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Questions tagged [geometry]

A puzzle related to shapes, geometric objects (polygons, circles, solids, etc.) of any number of dimensions, relative position of figures, and the properties of space.

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Twelve Labours - #04 Erymanthian Bar

This puzzle is part of the ‘Twelve Labours’ series. Previous instalments can be found here: Prologue | 01 | 02 | 03 Now one crate lighter, Hercules made his way back up the road to the Erymanthian ...
175 views

10x10 divided into the most number of rectangles of different area

How can a 10x10 be divided into rectangles such that there are as many as possible and they all have different area? Can you find multiple solutions that are not mirror/rotation of each other? Good ...
120 views

Rectangles formed from every tetromino, tromino and domino

Can you form a 4x7 rectangle from every tetromino, tromino and domino? There are 5 different tetrominoes, 2 trominoes and 1 domino. Can you find different arrangements that are not mirrors/rotations ...
81 views

In this cylindrical tank, by how much will the level of the water rise? [closed]

there. In the following picture is a puzzling question from a primary school math exercise booklet for selective high school exams in Australia. I don't think enough information is provided to solve ...
73 views

4x7 rectangle divided into 7 different rectangles

Can you divide a 4x7 rectangle into 7 rectangles all of different area? Can you find multiple solutions? Good luck! P.S. @Deusovi wanted me to make puzzles that have an "aha moment", so here is my ...
50 views

7x13 rectangle divided into 13 different rectangles

Can you divide a 7x13 rectangle into 13 rectangles all of different area? Can you find multiple solutions? Note that rotations and mirrors don't count as separate solutions. Here is a similar puzzle ...
264 views

Discrete Peaceful Encampments: Player 3 has entered the game!

Here's a variation of Discrete Peaceful Encampments: 9 queens on a chessboard (which itself is a variation of Peaceful Encampments). You have 4 white queens, 4 black queens, and 4 red queens. Place ...
1k views

Haselbauer-Dickheiser Test no. 3: Circle divided by lines between a blue dots

This is the test no. 3 from Haselbauer-Dickheiser Test. 3. These three circles below all have blue dots on their circumference which are connected by straight lines. These lines divide the ...
359 views

What's wrong with this D20?

Here's a D20 I produced by 3D printing and finishing. Something is wrong with it relative to the intended design. What is wrong and how did it get to be that way? Hint:
152 views

Find the least expense?

You want to build a shop between three roads in the shape of an equilateral triangle. What would be the best location for the shop so that you can reach each road with the minimum transportation ...
7k views

Cut a cake into 3 equal portions with only a knife

You have to determine a way to cut a circular cake into exactly three portions of equal size. The only marking on the cake is a candle in the very center. All you have to work with is a knife that is ...
138 views

Bake and share Fair and square

The chef ask each of the 4 judges to make a single slice on the whole round cake, so they'll all have a 1/5th piece to take. How the judges do it for fairness sake?
262 views

Line segments inside a square

A set of line segments inside or at the edge of a square with side length 1 should be positioned in such a way, that any straight line going through the square must touch or intersect at least one of ...
2k views

Minimum number of lines to draw 111 squares

Find the minimum number of lines to draw 111 squares. For example, you can draw a single square using 4 lines i.e 2 vertical and 2 horizontal. Similar, you can draw a 2 square in the grid using 5 ...
503 views

Three lines through a square

Is it possible to draw 3 straight lines through a square such that they divide it into 7 equal-sized regions?
748 views

Venn diagram with 7 equal regions

Can you draw 3 overlapping circles (Venn diagram) such that all 7 of the formed regions have the same area? For the case of two circles and 3 equal regions I found this answer: https://math....
89 views

Pentagon with sides, diagonals and area that are distinct integers

Can you find a convex pentagon (5 sides) such that all its sides, diagonals and area are distinct integers? Note that a polygon is convex if all its internal angles are smaller than 180 degrees. A ...
390 views

Quadrilateral with sides, diagonals and area that are distinct integers

Can you find a convex quadrilateral such that all its sides, diagonals and area are distinct integers? Note that a polygon is convex if all its internal angles are smaller than 180 degrees. Good luck!...
152 views

Area of the square

Can you find the area of the following square given the known lengths? Good luck!
545 views

4 identical shapes that touch each other?

It is known that one can have 4 shapes in a plane all touching each other, and not 5. You can add requirements to the 4 shape problem: Can you do it with 4 equal triangles? (No) Can you do it with 4 ...
2k views

Matchstick Puzzles

Puzzle #1: There is a matchstick: | Add 2 more matchsticks to make the number, 11. Puzzle #2: There is a palace made out of 11 matchsticks: Move 2 matchsticks to make 11 squares. Puzzle #3: ...
209 views

Unfold a right angle pyramid into a square

This puzzle refers to a feature of right angle pyramid: The relation between the areas of the three perpendicular faces and the diagonal surface area is given as - $S^2_x+S^2_y+S^2_z = S^2_d$ ...
2k views

Partition a cube into 6 congruent tetrahedra

A tetrahedron is a solid shape with four triangular faces, not necessarily regular or identical. Show how to partition a solid cube into 6 tetrahedra that are congruent, meaning identical up to ...
102 views

How many pyramids in a cube?

Knowing that a pyramid volume is computed as 1/3 of base multiplied by the height, how many pyramids may be constructed by connecting the corners of a cube to create pyramids with volume 1/3 of the ...
204 views

Cut a cube into 5 objects

Cut a cube into 5 3D objects with 6 edges each. Hint:
298 views

You could help me, couldn't you?

Introduction I am an enthusiastic geometry student, preparing for my first quiz. Yet while revising I accidentally spilt my coffee onto my notes. Can you rescue me and draw me a diagram so that I ...
674 views

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 ...
111k views

Five Angles in a Star

In a regular pentagram (5-pointed star), the angle in each point is 36 degrees, so the angles in all five points sum to 180 degrees: What about an irregular pentagram, such as the following? Now the ...
3k views

Help me, I hate squares!

There is $5$x$5$ equidistance matrix dot given as below; You need to remove dots from the figure where it will be impossible to form a square by drawing lines between dots at the end. So what is ...
116 views

The ultimate conversion of a square into right angle pyramid

This is a follow up of other puzzles. Here a general case of which the other cases are a subset. Given a square of any size, cut it into four pieces to be reassembled into a right angle pyramid (the ...
6k views

Simple geometry. Or is it?

I've got a regular tetrahedron and a square pyramid. Every edge of the two solids has the same length. If I perfectly attach one face of the tetrahedron to one of the triangular faces of the square ...
7k views

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?
978 views

3D? No-no! 3 Sides

Introducing the Isometric Nonogram! α) "Boar"ing Definition [oink] Column: Blue Part + Green Cell Row: Yellow Part + Green Cell Adjacent/ Continuous cells: Purple Cell + any of the Orange ...
230 views

Coin around shapes: A Geometric paradox?

Here is a circular coin with diameter D Figure A From its starting position the small coin goes completely around a bigger circular body of diameter 4D without slipping, always in contact ...
1k views

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 ...
6k views

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?
2k views

A dozen into six rows?

You were given 12 coins by your friend. He bet that if you could arrange these dozen coins into 6 rows of 4 coins such that it makes two similar shapes, he will give you 12 more coins. How will you do ...
776 views

The distance between David and Eric

Alice and Bob are looking at each other, both turn $10$ degrees and now they both can directly see Claire. If they continue turning in their same directions before, Alice will directly able to see ...
223 views

Shapes with 1/4 area of a quadrilatral

Given nine points connected as described by the black lines. G the middle of AC, I the middle of ED, and H middle of BF. By adding segments connecting points in the drawing, create shapes with area 1/...
269 views

A pyramid from a square

Given a square piece of paper. Cut it into 4 pieces that could be used to create a right angle pyramid - the 4 pieces are the faces of the pyramid.
491 views

Five 5-cent coins touching each other

Is it possible to position five 5-cent coins so that each coin touches the other four coins?
109 views

Run to a point in a triangle in shortest time [closed]

This is a generalization of a puzzle that dealt with an equilateral triangle. Assume three runners with the following speeds - 4.5, 6.2, and 8.7 meters/sec. They are at the corners of a triangle with ...
597 views

How can this fractal shape perfectly cover a certain platonic solid?

The following fractal shape has a surprising property: This two-dimensional shape can be folded onto the surface of a regular polyhedron (one of the five platonic solids) in a way that perfectly ...
8k views

A blanket for my baby snake

Mama snake wants to knit a blanket for little baby snake. She is not a dissipater and wants to make the blanket of a minimal size (area). But her baby snake is quite a lively baby and it always ...
2k views

How much water do you need to cross the desert?

This question is inspired by Terry Pratchett's "Small Gods," in which an army crosses a vast desert by making multiple trips and caching water along the way. 1. Provide an answer. 2. I doubt I'm the ...
480 views

Combine two squares into a square with the sum of the two

The red square is placed on top of a blue square The goal is to cut the red square into 4 pieces and assemble them with the blue square to create a larger square. The area of the resulting square is ...
1k views

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 ...
1k views

Create a cube from identical 3D objects

The diagram is the outline of the surface of a 3D object. Several objects, like the one created from this given surface, may be used to create a cube. Let me know if you need more clarifications to ...
Construct a simple polygon on a grid of equal-distanced points such that: all the polygon's vertices are grid points, there are exactly $i~(\geq 0)$ lattice points in the interior, and ...