[MUSIC] Hi, in this lesson we're going to have a look at a simple definition of what a problem is. While this definition may seem quite obvious, we'll refer back to it throughout the course. So it's important that you're familiar with this terminology. So what is a problem? If we use Robertson's definition, a problem must have three things. An initial state, a solution path, shown by the arrow, and a goal. We'll now look at two examples to illustrate Robertson's definition, one from maths, and one from everyday life. So as an example let's consider the following math problem. If a right angel triangle has one straight side measuring 10 centimeters and another straight side measuring 8 centimeters, find the length of the hypotenuse using the Pythagoras theorem C squared equals A squared plus B squared, where C is the hypotenuse. In this problem, the initial state is the right angle triangle with the missing X measurement. The solution path is Pythagorean's theorem. C squared equals A squared plus B squared, where C is the hypotenuse. The goal is the measurement for X, the hypotenuse side of the triangle. If we substitute the values of the other two sides so that the solution path is now x squared equals 10 centimeters squared plus 8 centimeters squared, we can easily find the solution by solving the equation. Therefore, we can now see that the goal x is the square root of 164 centimeters, or 12.81 centimeters. As Robertson arguments, a problem can arise from either not knowing the goal, as in the case we just discussed, or not knowing the solution path. An everyday example of a problem where the goal is known but the solution path is not known is the following. Imagine that it is Monday and you need $220 for rent by Friday, but you've just been fired. The goal of having $220 for rent for Friday is known but the path to obtaining it is unknown to the constraint of just having been fired. Which removes your usual solution path. To solve this problem, you would need to come up with an alternative solution path by looking at the various options available for you to pay your rent. So in general, a problem can be defined as something with an initial state of solution path, and a goal. As we've seen from the examples above in a problem, either the solution path or the goal is unknown. In the next lesson, we'll look more deeply at how we can categorize different problems, as this will help you to understand problem solving theory and how to approach problems at university. [MUSIC]