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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.

13
votes
12answers
806 views

A man is trapped in a cage and wants to escape but doesn't, even when given the keys. Why? [on hold]

Note: I have invented this puzzle myself as far as I know. I'm certainly not aware of having read it anywhere else. I have no idea whether it will be hard or easy. A man is imprisoned in a strong ...
10
votes
4answers
2k views

Where does the emperor sit and why the earplugs?

The Emperor is annoyed that the crowd routinely chant out of step at the Empire's largest circular amphitheatre. For example, they are supposed to shout phrases in unison such as "Hail to the Emperor, ...
7
votes
5answers
358 views

Cutting a Slice of Cake Into Two

Driven out of a serious question, when sharing a slice of cake in a coffee shop how can my two friends split it without going down the middle (the cake is likely to crumble if you do this!) Given a ...
0
votes
1answer
66 views

What is the area of the shaded region? (Overlapping areas) [closed]

What is the area of the region poly1 formed by the arcs 'cdke'. The square is of sides 10 units long. The region poly1 is formed by four overlapping quadrants.
4
votes
1answer
126 views

Dystopian Tax Collection

The year is 2081, and... oh, what can I say? Dystopian stories have been done to death. I have a much more practical problem, though. I need to... gasp... pay my taxes. I owe five different taxes: ...
14
votes
1answer
278 views

Hidden numbers (hand drawn)

I like doodling and had an idea based on a flash game, where numbers are hidden in a picture, and it's ended up better than i expected. So have fun with it. And if you can give feedback on it that ...
6
votes
1answer
430 views

Where are the extra coins?

I am a manager of a coin casting foundry. We produce perfectly round coins with some (fixed) thickness and a diameter of exactly 1 inch. The working room is well-secured such that if any coin tries to ...
4
votes
2answers
144 views

Traverse a 3 × 3 × 3 cube; starting from the center [duplicate]

Consider a 3 by 3 by 3 cube — in essence, a Rubix cube — like the one pictured in the following image: Start from the cube in the middle, enclosed on all sides. Moving to only cubes that are directly ...
1
vote
3answers
105 views

Determining The Piangle

The Piangle is a unique triangle. Every circle has its unique Piangle. To create a Piangle, you cut a circle along its bottom radius, then you unroll the left side of the circle up and over to the ...
8
votes
2answers
175 views

What is the largest number of cubes that can be cut?

Consider a cube made up of 27 unit cubes. If you consider a plane going through the middle of the larger cube it cuts through a number of the unit cubes. The number of cubes that are cut depends on ...
14
votes
5answers
1k views

When did I make this puzzle?

I was flipping through some of my old puzzling notebooks, and I found an old puzzle of mine I don't quite remember. I tried to find when I made it (I put the date I made all of my puzzles on them), ...
5
votes
1answer
128 views

Horror Episode #1: Shapely Shedding Light

I shined my flashlight on a wall in terror. It was 2 in the morning at my place and I thought I heard a voice in my head. At first when I saw what was in my light, I jumped back because it looked ...
10
votes
4answers
515 views

Mirrored clocks

Triangulating for the simplest puzzle that is still at least somewhat interesting to solve.. On the left side wall in this picture, we have two particular clocks: 1: an analog clock with identical ...
9
votes
3answers
325 views

Special triangles in convex polygons

Given identical 30-60-90 triangles, what is the convex polygon with the highest number of sides that I can build from them? This seems a very easy task by first look, but I’m totally stuck right now. ...
1
vote
0answers
93 views

Golden Ratio plus 1 [closed]

There was an interesting puzzle by Presh Talwalker in 'MindYourDecisions' about finding the radius of a circle that was cotangent to two larger circles. https://www.youtube.com/watch?v=i0dZukEw1JY I ...
6
votes
2answers
474 views

Cutting a cross made of 5 equal squares by 2 straight cut into 4 figure to together form a square

A figure consists of 5 equal squares in the form of a cross. Please show how to divide it with two straight cuts into 4 equal pieces which will fit together to form a square. A MSE told me I need to ...
3
votes
2answers
426 views

Which polygon is the one?

There is a unit-radius circle and you must form a polygon all of whose vertices are located on the circle, such as below: What is the biggest possible value of the sum of squares of side lengths of ...
7
votes
0answers
152 views

A small team doing their job

Find the unique solution to $$ 5\,ninja + retook + quarter + turn = \_\,\_\,\_\,\_ + \_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_\,\_ $$ where each unknown is a different _ _ _&#...
10
votes
7answers
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: ...
1
vote
1answer
247 views

Which of the six tiles is missing? — An IQ Test Question

Which of the six tiles below is missing? I honestly do not know the answer. I took a screenshot of this from an online IQ test a while back. If you know where it is from, please let me know, and I ...
1
vote
1answer
67 views

Points in the tetrahedron

There is a regular tetrahedron with edge ledge of $2$ units. Your task is to put as many points within the volume occupied by the tetrahedron. But there is a condition: there has to be at least $1$ ...
2
votes
1answer
99 views

can only enter each room once question [duplicate]

3x3 cube with no center square so 26 cubes, You can start where ever you like and need to visit every room(cube exactly once) A valid operation is going any adjacent cube that is not diagonally ...
2
votes
1answer
148 views

Hexagon in a circle

Similar and Hint to: Dodecagon in a big circle There are $6$ bars which comprise two groups of $3$, $3$: each group has identical bars but every group has a distinct length of bars. For example; ...
3
votes
1answer
153 views

Dodecagon in a big circle

There are $12$ bars which comprise three groups of $6$, $3$ and $3$: each group has identical bars but every group has a distinct length of bars. For example; Group 1 may consist of six ...
-1
votes
2answers
93 views

Mr. Sloane's Tree

Mr. Sloane is a man that likes to draw trees with dots. Give him two dots and he'll draw you one tree, but give him three and he'll draw you no tree. How many trees can he draw with 6 dots? and with ...
7
votes
3answers
117 views

Lots of Parallelepiped

A,B,C,D are four points which are not on the same plane. How many different parallelepiped can be constructed whose vertices are these points? Parallelepiped is a solid figure with six faces ...
7
votes
3answers
401 views

Rectangular Prisms

Eight corner bricks are taken out from a 5x5x5 block, which is something like below: How many rectangular prisms of all sizes can be counted in this block? Source: Oyun 2018 Final Exam Question
3
votes
1answer
108 views

Inner Triangles in the circle

$18$ points are selected on the circumference of a circle, all of which are connected to each other by straight lines. If no three lines intersect at a common point, What is the number of a ...
1
vote
3answers
140 views

Too many Circles

Using 20 Circles, what is the maximum number of intersecting point that can be obtained? For example, if there were 3 circles, the answer would be $6$ as shown below:
7
votes
1answer
140 views

6 piece mystery puzzle help!

So I have NO CLUE how to put this back together. I don't even remember what it looks like or what it's even called. I took it apart 3 years ago and it's still driving me crazy. Anyone have any ideas?!?...
5
votes
1answer
308 views

A Stick and Two Similar Triangles

You have X centimeters of a straight stick. You divide this stick into 4 pieces. All sticks have distinct integer centimeters lengths. After that you form a triangle, then take one of the stick of ...
1
vote
3answers
273 views

Form Common Geometric Shapes

You are given 1,000,000 units of straight thin stick and your task is to create one triangle, one square, one rectangle by cutting the stick into sides. None of the side of each shape has common ...
7
votes
2answers
226 views

A coin fitting puzzle [duplicate]

I recently heard about this intriguing puzzle: I have a tray of length 5 and width 2 so 10 round coins of width 1 will fit in it snugly without overlaps. No room for another. Similarly, a tray ...
9
votes
1answer
476 views

Moving 4 sticks to form 8 equilateral triangles

We have $6$ thin sticks with the same length parallel to each other shown below: The distance between neighbor sticks are unknown and for sure smaller than half the length of the sticks themselves as ...
6
votes
1answer
180 views

15 squares into 3 stars

You are given $15$ unit squares as shown below: You would like to create $3$ six-sided stars as something like shown below by only using given $15$ squares: How is it possible if possible?
2
votes
1answer
178 views

What is the area of the shaded region? [closed]

The area of the square is 16 sq. units. A semicircle is inscribed on a side of the square with its diameter being that side of the square. An equilateral triangle rests with its base, on the opposite ...
2
votes
1answer
608 views

$\verb|Eight Circles|$

An entry in Fortnightly Topic Challenge #37: Rare and Endangered 1 Materials Pencil; Eraser; Blank A4 sheet of paper; and A ruler (also to use as a straightedge). Puzzle: Draw a square with a side-...
5
votes
1answer
214 views

Light Amplification by Stimulated Emission of Radiation

The following is a "Laser Maze." The goal is to place the tools into the maze so that when the power is turned up to maximum: The beam will split into two beams The beams (collectively) will ...
18
votes
2answers
580 views

Piece of Cake for King Solomon

Today (7th of July, 2018) marks 40 years of independence for the Solomon Islands. To celebrate, I have decided to bake a cake! And what a pretty cake it's going to be: When viewed from the top, ...
4
votes
2answers
130 views

3 points on a circle [duplicate]

There is a circle where you put 3 points randomly on it as shown below: What is the chance of these randomly chosen three points passing on an half circle? Reference: Bilim Teknik Dergisi 2018-07
-1
votes
1answer
101 views

Train Rail Length [closed]

A 100 meter long train rail expanded under the sun. The center of the rail went up 1 meter above the group while the two ends are still attached to the ground - The whole rail forms an arc. How long ...
3
votes
1answer
200 views

Create a map of a game's portals

Given a set of rooms, each with a N, a S, an E, and a W exit/entrance to another of the rooms, create as simple a map as possible that graphically represents their connections. The rooms in question ...
4
votes
4answers
787 views

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 ...
2
votes
2answers
162 views

Tiling rectangles with a Heptomino plus 2x2 square

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
1
vote
2answers
115 views

Tiling rectangles with Heptomino plus rectangle #7

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
9
votes
3answers
453 views

The Dollar Bill

Bill was asked to form as many triangles on top of a flat table using his 5 pennies (3 coins on the table where centers are connected by imaginary lines to make a triangle). His teacher told him that ...
5
votes
2answers
224 views

Tiling rectangles with Heptomino plus rectangle #6

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
3
votes
2answers
130 views

Tiling rectangles with Hexomino plus rectangle #3

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...
2
votes
0answers
630 views

This is a Mensa IQ test from Norway. The last puzzle. [duplicate]

I solved all of the questions except this one. I checked and the answer in the bottom left one. I couldn't find any pattern or relations that would help me understand why or how one reaches the answer....
3
votes
2answers
120 views

Tiling rectangles with Heptomino plus rectangle #4

Inspired by Polyomino T hexomino and rectangle packing into rectangle See also series Tiling rectangles with F pentomino plus rectangles and Tiling rectangles with Hexomino plus rectangle #1 ...