0:18

Maybe you saw this puzzle before and you remembered the solution.

Â That's one way to solve it, right?

Â That's great.

Â But if you wrote down that solution and stopped, or

Â simply felt that you saw it before and remembered it,

Â and we just continue on, then I'm going to point out right now that this was intended

Â to be a puzzle to illustrate creativity, and you decided to rely on habits instead.

Â That's pretty common, actually.

Â Why be creative if we have solution and it works?

Â Well, we might find a better solution.

Â And we might learn by finding different ways of solving even the same problem.

Â It's helpful to remember though that creativity usually only happens

Â when we stop relying on habits of mind, and our usual ways of behaving.

Â For those of you who are new to the problem,

Â never seen this before, here's the classic solution.

Â 1:07

This puzzle is the origin of the phrase think outside the box,

Â because you have to draw outside the box formed by the dots to generate it.

Â But people told to draw outside the box,

Â don't seem to do any better at the problem.

Â Instead the problem seems to be that too many dot to dot puzzles

Â when we were children.

Â So if you did too many dot to dot puzzles then it may make you think

Â that the action of drawing lines has to connect two lines at a dot.

Â But we could take a different perspective on the action of joining lines, and

Â in that case new solutions are possible.

Â Okay, now what about the other solutions you generated, or

Â did you just generate one solution and stop?

Â This is a creativity problem.

Â Why would you stop with the first solution you found,

Â rather than continue this if you could find another one, maybe a better one.

Â This is another tendency that keeps us from being creative.

Â It's often difficult to go through a creative process and

Â change our perspectives.

Â It's much easier to rely on habits.

Â And it's even easier still to watch the video and let us do all the work.

Â But you're trying to learn to be creative, so give it a try.

Â Try to change your perspective on the problem and

Â see if you can generate another solution.

Â [MUSIC]

Â The way I would generate another solution is to think about PAGES.

Â What are the parts of the problem, well there are some dots.

Â That's obviously a part of the problem.

Â We can think about them a little bit, they're dots, spots on a page, polka dots,

Â arranged in a rigid way, little circles.

Â Dots and circles can be little.

Â But dots and circles can also be big.

Â What if we made a change a drew the dots a little bigger?

Â What would that do?

Â Now when we draw lines, the lines might only go through the edge of a dot

Â instead of the middle or the entire dot.

Â That gives us an opportunity for a solution with just three lines.

Â 3:25

What about the other parts of this problem?

Â We talked about the dots.

Â We talked about the lines.

Â What else is there?

Â Well, what about the paper?

Â What thoughts do we have about that concept?

Â Perhaps we've been assuming that paper needed to stay flat, but

Â we can make changes to the paper.

Â For example, we can roll the paper in a cylinder, tilt it a little bit and

Â draw a line around and around that goes through all nine dots.

Â That's another solution.

Â Any other assumptions we're making when we're thinking about the paper?

Â My younger daughter's favorite solution to the problem is this one.

Â Who said the paper had to remain whole?

Â What if we ripped the dots out of the paper, put them in a line, and

Â draw a line through them all?

Â 4:06

At this point, we have seen changes to parts, dots of different sizes,

Â lines of different sizes, paper shapes.

Â Changes to actions, lines connecting not as dot,

Â ripping dots out of the paper and changes to our goals.

Â A four line solution, a three line solution, a one line solution.

Â These changes might have seemed delightful.

Â But sometimes some people think these changes seem like cheating.

Â And this happens with creativity.

Â When you're changing perspectives,

Â sometimes you find yourself thinking that you are breaking the rules.

Â Worse, sometimes a change that you think is creative,

Â other people think is breaking the rules.

Â Creativity can be dangerous, disruptive, threatening, so

Â what might make someone upset about our discussion of this problem?

Â Well, I usually find that people who think these solutions are cheating have

Â taken a perspective drawing from geometry.

Â They think the event here is to solve a geometry problem.

Â And their self concept includes the value that it is good and

Â appropriate to adhere to the rules of classic Euclidean geometry.

Â The dots are points.

Â The line is a classic geometry line that so it has no width.

Â And everything is set in a single plane.

Â In this case,

Â the classic solution is probably still perceived as a genuine solution.

Â But everything else probably feels like cheating.

Â One question is, why did we take this perspective on this puzzle?

Â Why was this a geometry event?

Â And why was there a self concept so committed to that interpretation?

Â But okay, let's take that perspective as a given.

Â Is there anything we can do?

Â One of our colleagues here at Illinois proposed a solution following from

Â an observation of Einstein's.

Â All parallel lines meet at infinity.

Â We'll leave it to you to decide if this counts is not picking up your pen.

Â The nine dot puzzle is a classic problem in the history of creativity.

Â [MUSIC]

Â The nine dot puzzle is a classic in the history of creativity.

Â >> [LAUGH] Yeah, I think that's fair to say.

Â >> [LAUGH] I mean there are tons of papers using it.

Â I mean- >> Right.

Â >> Have you used it?

Â >> Absolutely, in classes over the years, right?

Â And it seems like people approach it in so many random ways, right?

Â But the nice thing about PAGES is that it gives us a systematic framework for

Â thinking specifically around how do we approach the problem and

Â solve it more deliberately, right?

Â >> Yeah, and well,

Â what was changing when they came up with that seemingly random solution, right?

Â >> Right, right, right.

Â >> They flipped the event, or they flipped the part.

Â >> Right, and so all those inside skin, we have to reinvent the wheel.

Â >> [LAUGH] >> We have a way of getting there through

Â a systematic process.

Â >> Yeah, yeah.

Â No, and there are wonderful histories on this.

Â So, if you're really jazzed by the nine dot problem,

Â I think one of my beginnings of this was James Adams work and conceptual block

Â busting, sort of a really fun book with 8 million ways to change your mind, right?

Â >> Right.

Â >> And- >> It's travel far from there, right?

Â >> [LAUGH] >> There's a Taco Bell ad campaign,

Â think outside the bun, right?

Â >> [LAUGH] >> [LAUGH]

Â >> How far we've fallen?

Â [LAUGH] So yeah, and that was the reason to use it here,

Â let's start with a classic problem.

Â But I think the fun part from here is maybe we can move on and

Â look at this in maybe some other kinds of problems that are a little more every day.

Â A little more approachable, and see pages work there too, so that we can think about

Â how we can use it to systematically change our thinking and generate new solutions.

Â >> Sounds good.

Â [SOUND]

Â