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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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7
votes
1answer
803 views

A purposefully obtuse Euclidean geometry riddle from an old interactive fiction game

I've been playing Praser 5, an old interactive fiction game (like Zork) made a few decades ago, and available here. In it, you wander from area to area solving riddles posed by mythical animals. Many ...
15
votes
1answer
1k views

Which Way did the bicycle go?

I found this puzzle which simply asks which way was the bicycle going, from its wheel marks on the mud shown in the image Now there is a simple way to find which mark(line) was made by the front ...
9
votes
4answers
2k views

How many different non congruent polygons can you make on a 3x3 dot grid?

There is a $3\times3$ dot grid. How many different non-congruent polygons can you make on the grid? Rules: All vertices of the polygon must be on the grid Only non self intersecting polygons Only ...
2
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1answer
231 views

Klotski Puzzle 3

Another Klotski Puzzle, "The Great D-vide": Rules Here Klotski Puzzle 1 Klotski Puzzle 2
6
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1answer
205 views

Klotski Puzzle 2

Another Klotski puzzle! (rules here) Klotski Puzzle 1
12
votes
1answer
959 views

Klotski Puzzle 1

Klotski is a sliding-blocks puzzle game very similar in nature to rush-hour/unblock me. In a given puzzle, a certain number of blocks labeled Z, A, B, C, .... are given. The goal is to move the Z ...
6
votes
2answers
506 views

Block the snake from reaching points

Solution for Version 2 pending.... There is a $100\times 100$ grid. The upper left corner has coordinates $(1,1)$ and bottom right corner has $(100,100)$. A 'snake' starts by occupying a single cell ...
10
votes
3answers
2k views

Precision Tag - can the lion win?

This is a spin-off motivated by Lopsy's interesting variant of Gamow's lion and zebras puzzle. It arose from a line of enquiry that tried to extend the vertical run past 5000km (or characterise the ...
8
votes
3answers
824 views

The Erasmus dissection of a square

Professor Erasmus claims that he is able to cut a square into 100 rectangles by making nine horizontal cuts and nine vertical cuts (parallel to the sides of the square), so that exactly 9 of the ...
6
votes
1answer
276 views

Two potatoes and a loop of wire

You are given two potatoes. You want to make a finite loop of wire so that you can put it on either of them at some location at your choice, so that there are no gaps between the potato and the wire. ...
36
votes
3answers
3k views

Which 3D shape can you make out of this?

The above shape can be folded into a closed 3D shape using no more than 14 distinct folds, with no parts overlapping. What is special about the shape that results? Rules and clarifications: Every ...
6
votes
2answers
836 views

Geocaching Geometry Puzzle

I am looking for help with a math puzzle. The answer is the final coordinates to a geocache. I have put in quite a bit of time and lots of graph paper trying to solve this one. I have tried programs ...
4
votes
1answer
709 views

Points on a cube

Professor Halfbrain has spent his entire weekend by placing colored dots on the surface of a huge wooden cube. His objective was to find large groups of dots that form the vertices of a regular ...
8
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5answers
1k views

Polyomino Z pentomino and rectangle packing into rectangle

See my similar question about T hexomino (Polyomino T hexomino and rectangle packing into rectangle) This is exactly same but with other polyomino - Z pentomino. Let's pack some (one or more) Z ...
4
votes
1answer
2k views

Find the angle (hardest easy geometry) [closed]

This is a question which is related to the hardest easy questions. Note that the general solution belongs on math.se and is not solved in simple way. This question is a puzzle and you need to prove ...
1
vote
1answer
813 views

Four similar triangles

The challenge as described hereafter is to create a total of 4 similar triangles by drawing 4 triangle in a scalene, acute triangle - out of the 5 resulting triangles (4 that make the original one) ...
32
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10answers
3k views

Variant of lion and 100 zebras

Note: This problem remains unsolved, as of 4 Feb 2018, so do try it out This a variation of this question by @Gamow Suppose there are $100$ lions and $100$ zebras. The lions function together as a ...
8
votes
2answers
990 views

Triangle area equals quadrilateral area

Here is a diagram and challenge description that should be clear and simple to understand.
-4
votes
1answer
146 views

Polygons circumscribed by lines [closed]

You have a plenty of segments of the same length at your disposal. Put a segment and put another to meet at their ends. Set the counterclockwise angle between two segments at 180/5 degrees. If you ...
17
votes
3answers
1k views

Pythagorean walk

It's a hot day. You are in the middle of a flat sandy plane that stretches as far as you can see. Your hands are shackled and you are surrounded by soldiers of the mighty Pythagorean Brotherhood. Ten ...
4
votes
2answers
208 views

A stroll in the park

Professor Erasmus has returned from his saturday walk in the park. He has counted the number of trees in the park and also the number of lines formed by these trees. Professor Erasmus claims that ...
5
votes
1answer
744 views

Now help me choose a new lock pattern for my phone

Well, thanks to Len, I managed to unlock my phone again, but now everyone knows my pattern, so I need to choose a new one. For brevity, I won't include the explanation of how an Android pattern lock ...
16
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2answers
9k views

Help! I've forgotten my phone's lock pattern!

I have an Android phone with a pattern lock screen, which if you've never seen one allows you to unlock your phone using a pattern drawn on the screen over a 3x3 grid of dots. So for example, if we ...
31
votes
1answer
3k views

Ernie and the Island of Stability

Unfortunately, it appears that I may have misled you a little in this puzzle (as you probably know - my memory of events isn't always perfect). When I was writing it, I re-checked the Kzijekistanian ...
12
votes
2answers
562 views

Polyominoes on a checkerboard

Professor Halfbrain has spent his entire weekend by cutting lots of wooden $50\times50$ checkerboards into lots of polyominoes. He looked at various pattern polyominoes with area $49$, and always ...
12
votes
5answers
1k views

Triangle in a circle

Suppose three points are chosen at random in a circle. A triangle is made with these three points as vertices. What's the probability that the triangle contains the origin of the circle? (Although I ...
13
votes
7answers
3k views

Fair n-sided dice

I have recently bought a fair $10$-sided dice for generating equally distributed random numbers from the range $1,2,\ldots,10$. Let me describe this dice in some more detail. Consider a regular 5-gon $...
10
votes
2answers
746 views

Polygon wrapping a cube

A polygon is folded to perfectly wrap a cube, covering all of its surface area with no overlap. Show that the polygon had at least two equal angles.
7
votes
1answer
628 views

Smallest number of matchsticks for a 3D structure with 6 matchsticks at each vertex

Make an as small as possible three dimensional structure of matchsticks, all of which have equal length, such that the end of each matchstick meets exactly five other ends. A matchstick is not allowed ...
8
votes
1answer
275 views

The Erasmus tedrahedron

Professor Erasmus has constructed a special tetrahedron that he modestly calls the "Professor-Erasmus-tetrahedron". The professor claims that all four faces of his tedrahedron are right-angled and ...
23
votes
6answers
3k views

Fair share of a square watermelon?

One hot day, Stan, Kyle, and Kenny were sitting outside with a square watermelon (actually it was a cube like the picture below). Stan says "Let's cut the watermelon into 3 equal slices (like the ...
8
votes
2answers
876 views

Ant on a rectangular box

An ant walks in constant steps from corner to corner over a rectangular box, always chosing the shortest path. From any given corner, the ant observes the shortest paths to the other seven corners all ...
3
votes
2answers
279 views

Find seven points so any three contain two of distance one

Choose 7 distinct points in the Euclidean plane so that among any 3 of those points, there are (at least) 2 that are a distance of exactly 1 apart.
10
votes
3answers
692 views

The Erasmus isosceles triangle

Professor Erasmus has constructed a special isosceles triangle that he modestly calls the "Professor-Erasmus-triangle". The professor claims that he can cut his triangle into three smaller triangles, ...
15
votes
1answer
1k views

Touching matchsticks with compass and straightedge

The question Touching Matchsticks asked for the smallest matchstick graph where every node is connected to four distinct edges. The Harborth Graph is the smallest such, with 104 edges connecting 52 ...
4
votes
2answers
741 views

Puzzle pieces, each in contact with 5 others

You are asked to create puzzle pieces by joining together identical squares. This needs to be done such that the puzzle pieces can be arranged in a pattern with each piece being in contact with ...
14
votes
3answers
1k views

Touching Matchsticks

You are asked to place matchsticks on a flat surface such that each matchstick end meets three others, and no matches cross. It is easy to achieve this for patterns that extend indefintely: The ...
8
votes
4answers
2k views

Find the width of the river

You find yourself with a friend on a completely deserted (devoid of objects or people) and flat plane. The only thing of note is a wide river; you can just manage to see the other side of it. There is ...
10
votes
2answers
849 views

Dissecting a square

You are asked to dissect an $N \times N$ square into polyomino pieces such that each piece shares portion of its boundary with exactly $D$ other pieces, and no piece has area exceeding $N$. This can ...
12
votes
2answers
1k views

Escaping a hungry lion you can't outrun

You are at the edge of an enormous circular arena. A hungry lion is eying you from the centre of this area. You are both capable of running at the same maximum speed, but constraint within the arena. ...
12
votes
2answers
908 views

Find smallest rectangle divided into figures so each figure has 5 neighbours

The following 3x4 rectangle can be cut into pieces along grid lines, so that each piece has exactly three neighbors: Problem: Find the smallest rectangle on the integer grid that can be cut into ...
5
votes
1answer
242 views

Optimal size of n circles to fit an area

Let us say that I have a rectangular area that has to always look "filled" with circles. (the void spaces with the given number of circles should be minimal)(Goal) Let us assume that, I am also told ...
1
vote
3answers
349 views

Marker and the cube

If a marker is located in one of the corners of a square cube and we begin to draw according to the following conditions, how many edges of the cube can we cross ? A) You can cross every edge only ...
12
votes
2answers
988 views

Hidden planet area

A solar system contains some number of stationary perfectly-spherical planets of equal radius. Call a point on a planet's surface private if it can't be seen from any other planet. Show that the total ...
31
votes
3answers
9k views

What is the minimum number of straight lines to connect all the dots on this grid?

Recently a question was posted with this picture of a 7x7 grid of dots, asking for a possible configuration with 12 lines where you can draw them without lifting a pencil. But is it possible with 11 ...
3
votes
1answer
529 views

Three 3 x 3 x 3 Polycube Dissections

The Soma cube is perhaps the most well-known polycube dissection. Here are three more dissections to be assembled into 3x3x3 cubes. The best answer will provide: the first correct solution for ...
11
votes
1answer
387 views

Dissect the pixel-heads

Here are two figures, each composed of 54 pixels. Cut each figure into six nonominoes having the same shape and size. Both figures use the same nonomino The nonominoes could be rotated, reflected, ...
18
votes
4answers
799 views

Stitching together two identical planar shapes

A 3 x 1 rectangle has a perimeter of length 8. Two of these rectangles can each be bend in a U-shape and stitched together to yield a cube of unit volume. Surely we can do better than that! What ...
18
votes
1answer
657 views

Dissect the frog

Cut the stylized frog in the picture into six pieces having the same shape and size, possibly mirrored. The white dots are guide points. They help recognizing the shape's geometry. You are not ...
8
votes
2answers
452 views

Squaring the new year

Happy new year! You are asked to cut a rectangular strip 2015 times longer than its width into pieces that can be reassembled into a square with area equal to that of the original strip. How many ...