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A Maths Puzzle: The Missing Square Solution


Hello, everyone! Last time, I showed you this puzzle. Now, this is a 7 by 7 unit square, and I can show you that’s true by using this transparency. I’m just going to lie it on top. So you can see it’s a 7 by 7 unit square, which has an area of 49 square units. And then I showed you that something strange happens when I move the pieces. So let’s do that. If I move the pieces and I just put these final pieces back in, what happens is we end up with this missing square right there in the center of the puzzle. Now, why is that? Well, in fact, what we’ve made is a rectangle, and I can show you this as well. Using the transparency again, If I put that on top, and I hope you can see this, what we’ve got here is a slight gap there, just underneath the square. In fact, what we’ve made is a 7 by 7 and 1/7 rectangle, which has an area of 50 square units, which explains then why we’ve got 49 square units here, and then one in the center. Now, these puzzles have been around for a long time, at least 150 years. Lewis Carroll used to do one. Sam Loyd, the American puzzle expert, used to do them, as well. But this is one of the best I’ve seen, because the ones I’ve seen before, tend to do this trick with the gradients, which means you end up with gaps when you have to sort of fudge it, a little bit. And I like this one, because everything is nice and flush. So that’s one of the best I’ve seen. Credit where credit is due, I first saw this in an Ericsurf6 video a couple of years ago. And that’s it for now. So if you have been, thanks for watching.

Bernard Jenkins

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