Problem number nine. You have to close two of the five gates so that the mouse cannot reach the cheese. Which gates should you close? A, one and two, B, two and three, C, three and four, D, three and five, E, four and five. One way to solve this problem is to work backwards. We can go through the gates and see if we can reach the mouse that way. Because if we can, then the mouse can reach the cheese through the gate. If we can't, that is not a gate that the mouse can reach the cheese through. And therefore it's not a gate that we need to close. Let's start with gate one. If gate one is closed, the mouse cannot walk through here. To get to that point, the mouse could have come from the right, which she already would have been able to get at the cheese, or she could have come from the top. So following this up, here's a dead end. Going back this way. Another dead end. Go around. That's a dead end. Can get in here. Now we're to gate two, so we'll have to check that again. Or she could get back to the cheese. And if the mouse had not taken that turn, she can go in this area, which is a dead end. Unless the mouse is already coming for where the cheese is, closing gate one is not going to keep her from going anywhere. Now let's look at gate two. Gate two closes off this area. And to go through it, it seems like the mouse would have come the same way as from gate one. It almost makes a loop and that the mouse could go around here and walk through. But again, to get in here, the mouse would have already had to been by the cheese. So closing gate two is not going to help anything. So now we can eliminate answer choice A because gates one and two are not the ones that need to be closed. It also should eliminate answer choice B because gate two is not one of the two gates that has to be closed. But let's double check that. Gate three is right here. Let's see if this is a path that the mouse could have taken. Go back here. It's pretty much a dead end. So that does not keep the mouse away because the mouse can't even get here in the first place. That leaves us with gates four and five. Let's see if those are the two gates that the mouse can use to get to the cheese. Gate five is right here. If we close it, the mouse could have come like this. It's tracing the path backwards, it gets us to the mouse. And if the mouse had come that way, it could have also gone like this. And if gate four is open, she could get in. If it were closed, she has to go around. Here hits a dead end. So both gates four and five connect the mouse to the cheese. And also we see that if we close them, there's no way that the mouse can get to the cheese. So the answer is E. Gates four and five need to be closed.

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