# Questions tagged [dissection]

A geometric puzzle where a given figure has to be cut into a number of pieces subject to a number of constraints.

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### 3³+4³+5³=6³ Puzzle

A classic puzzle asks us to break a 6x6x6 cube into the smallest number of pieces which can be reassembled into 3 physically separate cubes of sizes 3, 4, & 5. 3³+4³+5³ =27+64+125 =216 =6³ An 8-...
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### Make a square table top with the minimal needed amount of straight cuts

inspired by : Make a square table top with six (or fewer) pieces A carpenter has three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square, respectively. They want to use ...
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### Make a square table top with six (or fewer) pieces

A man had three pieces of beautiful wood, measuring 12 inches, 15 inches, and 16 inches square respectively. He wanted to cut these into the fewest pieces possible that would fit together and form a ...
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### A pizza dilemma

You are a waiter at a restaurant. The restaurant is known for its signature dish: the Donut Pizza. The Donut Pizza is a 5-inch square pizza with a 1-inch square hole in the middle. After several ...
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### Pythagorean pentagons

To follow up on the theme of so called "pythagorean" dissections, here is one more for you to chew on. I hope you don't get bored. The pentagons above have sides respectively 3, 4 and 5. ...
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### Dissect this figure into four pieces which can be reassembled to form a square

How can you cut this figure into four (not necessarily identical) pieces which can be reassembled to form a square? Rotating and flipping the pieces is allowed. Hole(s) in the final square are allowed....
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### Dissections of the "hat" aperiodic monotile

We all know the "hat" monotile by now, right? It can obviously be dissected into 8 congruent kites, or 4 congruent pentagons. Can it be dissected at all into 2 congruent shapes? What about 3?...
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### A dissection puzzle where you're allowed to use dilation

You may be familiar with Dudeney's famous dissection of the equilateral triangle into a square. (A nice physical version is demonstrated here.) His dissection uses four pieces. I believe this to be ...
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### Dividing a square field into 5 equal regions

A farmer has a 10m x 10m field that has fences around the perimeter. What is the least number of 1m fences he needs to add to divide the field into 5 regions of equal area?
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### Put three pieces of cake into a round box

You're about to cut three pieces from a large cake to put in a round box of radius 1. If the pieces must be congruent triangles, and cannot overlap, what shape gives you the maximum amount of cake?
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### Breaking the Heart geometrically

The King of Geometro nation has 2 very smart wives. On the Geometro Wives day he gets a nice heart shaped cake made. It has a number of icing flowers on it. The King wants to split the cake in half so ...
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### Three lines to get twenty triangles

Shown below are five squares. Starting at any point, draw three straight lines without lifting the pen, and create exactly twenty (20) triangles. It is understood that this will create some other ...
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### Ernie and the Christmas Stars

Although Ernie professes to be an atheistic rationalist, he does love the Christmas season. He thinks long and hard to find appropriate gifts, brushes up on his Christmas Carol repertoire, plans a ...
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### Dissecting a figure into 2, 3, 4, and 5 parts but not 6

This figure is divided in 2, 3 and 4 equal parts of same size and shape, but it is not possible to do it in 5 equal parts of same size and shape. Is it possible to find a figure that can be divided ...
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### A piece of paper repeatedly cut into 8 or 12 pieces

You are given a piece of paper. It will be cut into 8 or 12 pieces. Each of those new pieces can be cut again into 8 or 12 pieces or left uncut. This process is (theoretically) repeated as often as ...
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### Dissecting a figure into three congruent parts in three different ways

Figure 1 is divided in 2 equal parts of same size and shape in 3 different ways Figure 2 is divided in 3 equal parts of same size and shape in 2 different ways Is it possible to find a figure that ...
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### Clash of the Robinsons

"Ridiculous!" you think "What can be the odds? Either I'm hallucinating or the amateur writing this story plunged to new depths of incompetence." Both being equally likely you don'...
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### Ernie and the Cuboidal Crystals

When passing Ernie's letterbox this morning, I found a courier bag about the size of a shoe-box, resting inside (along with a smaller unlabelled bag). I immediately guessed that it was the special ...
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### Pythagorean triangle dissection

This is a variation of Pythagorean quilts. I will make it short, this time. Pythagoras's theorem also works for triangles. This leads to the following variation: Dissect the triangles of size 5 and ...
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### Cutting off one's nose to spite one's eyes

Disclaimer: to keep graphic depiction of gratuitous violence to a minimum the face to be spited has been deliberately kept abstract. You are required to further reduce any distress this puzzle may ...
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### Any comparison between some variations of T puzzles? [closed]

I spent time to experience some variations of the classical T puzzles in here - a kind of dissection/tiling puzzle (Gardner's T, Nob's T, and Asymmetric T). They are 4-piece tangrams. They all give ...
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### 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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### How can the white cross be cut into 5 smaller pieces that can be resembled into the two smaller red crosses shown?

How can the white cross be cut into 5 smaller pieces that can be reassembled into the two smaller red crosses shown? Puzzle created by Henry Dudeney on The Strand Newspaper long time ago. Source: Saw ...
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### Hollow Cube Cuts

The 2x2x2 inches seamless hollow cube with aluminum surfaces can be cut using a box knife. How to cut it into 4 pieces that can be bend to form smaller 1 inch cubes?
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### Making *9* congruent triangles from the pieces of a triangle dissection

Working on the making 7 congruent triangles from the pieces of a triangle dissection question I realized it's possible to do even better! So here it is for extra points: Use six lines to cut a ...
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### Making 7 congruent triangles from the pieces of a triangle dissection

I got this challenging geometrical conundrum from a Russian geometrical magazine. It states: (A. Soifer) Use six lines to cut a triangle into parts such that it is possible to compose seven ...
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### Sharing a field among 4 sons

A wealthy famer has a large estate in the shape of an irregular squarish octogon. In the middle he has a rectangular retention basin for storing water. He is getting old and discusses with his wife ...
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### Can you fold a square into a square of one-fifth the area?

I love origami, and it recently gave me an idea for a very hard but beautiful puzzle. I'm really curious whether anyone here can solve it. So here's the puzzle. You are given a large perfectly square ...
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### Picture puzzle: Leaf to Heart

Background Once upon a time there lived a poor man. He was so poor that he had nothing but a low-quality scissor that could only cut three times. On Valentines day, he wanted to make a card for his ...
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### Pythagorean quilts

The King requests Pythagoras to his palace to discuss an important matter. After the usual formal greetings the King asks: - I have been told that you have a marvelous formula about adding squares ...
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