# 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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### I cannot make any triangle with sticks

There are $13$ sticks with different lengths, and you try to form a triangle by using $3$ sticks (making every stick is a edge of a triangle) but somehow whatever $3$ sticks you choose, you cannot ...
1k views

### What's the missing pattern? 3x3 grid, dot pattern

What is the missing piece to this pattern? Got it as a quiz at work - no one here knows what it is!
772 views

### Ernie and the Uneconomical Flat-breads

When I arrived at Ernie's place last weekend I had some exciting news for him. "did you know", I announced "that a new Kzijekistanian fast-food shop has just opened in town?". "I did", Ernie replied, "...
752 views

### Unlimited paper folding

You have a squared piece of very thin paper. You can fold it and glue together to get a piece of paper with other shape. You can make it as many times as you want. Are there convex polygons, which you ...
611 views

### What is the answer for the question 23 and 22 in the image below?

Source- NTSE Chattisgarh 2015. Sorry, didn't know I cannot post Exam questions.
203 views

### Find the angle in the shape [closed]

I'm back again with another controversial puzzle for you. If you try this puzzle for yourself, you will notice that it does not seem possible at first. Please provide a proof for your solution. You ...
418 views

### Find the angle in this shape [closed]

The aim of this puzzle is to find the angle marked '?'. Answers must be in the format of exact values. You will have to assume some basic geometric constraints. e.g. points which look like they are ...
210 views

### Engineering drawing put to some good use

In engineering, objects/machine parts are often expressed using orthogonal projection, in which line drawings are created for their front/side/top views as seen from planes that rest 90° ...
2k views

### Building a Square out of a rope

This was a challenge given to us in our Team Building exercise in an MBA course I took. Needless to say our team didnt do well. So I am asking the Stack community if there is a clear way. We were in ...
494 views

### What did Louis do to measure the cardboard box?

When Louis arrived at his apartment in Europe he found a note pinned to the wall in his study. The note was pinned on a 10 Euro bill. It was from his yankee roommate Jack, who always liked to play ...
1k views

### What's the most complex pattern to decipher if you have seen the pattern

I am trying to set a lock pattern for my phone with a snoopy guy behind. If he is able to see what my pattern looks like at the end, what is best possible sequence i can set so he will take maximum ...
643 views

### Can two colors ever be orthogonally adjacent in a flexi puzzle?

A flexi puzzle is a fun little toy, consisting of wood blocks and a string that runs through it. The pattern of colors is repeated twice; if a color is found at position $N$, it is found a second ...
431 views

### Constructing 0.35 Unit Length

The Problem The medieval equivalent of Bob the Builder has a new job offer: He is to build a box with the measures of $0.35$ units by $0.35$ units by $0.35$ units for a king. There is a little ...
814 views

### Squares splitting into 4 congruent shapes [closed]

how many ways can you divide a square into four congruent shapes? Remember that the answer cannot be infinity because rotations of one pattern still result in the same four congruent shapes.
152 views

### Is this six different views of the same block or is there a consistent view with 1 or more that is 'odd'

The answer book of this puzzle book says that the first five are all consistent but the last one is not because the Z has to be a U. I can't seem to agree with this as U seems to be attached to N, P, ...
584 views

### How many different pentagons in this grid? [duplicate]

The 3x3 grid is given as below; How many pentagons could be drawn by connecting the dots by lines in the grid? Rules: Pentagons could be convex or concave. The lines cannot intersect each other. ...
1k views

### The Four Coins Puzzle [duplicate]

Four coins lie on a table and form a square. Now you are allowed to jump with a coin over another one, in any direction, i.e. also diagonally or however. You always have to jump all the way to the ...
209 views

### Three-dimensional snooker

Bert practises potting snooker balls on an elliptical table. He places a ball at one focus, strikes it with his cue in a random direction so that it travels towards the edge of the table, and when it ...
385 views

### Dissecting a triangle into 4 pieces [closed]

How can I dissect a triangle into 4 piece and form a square? I took A right triangle with sides 3,4,5.i was able to get a rectangle of side 3 and 2,if I dissect that I was able to get 3 squares of ...
320 views

### A different cyclicity condition

Note: Although this may seem maths-related, I did do some research on meta and it seems that questions which take an 'elegant' solution are on-topic. There are many ways to tell if four points are ...
498 views

### Overlapping Tiles

Suppose you had two stained-glass tiles in the shapes of polygons and you laid them on top of each other. Their overlapping area also forms a polygon, like the ones I have shown in the image: Notice ...
982 views

### How many boxes do you see?

My professor gave us this puzzle at the beginning of the semester but would not reveal the answer: There is only one question: How many boxes do you see? We were not given any other information and ...
778 views

### 6 Points in a rectangle

Here is an (unoriginal) question which I found quite nice. I've got no idea where the original question came from. Given 6 points in a $3\times4$ rectangle, prove that two lie within $\sqrt{5}$ of ...
1k views

### Is there a simple algorithm for solving Kami 2 puzzles?

I'm finding my life has been consumed by Kami 2, partly because I seem to have achieved some "insight" and am able to solve the puzzles reliably, almost always on the first try. The rules are simple: ...
711 views

### Ernie and the Optical Gyroscopes

I almost always take up Ernie’s offers to crew on his boat, when he suggests an overnight expedition. But when he phoned last Thursday I had to remind him that it was TV night, and Acme Satellite ...
187 views

### Cover 3*2.6 rectangle with the least number convex polygons cut from sheets of given size 1.2*2.4

I want to cover a rectangle of given dimensions ($3\times2.6$) with a minimal number of convex polygons cut from rectangular sheets of material of given size ($1.2\times2.4$). These polygons don't ...
321 views

### Who let the dogs off?

Four people, A, B, C, and D brought their dogs to a square park, 1 (mile/km) on each side. They stood at the four corners. Suddenly all four dogs broke free from their lea(shes/ds) at once. A ran at ...
1k views

### Can you divide this figure into two equal parts? [duplicate]

This is very simple when I see the answer, but I was not able to answer it(by thinking of single line), So posting for you.
710 views

### One a puzzle, two a puzzle, Hot Cross Clocks

It's Good Friday! I want to make perfect hot cross buns by superimposing two 12-hour clock faces on top of each other. Is this possible, and if so, how many ways are there of doing so? In other ...
405 views

### Mr. Allen at the Mall

Mr. Woody Allen is standing at one of the three entrances (A) of a 5 story Manhattan Mall. He needs to go from A to the other end (small shop) on the 4th floor at location (X). Ground floor is First ...
1k views

### Thinking of a shape

This is on a similar thought process as a 2 year old puzzle on this site: You have one question to tell whether the number I'm thinking of is 1, 2, or 3 I am thinking of a shape. It is ...
1k views

### Which tile completes the set?

This one puzzles me. I hope you can solve it.
198 views

### Conveyor belt brain teaser [closed]

Okay folks, I'm keen to get a response to this brain teaser!!! Let's say you're looking at a conveyor belt... The width = 2m, and the length = 10m. Okay... This conveyor belt is moving from right ...
809 views

### Building a pyramid from di-spheres

Suppose you want to build a square pyramid made up of 30 spheres. So the bottom layer is a 4x4 square arrangement of touching spheres, and it has 3x3, 2x2 and 1x1 layers on top. The building blocks ...
715 views

### Dissecting the holey octomino into a square

This is a pure dissection problem, with no added twists. Cut the holey octomino (i.e., a square with the middle third removed) into several pieces, and reassemble those pieces into a square with no ...
276 views

### Can you mark the SPOTS?

You are in a room which is 300 wide x 300 long x 300 tall in cm. Your job is to mark a couple of spots on one of the (non-window) walls. Spot 1: about 73 cm high on the side of the wall (x and y ...
149 views

### Brother Trouble [closed]

Three Brothers Decided to purchase circular land(marked in red) if the price of entire Circular land(circle P) = \$29670 How Much They have to pay for the land marked in RED ?? Useful information: 1)...
1k views

### Circular geometry puzzle [closed]

Look at the images and pick the first one, then prove that the blue area = the white area here's my failed attempt: let radius of large circle = 1, so radius of small circle = 0.5 and length of ...
531 views

### Eight identical spheres fit inside a cube

Eight identical spheres fit inside a cube with side length of 1 unit. What is the largest possible radius for a sphere which would fit between those 8 spheres (in the center)? There are no gaps ...
483 views

### Make a tetrahedral pyramid with these puzzle pieces.

Recently on a local fair (mela) I bought this puzzle from a magic-stall. It contains the following parts (each part is rigid, inflexible) Fig- 1 : Dismantled pieces in 1 set. It contains : ...
423 views

### Can you arrange 36 trees so that there are 9 rows of 8 trees?

How could you arrange 36 trees into 9 rows of 8? (Note that a row is a straight line that can go in any direction.)
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### Find the side view and simple 3d [closed]

Find the side view and simple 3d associated with these views.It is given that there are no hidden lines (lines which are not visible from the side or top view).
2k views

### Create a 3 inch measurement

How will you create a 3 inch (within say plus or minus 0.05 inch) side on a standard piece of paper ( 8.5 x 11 inches) merely by Folding? No marking of any kind allowed. Only one paper available. ...
454 views

### Infinitely simple polygon solipsism

Solipsism — The self is all that can be known to exist. Above is a simple polygonal region divided into infinitely many different-...
364 views

### Unreflected infinitely simple polygon reflexivity

(This was retrofitted to more tightly match a surprise solution and to allow for another puzzle with the original intent.)                   &...
3k views

### Find 77777 solutions

You have three flat pieces, as shown: Arrange them flat, without overlap, such that the shape formed by the black parts is congruent to the shape formed by the white parts. Rotation and reflection ...
3k views

### Find 7 solutions

You have three flat pieces, as shown: Arrange them flat, without overlap, such that the shape formed by the black parts is congruent to the shape formed by the white parts. Rotation and reflection ...
155 views

### Connect three rings

Is it possible to arrange three rings so that they are connected and cannot be separated without cutting one, but once any one of the rings has been cut, the remaining two can be separated without ...