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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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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 ...
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 ...
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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 ...
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Klotski Puzzle 3

Another Klotski Puzzle, "The Great D-vide": Rules Here Klotski Puzzle 1 Klotski Puzzle 2
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Klotski Puzzle 2

Another Klotski puzzle! (rules here) Klotski Puzzle 1
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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 ...
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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 ...
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 ...
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 ...
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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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) ...
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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 ...
990 views

Triangle area equals quadrilateral area

Here is a diagram and challenge description that should be clear and simple to understand.
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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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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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. ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
387 views

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, ...
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 ...