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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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3
votes
1answer
175 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
104 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
129 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
415 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
127 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
152 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
159 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
336 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
296 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
381 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
556 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
199 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
235 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 ...
3
votes
1answer
795 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
245 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
622 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
138 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
106 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
212 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
821 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
206 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
150 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
469 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
238 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
147 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
2k 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
134 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 ...
2
votes
2answers
92 views

Tiling rectangles with Hexomino plus rectangle #2

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
1answer
131 views

Tiling rectangles with Heptomino 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 Next ...
5
votes
1answer
238 views

Tiling rectangles with Hexomino plus rectangle #1

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 Next ...
6
votes
2answers
380 views

A construction on an infinite 2d grid, part 1

Recall the classic old problem where we're asked whether a line segment of specific length can be constructed with compass and straightedge, given an initial line segment of length 1? We're going to ...
6
votes
1answer
177 views

Tiling a rectangle with an odd number of Y pentomoes

Follow-on from Tiling a rectangle with just the Y pentomino Two questions: Find the smallest rectangle that can be tiled with an odd number of Y pentominoes, or prove it impossible Find the smallest ...
9
votes
3answers
545 views

Tiling a rectangle with just the Y pentomino

Inspired by this question series, which was inspired by this question. They give rise to beautiful pictures (at least in the eye of the beholder mathematician) and some nice generalizable solutions. ...
11
votes
1answer
457 views

6 nails String Art

String art is an arrangement of thread strung between nails to form geometric patterns or representational designs such as a ship's sails, sometimes with other artist material comprising the remainder ...
12
votes
1answer
478 views

Ernie and the Case of the Singing Sisters

On my way to work each morning I pass a news-agency that usually has a sandwich-board displaying the latest headlines of a somewhat disreputable tabloid newspaper (not that I would ever buy such a ...
2
votes
1answer
139 views

Tile a square with five rectangles with 10 distinct edges

The baby brother of: Cutting a square into seven rectangles Tile a square with five rectangles. Select the lengths of the edges of the rectangles from the set $1$ through $10$, with no length ...
5
votes
2answers
232 views

20 right isosceles triangles into a square

Similar: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles ...
18
votes
2answers
2k views

Maximal-volume cube net from unit square paper

Given a square piece of paper (say 1x1), what is the largest cube net you can cut out of it? ('largest' meaning with maximal volume; 'net' meaning it's possible to fold into a cube (somehow)) This ...
2
votes
2answers
143 views

Two difficult “Seventeen right isosceles triangles into a square” tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Five graded difficulty isosceles right triangle into square tilings V.hard problem, 20 right isosceles triangles ...
5
votes
2answers
197 views

Five graded difficulty isosceles right triangle into square tilings

Similar to: Unlucky tiling: Arrange thirteen right isosceles triangles into a square Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard problem, 20 right ...
12
votes
2answers
268 views

Unlucky tiling: Arrange thirteen right isosceles triangles into a square

Link to next puzzle in this series:Five graded difficulty isosceles right triangle into square tilings Two difficult "Seventeen right isosceles triangles into a square" tilings V.hard ...
6
votes
3answers
290 views

Tiling rectangles with X pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
6
votes
2answers
242 views

Tiling rectangles with V pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
3
votes
3answers
194 views

Tiling rectangles with U pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
8
votes
2answers
227 views

Tiling rectangles with T pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
7
votes
6answers
462 views

Tiling rectangles with N pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
7
votes
3answers
494 views

Tiling rectangles with F pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with N pentomino plus rectangles Tiling rectangles with T pentomino plus rectangles ...
14
votes
2answers
521 views

Tiling rectangles with W pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle Also in this series: Tiling rectangles with F pentomino plus rectangles Tiling rectangles with N pentomino plus rectangles ...
-4
votes
2answers
246 views

Random chord to a circle around a triangle

This puzzle is literally a math textbook question. Its only redeeming feature is that it also happens to be too broad in a surprisingly interesting way. The problem Given the circle $\mathbf O$ ...
10
votes
3answers
575 views

For n nodes that are connected to at most m and at least 2 other nodes, what values of n and m always allow the connections to not intersect?

I am trying to develop a puzzle game where $n$ nodes are generated and placed randomly on the screen. Each node is connected to at most $m$ and at least 2 other nodes by straight lines. This is an ...