outlines the goals and objectives of the design project. It articulates the desired outcomes or results that the design team aims to achieve. The design statement helps to guide the creative direction of the project and ensures that the team is working towards a common vision.
Those are clear explanations, thank you very much. Could you perhaps give me a couple of examples using the same design brief so I can compare the two directly?
Sure, let's say the design brief is to create a new mobile app that helps people find healthy recipes based on their dietary preferences. Here are some examples of a problem statement and a design statement for this brief:

Problem statement: Many people struggle to find healthy recipes that fit their dietary restrictions or preferences. There is a need for a mobile app that can quickly and easily provide personalized recipe recommendations.

Design statement: Our goal is to create a mobile app that makes it easy for people to find and cook healthy meals that fit their dietary preferences. We want to create a user-friendly interface that provides personalized recipe recommendations based on user input.

As you can see, the problem statement identifies the specific challenge that the design project aims to solve, while the design statement outlines the specific goals and objectives that the design team wants to achieve.