Question number 27. Which of the following nets cannot be folded into the solid as shown over here? So for this problem, visualizing the nets folding is pretty much necessary. And so we will have to go through this one by one to see how they end up being folded. So for A, let's match this plus on the net to the plus in this box. So in order to do this, fold the net along the edge between this dash over here and the plus right here. And now the two dashes over here and the plus match with the picture. Of course, the blank squares adjacent to the plus can be folded to make the back face. And then these will be folded down to make the top face. And with that, we also get these two lines that are necessary for the solid to be made. And then the rest of the squares kind of wrap it up to make a perfect box. And A is possible and can be eliminated. Moving on to B, the edge between this plus and this plus has to be a folding edge because one of the two pluses must be visible, but the other one is not. So if we take this left plus and we match it up over here, we can't form a box actually because there's some overlap between some of the squares and the box ends up not being able to be formed. So we have to use the right plus to match up over here. So if the other plus is not visible, then the square of the invisible plus is either a part of the back face over here or a part of the bottom face. If it's the first case, then one of the dashes of the top face is incorrectly parallel to the dash of the front face. So that means this is in the wrong orientation when this plus is a part of the back face. And if we kind of visualize this, what we'd have to do is we'd have to flip this and I believe this one would be the one that is parallel to the ones on the side. Or sorry, this one. Yes, this one would also be horizontal as these two are the ones that correspond to this. And this one would be parallel or also horizontal and this one would be vertical. In the second case, if this plus is on the bottom face, then we find that all four, it would be these four that are visible over here. And all four of them are, of course, incorrectly parallel. So it is not possible to make the given box from B. In the competition, you might want to stop there. But maybe B is not the answer that you get to second. And so for the sake of this video, we'll go through every single one of these answer choices. So for C, notice that these two dashes and the two verticals are already adjacent to one another. So that is basically what's over here. Quite simple. So we fold these such that they become the top faces and the two dashes remain the front face. And then the two squares directly above these two squares over here are folded to become the back face. And so these guys are not visible. These two become the bottom face. And then this becomes this face on the right. This one is also not visible. So C is quite easily shown to be possible and can be eliminated as an answer choice. So for D, we can match this is the only plus that we have. We can match this plus to the plus of the box and we fold it along this edge right here. And then we fold this blank square to the left of this minus to make this face on the left. And then we can fold these two down to form the top faces. And of course, these remain. Once we do that, these two dashes become vertical and these dashes remain horizontal. And that solves into this solid. So finally, for E, match this right plus on the net to this plus. And then we fold along this edge over here and then this edge over here. And then very similar to in this problem where these dashes become vertical, the same thing happens and they become vertical over here and they are perpendicular to these. The back face is made up of this one and this square and it's totally blank. And the top and the front faces match the picture. So E is also possible. And that means that, of course, B is the only one that is not possible. B is the correct answer. With some luck, maybe you get to B earlier. If you don't, then, well, that's just unlucky. Hopefully that makes sense and you're able to visualize how all of these nets are formed.

visualization

solid shape

net folding

incorrect alignment

step-by-step analysis