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The following figure is folded to form a box. Choose from the alternatives (A), (B), (C) and (D) the boxes that is similar to the box formed.

Dice_1 Options

Source: YouTube Video

How to answer these type of questions? How to decide whether triangles will be anticlockwise or clockwise in the closed box?

In the above YouTube video while explaining the answer, he claimed that since 1,2,3,4 are clockwise in given question they will be anticlockwise when they are closed to form a box. Is it true? If true then please prove it.

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  • $\begingroup$ Not sure this answers your question but whether or not the numbers would be clockwise is nearly irrelevant for this question, as the triangles-with-numbers side wouldn't be visible at all in (A), (B) or (C) so the answer must be (D). $\endgroup$ – SQLnoob May 12 at 18:25
  • $\begingroup$ @SQLnoob Could you explain why the triangles with numbers won't be visible in (A), (B) and (C) but will be visible in (D)? $\endgroup$ – Sourabh May 12 at 19:18
  • $\begingroup$ In (A) if you're looking at the folded cube with A on the front and D on the top, the side on the right (where the numbers are pictured) would actually be side B. Similarly in (B) the right side would be C and in (C) the right side would be B. (This assumes the unfolded diagram is showing us the outside of the cube, and we're folding the sides away from us. If it's actually the inside and they fold towards us then (C) would be the correct response.) $\endgroup$ – SQLnoob May 12 at 19:38
  • $\begingroup$ I'd say both C and D are possible, unless there's some unstated assumption about the directions of folds or visible/reverse side of the paper vs. outside/inside of the folded shape. $\endgroup$ – aschepler May 12 at 22:40
  • $\begingroup$ @aschelper (C) isn't possible as with face C at the front and face E in top, the triangle face would have to be on the hidden side (opposite where it is shown). This, of course, assumes that the 'figure' to be folded only has printing on one side (the one we can see). $\endgroup$ – Penguino May 13 at 4:02
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A is impossible because 1 cannot be opposite of 2. 1 is opposite of 3.

B is impossible because there is no edge connecting D and 2.

Now between C and D, one is right and one is wrong. Let's place 3 and E, but with E having the correct orientation (3 is at the bottom of E):
enter image description here

It should now be obvious that the front is A, because A is at the "back" side of E, whereas C is at the front. Thus, (D) is correct.

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  • $\begingroup$ I didn't understand the explanation for option (C). Could you explain it in more simpler terms on how you have arrived that E should be facing upwards rather than front facing as shown in option (C)? $\endgroup$ – Sourabh May 23 at 5:06
  • $\begingroup$ Well, the letters of the options you are given represent the edges, but do not show correct orientation, like my explanation did. Else, even D would be wrong. About (C): E cannot have A "under" it, because 3 is under it instead. $\endgroup$ – George Menoutis May 23 at 12:12

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