# Questions tagged [paper-folding]

A puzzle based on the folding of a piece of paper (also known as origami).

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### ORIGAMI: Above and beyond

It's been a long time since I've posted an origami puzzle! An origami puzzle is solved with some thickness $x$ iff it can be folded into a rectangle (possibly a square) with thickness $x$ everywhere. ...
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### An infinite series of origami puzzles

fold the 3 shapes below into rectangles with two layers of paper everywhere. the white part of the image is the puzzle. I'm sure you noticed the pattern in the shapes. now extend it and solve all ...
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### origami SNY t28

It's been a long time since I've posted an origami puzzle! Fold the shape into a rectangle such that the rectangle is 28 layers thick everywhere. The purple part is the puzzle. Although solutions are ...
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295 views

### origami J-SHAPED t2

It's been a long time since I've posted an origami puzzle! Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The red part is not included in the puzzle; the purple ...
• 3,183
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### ORIGAMI PUZZLES completed version

You may have seen some posts by Sunny Lu here on my origami puzzles. Now, the full version is out! The goal is to fold the paper into a rectangle (or square) with constant thickness (see examples), ...
• 405
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### 🐍 In the Loop 🐍

Follow the ouroboros down valleys and over mountains. Is it even going anywhere? EDIT (7 days after initial posting): The grid and Penpa+ link have been updated to an easier version, with more numbers ...
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### April Fools Origami Update

Me (Sunny Lu) and Ωmega_3301 have made a special April Fools edition of origami puzzles. The objective is to fold a shape into a rectangle with uniform thickness. The thickness will be given to you. ...
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### origami WAVE t2

Fold the shape into a rectangle such that the rectangle is 2 layers thick everywhere. The grey part is not included in the puzzle; the purple part is the puzzle. Although solutions are not required ...
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### origami USHAPE t3

Fold the shape into a rectangle such that the rectangle is 3 layers thick everywhere. Although solutions are not required to be applicable in real life, using an actual sheet of paper is a great ...
• 3,183
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### ORTHOGONAL origami FISH t8

Since the last puzzle got cheesed, we're adding a new restriction (in italics) Fold the shape into a rectangle such that the rectangle is 8 layers thick everywhere. All folds must be orthogonal ...
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### origami FISH thickness 8

Fold the shape into a rectangle such that the rectangle is 8 layers thick everywhere. A puzzle for this type of orgami puzzle game made by Ωmega_3301, similar to this question.
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### Folding to One Triangle

Given a strip of 10 equilateral triangles, how many folds are necessary to reduce it to a single equilateral triangle? You may only fold along the grid lines. Multiple folds along collinear segments ...
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### Seven octahedral nets to cover an octahedron

After solving Cover a single cube with FIVE identical cube nets I had the idea for this puzzle, which may be regarded as a natural generalisation to triangular grids. Find two different nets, A and B, ...
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### Cover a single cube with FIVE identical cube nets

Start with five identical cubes: Your challenge: Cut and unwrap all five cubes into five identical cube nets. Show how to re-fold these five cube nets to form the surface of a single larger cube, ...
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### A Weapon or a Toy?

This puzzle is part of the Monthly Topic Challenge #5: On-and-onogrami Hello, fellow puzzlers! Here's a nonogram I made for you. But it's not just a nonogram. There is a hidden object in it! Can you ...
• 7,311
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### A pentagon using less than 5 lines

A pen and paper challenge: Draw a pentagon on a piece of paper only draw straight lines draw less than 5 times! The pentagon has to be fully drawn in ink, on the paper in unfolded state. I am not ...
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### Turn two cubes into one!

Here are two identical cubes: Your challenge: Start with two cubes of exactly the same size. Cut the surface of each of these two cubes along its edges and unfold the surface into a 2D shape. (So ...
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If you take a cube, and grow a new cube out from each of its six faces, you will get a "hyper plus sign": This 3D solid has an interesting property. It can be sliced along its edges and ...
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### Creative Paper Folding

Shown below is 6x5 grid drawn on a paper with various numbers (1 to 9) and letters filling the 30 boxes. By folding the paper grid 5 times or less can you get to a 3x3 grid showing only the numbers 1 ...
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### Folding a piece of paper with numbers in sequence

Divide a rectangular sheet of paper with a side length of 2 × 4 into eight 1 x 1 unit squares and label them as shown in the sketch. Then fold the sheet of paper along the boundaries of the square so ...
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### Aluminum Foil Folds and Cut

Your task is to convert a diamond shape monomino that is made from aluminum foil into an x-shape pentomino (see figures). You may fold the monomino and make one straight cut with a pair of scissors. ...
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### Can you produce a wolf's template? Part 2

Here is the first question. You are given a square piece of paper with no marks on it. With this paper, you have to make a wolf's template. You are given no tools such as a ruler or scissors, and all ...
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281 views

### 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 ...
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210 views

### Dissection puzzle from the Gardner's book. How to define points without tools?

The figure shows a fairly well-known puzzle from the book by Martin Gardner. You need to cut the regular hexagonal star into pieces and fold the square. Question: how to define points (marked in red) ...
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### Can you fold a square into a square of one-third the area

I do not love origami, but Mitsuko gave me an idea for a extremely hard and (not that?) beautiful puzzle. I'm really curious whether anyone here can solve it. So here's the puzzle. You are given a ...
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### Ernie and the Lock-down Puzzle

During lock-down I was feeling a bit lost for something to do, so one one day I sent Ernie a text reading "Bored". He responded with a text-less message and an attached image (see below). I ...
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### Two chunky pixelated X's locked in mortal combat!

In this dramatic image, we witness two rather chunky pixelated letter X's (having recently fattened themselves up for the approaching winter) locked in mortal combat, fighting to the death for the ...
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### Wrap a squashed, bullet-riddled lowercase lambda around a cube

The following rather squashed and bullet-riddled lowercase lambda: ...can be wrapped onto the surface of a cube in a way that perfectly covers the entire cube, with no gaps and no overlaps. How can ...
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220 views

### Icosahedron-Wrapping Monstrosity

The following monstrosity of a shape: ... can be wrapped onto the surface of an icosahedron in a way that completely covers the entire icosahedron with no gaps and no overlaps. How can it be done?
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The following tri-bladed boomerang shape: ... can be folded onto the surface of an octahedron in a way that perfectly covers the entire octahedron with no gaps and no overlaps. How can it be done?
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### A Slightly Moth-Eaten Integral Sign

The following slightly moth-eaten integral sign: ... can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done? (You ...
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597 views

### Wrapping a Galaxy Around a Cube

The following galaxy-like shape: can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done?
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### Early 1900's Paper Puzzle - Release the Key and Live Forever

This puzzle was found in an old attic and was a religious invitation. Release the key and you could send it in to receive a Bible based book. Apparently 1000's were made but I can find no more other ...
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1 vote
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### What does this message in paper say? [closed]

You wake up in an old horse wagon and get a piece of paper with strange symbols. What does it say? //Anyone can help me. Please!
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### Ernie and the Superconducting Boxes

I was in anticipation all last week. Ernie, who had been travelling for several months, was finally coming home. So over the weekend I dropped in on him. He was bursting with news. "Some wonderful ...
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### Cover a cube with four-legged walky-squares!

This is a four-legged walky-square: This shape has an interesting property: It is possible to map multiple copies of this shape onto the surface of a cube in a way that perfectly covers the entire ...
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### Can you perfectly wrap a cube with this blocky shape?

The following blocky shape: can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can it be done?
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### Can you cover a cube with copies of this shape?

The following shape has an interesting property: It is possible to map multiple copies of this shape onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no ...
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### How can this shape perfectly cover a cube?

The following shape: can be folded onto the surface of a cube in a way that perfectly covers the entire cube with no gaps and no overlaps. How can this be done?
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### Number of folds to form a cube, using a square paper?

Take a square paper of size $S \times S$ units and thickness 1 unit. How many half folds should we do to form a cube out of it? Consider infinitely foldable paper.
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### Folding a paper wouldn't be this hard

Alice and Bob started to play a game with a piece of A4 paper. Alice is going to cut that paper as she wants and will give it to Bob, then Bob will fold the paper from anywhere he wants. In the game, ...
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### How to make someone open an origami?

I'm offering someone an origami (rabbit shape) with a QR code written inside. This is the beginning of a series of riddles. My question is, how could I make the person I'm offering the origami to ...
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### Reach for the moon

A rectangular strip of 1 mm thick paper has length = 500 m and width = 1 m. It is lying on a horizontal floor and you are allowed to rotate and fold this inelastic paper as often as possible. What is ...
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907 views

### A Pentad of Paper Puzzles

I feel that paper is an underrepresented mechanic in puzzles, so this puzzle explores the many facets of this subject. It's (almost) all lovingly handmade, so please excuse any errors. Orikami ...
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### The Folding Maze

Four years ago, I drew a really nice maze. I have recreated it with the wonders of MS Paint for all of you to enjoy. Just begin at the green START, exit by the red arrow, and don't pass through black ...
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### Create a 1 meter measure

How many folding steps do you need to create a $1 \, \text{m}$ measure from an ideal DIN A0 sheet? This sounds easy, but consider that this paper has edge lengths of $\sqrt[4]{2} \, \text{m}$ and \$\...
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### Fold a standard paper to get a Rhombus

A follow up to the "Create a 3 inch measurement" post. Can you create a Rhombus ( a parallelogram with all sides equal AND which is not a square-- my restriction) using a standard letter size paper ( ...
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### Bigger Yoshimoto Cubes

I have been making a Yoshimoto cube, using 8 cubes. I am assuming, there must be some way to create a Yoshimoto Cube consisting of 27 cubes or 64 cubes (assuming the original formula is 2x2x2). Or ...
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### PFG: A pretty spiral!

PFG = Paper Folding Golf You bought a piece of paper from your local op shop, but your shop is always dodgy. So instead of a normal piece of A4, you got an infinitely long strip, a metre wide. (...
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