From Random to Systematic

Each of these activities challenges you to find all possible solutions. Have a go at the first one and think about how you can be certain you have not missed out any possibilities. Perhaps comparing each new answer with the ones you have already found as you go along will help you not to repeat solutions. Can you put your solutions into some sort of order? This might help you see whether you have missed any out. If you think you have found all the possible solutions, you might like to look at the solutions menu (on the left of each task page) to compare your answers and ways of working, with those of others. You could then practise these ways of working as you have a go at the second and third problems below.

As a whole group, these tasks will give you opportunities to work in particular on the reasoning, problem solving and attitude strands of the rope model, which altogether describes five key ingredients that make a successful mathematician. To find out more about these five ingredients and suggestions about how you can reflect on becoming a better mathematician, take a look at our short article What Makes a Good Mathematician?.