 This is a mathematical snack from the Association of Teachers of Mathematics. This is called forest fires. We're going to model how a forest fire might spread. In each of these squares I want you to imagine a tree. A lightning strike sets this tree here on fire. So right at the beginning I have one tree burning. The fire spreads according to this rule that in every adjacent square the tree will catch fire. I'm going to use blue and hopefully you'll be able to tell the difference between the original one in black and here's blue. So that catches fire, that catches fire, that catches fire and that one does also. The diagonal trees don't catch fire in this particular model. We've now got five trees burning or burnt. Make a note. Let's see what happens over the next hour. Each of those blue trees will set off another tree. I'm drawing them in pink so you can see. So that will be set off by both trees, won't it? That one, not that one, this one. Let's see how many trees are now ablaze. One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen. We have thirteen trees ablaze. We'll work the next one together as well. Each pink tree sets off another tree. So here we go. That pink will set off that tree over there. Definitely that one and that one. Let's count. See how far we've got. One, two, three, four, twenty one, twenty two, twenty three, twenty four, twenty five. I want you to continue this. Start looking for patterns and then we can make predictions. Can you predict how many trees would have burnt down in ten hours? And how long before five hundred trees have burnt? I'll leave that for you to work on.