When it doesn't make sense …
Why were you asked to try to understand some mathematics which was not clearly written? There will be times (hopefully not too many!) in the course of your mathematical studies when you will not immediately be able to follow a mathematical argument. In such circumstances it is very easy for your mind to boggle at the complexity of it all and to give up, feeling that you cannot understand any of it.
In Activity 8 you were asked to ‘make a note of the point when it becomes very difficult to understand’. Identifying precisely the actual cause of the misunderstanding is often a means of overcoming the difficulty. One technique that you might like to try in some circumstances is to go through the text, ticking line by line as you are able to follow an argument and marking clearly the point at which it is no longer clear. Then skip on a bit and see if there are lines further down the page where it is possible to follow the argument and tick those too. Then go back up the text and gradually you should be able to whittle away at the lines where there is lack of clarity. Eventually, the light may dawn completely, or you will have located a particular point which can subsequently be raised in the course Forum.
You may be wondering why anyone would want to spend time trying to solve a problem like the one in Example 3. Often, in the real world, problems arise that need to be solved—but this is not the case here. Rather it is one of a class of real-world problems that are provoked by curiosity rather than necessity. As your mathematical confidence grows, you may experience a greater curiosity about the world and a willingness to apply new-found mathematical skills to problems that you have posed for yourself. In Section 1.3, you will return to this theme, as you listen to some mathematical musings in which curiosity about the world plays an important part.
In Example 3, as has been already pointed out, one aspect of the problem was finding a suitable way of recording solutions on paper or, in other words, of developing a suitable notation. The author chose an essentially geometrical representation in which the different two-dimensional drawings represented various three-dimensional arrangements. It is possible to conceive all sorts of different recording systems; for example, labelling each of the seven pieces of the puzzle with a different letter or using some kind of three-dimensional coordinate system. The general point here is that often in mathematical problem solving the problem solver has to decide which symbols will be most appropriate. Frequently it is algebraic symbols that are used, as with the formidable-looking Example 4!