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Is it possible to connect the opposite numbers (2 and 4, 1 and 3) simultaneously? If not, give me an explanation.

Rules: 1. You can use any shape. (Torus, Möbius loop, etc.) 2. You can use any dimension. (2 and up) 3. No rips.

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closed as unclear what you're asking by f'', Deusovi, JonMark Perry, Aza Jun 30 '16 at 3:29

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    $\begingroup$ What do you mean by simultaneously? $\endgroup$ – newzad Jun 29 '16 at 22:17
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    $\begingroup$ What do you mean by "use any shape"? How are you supposed to "use" a torus? $\endgroup$ – Anon Jun 29 '16 at 23:23
  • $\begingroup$ Err, yeah: I guess you need to be a little clearer $\endgroup$ – Jonathan Allan Jun 30 '16 at 13:19
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Solution

Yes it is, nothing forbids the lines from crossing

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  • $\begingroup$ the question is worded a little poorly, but i believe the OP wants us to physically bend the paper to touch the numbers together. we're not drawing lines here. $\endgroup$ – earora4498 Jun 29 '16 at 22:34
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    $\begingroup$ @earora4498 What about the question title? $\endgroup$ – Anon Jun 29 '16 at 23:24
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It is possible to make all sides touch.

Make an origami square base and all the numbers touch

http://www.origami-instructions.com/origami-square-base.html

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Yes. So long as you are willing to accept two edges joining along their whole lengths simultaneously. If that is OK then 2x pairs of lines joining simultaneously is all you need. See visual below:

enter image description here

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    $\begingroup$ +1 for being the only one "visual" here. $\endgroup$ – BmyGuest Jun 30 '16 at 12:35
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It can be done.

Roll two sides backwards (make a cylinder with the numbers on the outside). It doesn't matter which numbers you pick, but for convenience lets say we started with the sides containing 2 and 4.

The boxes with 2 and 4 should be overlapping facing each other between the sides of the paper, the boxes with 1 and 3 should be on the opposite side of the cylinder, visible and in line with each other. Flatten the cylinder, keeping the overlap so the two boxes in back still touch, and having the other numbers front and center on the narrower strip remaining.

Double check - the paper should be a little less than half as wide, since both sides are folded towards the center of the page, with perhaps a half-inch (box sized) overlap in the middle). Then, take the flattened cylinder, and fold it forwards so the two remaining numbers (the 1 and 3 boxes) touch. The opposing pairs of numbers are touching simultaneously

Or, to put it another way (if my previous explanation got lost)

Turn the paper over. Fold one side (say, the side with the "2" box) over so the edge is a little over the center - about a half box-width (or maybeso a quarter inch) further than halfway across the page. Take the opposite side (with the "4" box) and mirror the fold, it should be slightly more than halfway across the centerpoint, giving a page that's about half as wide as it was, with a half-inch (or whatever the box length is) overlap.

The numbers will not be visible, but they are facing each other between the overlap of the sides. Turn the paper back over, and the remaining boxes ("3" and "1") should be visible at the center top and bottom of the narrower strip of paper. Fold the paper forward, so the numbers overlap - simply in half lengthwise will do. Both sets of boxes are physically overlapping each other at this point.

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