Maybe you saw this puzzle before and you remember the solution. That's one way to solve it. That's great. But if you wrote down that solution and stopped or simply felt that you saw it before and remembered it and would just continue on, then I'm going to point out right now that this was intended to be a puzzle to illustrate creativity, and you decided to rely on habits instead, that's pretty common actually. Why be creative if we have a solution and it works. Well, we might find a better solution, and we might learn by finding different ways of solving even the same problem. It's helpful to remember though that creativity usually only happens when we stop relying on habits of mind and our usual ways of behaving. For those of you who are new to the problem, never seen this before, here's the classic solution. This puzzle is the origin of the phrase, think outside the box because you have to draw outside the box formed by the dots, to generate it. But people told to draw outside the box don't seem to do any better at the problem. Instead, the problem seems to be that too many dot-to-dot puzzles when we were children. If you did too many dot-to-dot puzzles, then it may make you think that the action of drawing lines has to connect two lines at a dot. But we could take a different perspective on the action of joining lines, and in that case, new solutions are possible. Now, what about the other solutions you generated or did you just generate one solution and stop? This is a creativity problem. Why would you stop at the first solution you found rather than continue to see if you could find another one, maybe a better one. This is another tendency that keeps us from being creative. It's often difficult to go through a creative process and change our perspectives. It's much easier to rely on habits, and it's even easier still to just watch the video and let others do all the work. But you're trying to learn to be creative, so give it a try. Try to change your perspective on the problem and see if you can generate another solution. The way I would generate another solution is to think about PAGES. What are the parts of the problem? Well, there are some dots. That's obviously a part of the problem. We can think about them a little bit. There, dots, spots on a page, polka dots arranged in a rigid way, little circles, dots, and circles can be little, but dots and circles can also be big. What if we made a change and drew the dots a little bigger? What would that do? Now when we draw lines, the lines might only go through the edge of a dot instead of the middle of the entire dot. That gives us an opportunity for a solution with just three lines. Well, if the dots can be small or large, what if we think about another part of the problem and change that? What about the lines? Lines can be thin, lines can be thick. If we have a really thick line, we could draw a single line that goes through all nine dots. What about the other parts of this problem? We talked about the dots, we talked about the lines. What else is there? Well, what about the paper? What thoughts do we have about that concept? Perhaps we've been assuming the paper needed to stay flat, but we can make changes to the paper. For example, we can roll the paper in a cylinder, tilt it a little bit and draw a line around and around that goes through all nine dots. That's another solution. Any other assumptions we're making when we're thinking about the paper? My younger daughter's favorite solution to the problem is this one. Who said the paper had to remain whole? What if we rip the dots out of the paper, put them in a line, and draw a line through them all. At this point, we have seen changes to parts, dots of different sizes, lines of different sizes, paper shape, changes to actions, lines connecting dot to dot, ripping dots out of the paper, and changes to our goals, a four lines solution, a three lines solution, a one line solution. These changes might have seemed delightful, but sometimes some people think these changes seem like cheating. This happens with creativity when you're changing perspectives. Sometimes you find yourself thinking that you are breaking the rules. Worse, sometimes a change that you think is creative, other people think is breaking the rules. Creativity can be dangerous, disruptive, threatening. What might make someone upset about our discussion of this problem? Well, I usually find that people who think these solutions are cheating have taken a perspective drawing from geometry. They think the event here is to solve a geometry problem. Their self-concept includes the value that it is good and appropriate to adhere to the rules of classic Euclidean geometry. The dots are points, the line is a classic geometry line so it has no width, and everything is set in a single plane. In this case, the classic solution is probably still perceived as a genuine solution, but everything else probably feels like cheating. One question is, why did we take this perspective on this puzzle? Why was this a geometry event? Why was their self-concept so committed to that interpretation? But, okay, let's take that perspective as a given. Is there anything we can do? One of our colleagues here at Illinois proposed a solution following from an observation of Einstein's. All parallel lines meet at infinity, we'll leave it to you to decide if this counts as not picking up your pen. The nine dots puzzle is a classic problem in the history of creativity. The nine dot puzzle is a classic in the history of creativity. I think that's fair to say. I mean, there are tons of papers using it. Have you used it? Absolutely, in classes over the years. It seems like people approach it in so many random ways. But the nice thing about PAGES is that it gives us a systematic framework for thinking specifically around how do we approach the problem and solve it more deliberately. Yeah, well, in which what was changing when they came up with that seemingly random solution. Right. They flip the event or they flip the part. All those insights can, we don't have to reinvent the wheel, we have a way of getting there through a systematic process. Yeah, and there are wonderful histories on this. If you're really jazzed by the nine dot problem, I think one of my beginnings of this was James Adams work in conceptual blockbusting, a really fun book with eight million ways to change your mind. It's traveled far from there. There's a Taco Bell ad campaign think outside the bun. [inaudible] How far we follow. Yeah. Yeah, and that was the reason to use it here. Let's start with a classic problem, but I think the fun part from here is maybe we can move on and look at this and maybe some other problems that are a little more every day, a little more approachable and see PAGES work there too so that we can think about how we can use it to systematically change our thinking and generate new solutions. Sounds good. Yeah.