# Questions tagged [topology]

A puzzle about disentangling knots, folding paper, separating strings and wires, and understanding the connectivity properties of elastic figures. General topology questions are off-topic but can be asked on Mathematics Stack Exchange.

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### Changing baby's shirt

Baby needs a change of shirt, but baby is also sucking on a bottle (see this stock photo for a visual). If the bottle leaves baby's mouth, baby will start crying. Also, baby loves holding the ...
3k views

### Smallest Unicode Box Drawing

What is the smallest box diagram you can draw which uses all of the Unicode box drawing characters at least once, but without leaving any loose ends? For reference, you must use each of these ...
9k views

### Is there a proof that a map of the United States requires 4 colors?

The Four color theorem states that no more than four colors are required for any map. Can it be proved or disproved that 3 colors can be used for United States map?
7k views

### IQ Test Example

I'm reading up on various IQ tests, and a slideshow that I stumbled upon gave the following example: This doesn't make sense to me, as none of the options duplicate the conditions in the far left ...
2k views

### Turning My Pants Inside-Out

A 12-foot long rope has two ends. One end of the rope is tied around a man's left ankle and the other end is tied around the man's right ankle. If you are not allowed to untie the rope and you're ...
937 views

### Ernie and the Underground Network

I haven't seen Ernie for a few weeks - he's been on holiday in the People's Republic of Kzijekistan (PRK). But yesterday I got an e-mail and thought I would share it with you. It reads as follows: ...
2k views

### The three utilities puzzle

Here is a variant of the three utilities puzzle. Famously, It is impossible to solve it on a plane paper (Euler's theorem can prove that). But can you solve it on a coffee mug? ...
821 views

### How to generalise hang picture puzzle?

There is well known problem: The picture is attached to a string and you want to hang it on N nails so that if one takes out any of the nails, the picture falls. How do you do it? For those who ...
506 views

### Dragon summoning spell

The parchment shown below got stained with something. See if you can determine the obscured parts.
983 views

### Drawing a complete graph of 5 nodes on a torus

A complete graph of $n$ nodes is a graph where every node is connected to every other node. It is known that one cannot draw a complete graph of 5 nodes on a piece of paper (plane) without any ...
2k views

### How to use a Mobius strip for puzzle creation? [closed]

A Mobius strip is one of the basic concepts of topology. There are many interesting tricks using this strip (for example, interesting results of cutting the tape with a different number of turns). ...
182 views

### The grandest bridge in Appelhaken [duplicate]

In the capital of the grand country of Appelhaken there is a plane garden containing four magnificent monuments. So magnificent are they that the country has a Law requiring that there must be a ...
171 views

### Is it possible to create a knot that is locked only when the rope is stretched?

Is it possible to create a knot that is stable/locked when the rope is stretched? When the tension is relived the knot should open.
1k views

### 3D ring/rope wooden puzzle solution?

I have a Eureka 3d Puzzle G / Model G / Gringo: On the box there are 3 puzzles: Remove the ring Remove the rope Move the ring to the other side While Eureka does not appear to list this puzzle in ...
336 views

### Teacup geometry

Inspired by the three utilities puzzle from prog_SAHIL I'm now posting a similar puzzle that makes use of the topology of a cup with a handle: The question is: How many distinct points can you ...
309 views

### wandering knight

Suppose a land with a finite number of castles. Each castle is connected (via roads) with exactly 3 other castles. One knight leaves from his castle and starts travelling. He moves in the following ...
252 views

### Can this be undone to make a knotless loop?

Can this be undone to make a knotless loop?
3k views

### Connect the colored dots

I've got this: By connecting the dots, I get this: Could you do the same for this one: There is a unique solution. The rules are: You have to use every square, lines can't cross each other and you ...
150 views

### The grandest zoo in Appelhaken

In the magnificent country of Appelhaken there is a zoo. Not just any zoo, but a grand zoo, a magnificent zoo, called Appelhaken Grand Magnificent Magnificent Grand Grand Zoo. In this zoo there are ...
849 views

### Join six five-link chains to form a circular chain

Join six five-link chains to form a circular chain. To join two chains, you must cut, and then re-weld, a link. The final number of links in the circular chain will be 30. What is the minimum ...
1k views

### Are there any topology puzzles similar to The Seven Bridges of Königsberg?

Leonhard Euler proved that it is impossible to solve this puzzle: The challenge is to take a walk around the area depicted, and cross each bridge (yellow) exactly once. Using topology, Euler proved ...
105 views

### Topology puzzle: Glueing the edges of a square to itself

It is well known that if you start with a two-dimensional square and could glue — in the most straightforward way — the top and bottom edges to each other, and likewise the left and right edges to ...
1k views

### Connecting 6 dots with 6 curves

Can you connect 6 dots with 6 curves, such that every pair of curves touch each other exactly once? Curves can touch anywhere at their interior or at the dots, and the whole thing must lie in the ...
160 views

### Some puzzles just appear while doing diy [closed]

I had fitted a camera above the built-in wardrobe in our children's room. There was a socket behind the drawers. I could just remove the drawer to plug it in, but there was only enough room to slide ...
88 views

### Make a topological torus-with-a-hole out of congruent squares that may share an edge or a vertex with other squares

Suppose we arrange, in 3-dimensional space, 8 identical solid cubes in space so they form a square-shaped ring (using a 3x3 arrangement of squares except for the one in the middle). Its surface will ...
72 views

### Fair and square island hopping [duplicate]

If amateur fiction is not your thing skip to the bottom. As IP (Implausible Physics) expert for DREAM, the Department for Reckless Engineering and Advanced Megalomania you have been tasked by sheikh ...
178 views

### Pulling strings...not legs?

What happens to the two strings - of the logo of G20 Summit (currently happening in Germany)-if pulled either side (in opposite directions, away from the center) at the same time ? Your options are:...
678 views

### Is the following topology puzzle impossible to solve? [duplicate]

There was a problem I was introduced to in grade school which my teacher claimed that not even his graduate level students could solve, and it went a little like this. You have a set of boxes in a ...
656 views

### Number of ways to fold a 2x4 map

M.Gardner in his book "Mathematical puzzles and diversions" states that the following 2x4 map  \begin{array}{|c|c|} \hline 1 & \phantom{1} & \phantom{1} & \phantom{1} \\ \hline \...