# Can you fold a paper, make one hole and produce a bear's template?

You are given a piece of paper with no marks on it. With this paper (A4 or A5 size), you have to make a bear's template.

On the template the sell size is 5 mm, hole is not in scale.

You are given no tools such as a ruler or scissors, and all you can do is fold the paper and make an one hole with nail or hole puncher. You can produce the image anywhere on the paper. But all holes should be used. You can fold paper 7 or less times.

Can you fold the paper, make one hole, unfold it and obtain 12 holes?

• How large is the piece of paper? Oct 22, 2020 at 7:31
• The paper is A5 or A4 size.
– Nick
Oct 22, 2020 at 7:32
• I mean the dimensions respective to the size of the unit square in the grid. Oct 22, 2020 at 7:37
• That makes the sheet of paper somewhat large compared to the image region (I think the image is 11.5cm × 14cm, while an A5 is 14.8cm × 21cm). Is it OK to produce the image anywhere on the sheet? Is it OK to produce more holes as long as it isn't included in the region? Also, if you really have no marks and you need the holes at that precise points, you'll likely end up folding like 256 parallel lines on your paper. Is that OK? Oct 22, 2020 at 8:08
• It really doesn't make a difference if you start with the image already drawn on the sheet; it's just much more tedious if you start with a blank sheet and need to mark the 12 points from scratch. Oct 22, 2020 at 8:10

Yes, within 5 folds, the bear imprint can be made.

The approach taken here is to draw the bear design on the paper and start folding in symmetrical parts to match all the points onto one another.
Steps:
1.Fold the paper in half for symmetry. (fold-1)
all other folds will be done on the folded paper.
2.align the most bottom point and the second bottom point and make a fold in the middle. this is the 2 holes in the bottom. (fold-2)
only one point would be remaining at the bottom.
3.Fold the top trapezium in half. through the normal of the parallel lines. (fold-3)
4.Fold such that the two asymmetrical points of the trapezium match. (fold-4).
only one fold point would remain in the top section
5. Fold such that the bottom fold point matched the top fold point. (fold-5)
6. Punch a hole and unfold the paper completely to get the bear shape.

Note: fold point is the approximate location of the point where we punch as to get the image.
Also, all folds are done by hand, by matching the edges and an approximate location of the fold points, there could be a very precise and accurate way of doing this too, with angles and lengths.
This is a quick way of getting a rough Bear Imprint.

• @AyushGupta, good start on Puzzling. Could you please give a sketch?
– Nick
Oct 22, 2020 at 14:50
• I have added a sketch for the method, its essentially a basic folding to get the imprint. Its not accurate but that could be done with angles and lengths for fixed lengths. Hope the diagram Helps. and @Nick Thank you. Oct 22, 2020 at 15:09
• The picture really clears it up. Oct 22, 2020 at 15:58
• The bear's ear part does not have any kind of symmetry or parallel edges, so F3 does not precisely work. It only works if you allow the holes to be off by ~5mm. Oct 23, 2020 at 1:07
• @bubbler, here is the link puzzling.stackexchange.com/questions/104200/… on new puzzle with real template.
– Nick
Oct 26, 2020 at 23:45