[MUSIC] In this video, I'd like to look at an example of how questioning assumptions can help solve problems. To do this, let's take another look at the nine dot problem from Lesson 2.1 B. You might remember that the problem asks you to draw the nine dots as shown, and then draw four straight lines which go through the middle of all of the dots without taking the pencil off the paper. How did you go? Were you able to work it out? If you couldn't, you're not alone. Indeed, only 5% of college students given this problem are able to solve it within a few minutes, and only 20% are able to solve it after being given a clue. Now try it again, but this time for each step, explain to yourself why you chose to do it. Why are you starting there? Why are you stopping there? Why are you turning your pen at this particular point? Think about what constraints you put on yourself while attempting this puzzle. In this step, it's really important that you're honest and that you're thinking about what you're thinking. Take a minute to note some of the thoughts you have while doing it. Feel free to pause the video while you do the problem again. Let's take some time now to reflect on our thoughts and think about which are facts and which are assumptions. If we follow the first step in our problem solving process and take time to understand the problem, we get the following facts. Number 1, there are nine dots arranged in a 3x3 square. Number 2, we can draw no more than 4 straight lines. Number 3, the lines must be connected. Number 4, the pen cannot leave the paper. And number 5, you cannot retrace a line. These are the facts of the nine dot problem. But by talking with yourself, you may have realized that on top of these facts, you are making some of the following assumptions. Number 1, lines cannot go outside the square. Number 2, lines must go through the middle of the dot. Number 3, lines can only turn on a dot. Number 4, the problem exists in 2D space. And number 5, you can not manipulate the paper. How many of these assumptions did you make? Researchers think that these common assumptions are the reasons why people have difficulty with the problem. Number 1, in fact, is such a common problem that the English language created an idiom out of it. Namely, think outside the box. If you've ever wondered, what exactly is the box, here you have it. It's important to note that these are incorrect assumptions. They are imaginary constraints that for different reasons we place on ourselves, while attempting to solve the nine dot problem. The purpose of this problem is not because you come across many such connect the dot problems in your life, but because it should remind us, challenge constraints, deny the negatives, question every assumption you make. Assumptions like these should always be tested. [MUSIC]