# Why box (3) isn't possible and why box (4) is possible?

The figure given on the left hand side is folded to form a box. Choose from the alternatives (1), (2), (3) and (4) the boxes that is similar to the box formed.

Source: IndiaBix

I understood that box (1) and (2) are possible from given figure but I can't understand why box (3) isn't possible and how box (4) is possible? To solve this question, we are generally given time of less than 2 minutes. How to solve this question with such a less time. Any tips in solving these type of questions fastly?

• I think it might be helpful for you to physically try a few of these - actually print or draw the design on a piece of paper so that you can fold it and hold it in your hand. Doing it with a physical object might help you be able to visualize new ones. – Rob Watts May 13 at 8:56

Here's a (slightly crude, low-resolution) drawing of how the cube will fold:

• (First version of this answer had a particularly silly mistake on my part - thanks @Chris and @​hdsdv for pointing it out!) – Deusovi May 13 at 9:17

In the unfolded version, the two black and white sides share a vertex to which the diagonal line arrives. It is also easy to see that the other shared vertex will have to be "only white"; the "upper left" vertices of each side (as seen in the unfolded image) will meet.

In (3), the two sides share two vertices:

• One in which one side has the diagonal line, but the other side has a "only white" part.
• One in which one side has the diagonal line, but the other side has a "only black" part.

Since it does not comply with the rules that we can observe from the unfolded dice, they are not the same dice.

• Easier might be to talk about the edge that the two coloured faces share. Both have white along that edge. – Jaap Scherphuis May 13 at 9:11