 Let us look now at pattern recognition. Mathematics has been defined as the study of patterns and relationships, and also as the study of patterns and structures. In either case, the study of patterns is at the very essence of what mathematics is all about. In fact, out of the ten strategies that we've been discussing, logical reasoning and pattern recognition are probably the most important strategies, and if you were only to master two strategies, these would be the two, and they will take you very far. Let us look at a very simple example. All tables at a school are equilateral triangles and can sit three students, one on each side. If two tables are joined, four students can sit. If three tables are joined, then five students can sit, and so on. How many tables are needed to sit 50 students? This is the case when you have three tables and five students. Let us do a little chart, number of tables, number of students. When you have one table, you can sit three students. When you have two tables, this guy must move, say, over here, and you only have room for one more guy, so you have two tables, four students. When you have three tables, this guy who is sitting there must move here, so again, you only have room for one more person, three tables, five students. When you have four tables, this guy moves here, and a new guy comes and sits here. So again, only one new guy comes in, and this pattern goes on, so in order to sit 50 students, since the difference between the number of students and tables is always two, you would need 48 tables. Now, in reality, all these strategies come together when you're solving complex problems, and we will see how to solve some of those problems and how all these strategies come together in the process that I called the three-step cycle of problem solving. Thank you.