Communities

Writing
Writing
Codidact Meta
Codidact Meta
The Great Outdoors
The Great Outdoors
Photography & Video
Photography & Video
Scientific Speculation
Scientific Speculation
Cooking
Cooking
Electrical Engineering
Electrical Engineering
Judaism
Judaism
Languages & Linguistics
Languages & Linguistics
Software Development
Software Development
Mathematics
Mathematics
Christianity
Christianity
Code Golf
Code Golf
Music
Music
Physics
Physics
Linux Systems
Linux Systems
Power Users
Power Users
Tabletop RPGs
Tabletop RPGs
Community Proposals
Community Proposals
tag:snake search within a tag
answers:0 unanswered questions
user:xxxx search by author id
score:0.5 posts with 0.5+ score
"snake oil" exact phrase
votes:4 posts with 4+ votes
created:<1w created < 1 week ago
post_type:xxxx type of post
Search help
Notifications
Mark all as read See all your notifications »
Users Search
Help Dashboard Sign In Sign Up
Descriptions Incubator Q&A Meta
Incubator Q&A
Posts Tags Edits
Create Post

Welcome to the staging ground for new communities! Each proposal has a description in the "Descriptions" category and a body of questions and answers in "Incubator Q&A". You can ask questions (and get answers, we hope!) right away, and start new proposals.

Are you here to participate in a specific proposal? Click on the proposal tag (with the dark outline) to see only posts about that proposal and not all of the others that are in progress. Tags are at the bottom of each post.

Post History

60%
+1 −0
Incubator Q&A Closed loop on a side length 2 cube

Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop. If you want to try a simpler version first, there is Closed loop on a side length 1 cube. You may ...

1 answer  ·  posted 9d ago by trichoplax‭  ·  last activity 3d ago by Peter Taylor‭

Question puzzles grid-puzzles
#7: Post edited by user avatar trichoplax‭ · 2026-09-10T20:26:39Z (7 days ago)
Add hint that this does not require a brute force search
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Each of the images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Each of the images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • <details>
  • <summary>Hint</summary>
  • <!-- An empty line is required for markdown to render -->
  • This is not intended as a brute force puzzle where you try all the combinations until you find one that works. There are some insights that will make this puzzle practical to solve even for larger versions.
  • </details>
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
#6: Post edited by user avatar trichoplax‭ · 2026-09-08T22:31:03Z (8 days ago)
Improve wording
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Each of the images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
#5: Post edited by user avatar trichoplax‭ · 2026-09-08T22:26:10Z (8 days ago)
Explicitly mention rotation
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • You may rotate each tile by any multiple of 90 degrees.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
#4: Post edited by user avatar trichoplax‭ · 2026-09-08T22:14:46Z (8 days ago)
Mention tiles and squares are identical sizes when opened in a separate tab
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab (which will display the tiles and the squares on the cube faces at exactly the same size) if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
#3: Post edited by user avatar trichoplax‭ · 2026-09-08T21:10:49Z (9 days ago)
Show individual tiles for clarity
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles
  • - 12 double arc tiles
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles: [![tile with an arc joining 2 adjacent edges][single arc tile]][single arc tile]
  • - 12 double arc tiles: [![tile with arcs joining 2 pairs of adjacent edges][double arc tile]][double arc tile]
  • Here are 12 of each that can be printed and cut out:
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [single arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/single-arc-tile.svg
  • [double arc tile]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/double-arc-tile.svg
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
#2: Post edited by user avatar trichoplax‭ · 2026-09-08T20:22:10Z (9 days ago)
Link to simpler version
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles
  • - 12 double arc tiles
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
  • Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.
  • If you want to try a simpler version first, there is [Closed loop on a side length 1 cube](https://proposals.codidact.com/posts/296638).
  • The tiles to be used are equal numbers of 2 kinds of tile:
  • - 12 single arc tiles
  • - 12 double arc tiles
  • [![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]
  • Here is a net of a cube to place the tiles on:
  • [![24 squares that can be folded up to give a cube][cube net]][cube net]
  • Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.
  • [tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg
  • [cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
#1: Initial revision by user avatar trichoplax‭ · 2026-09-08T20:18:59Z (9 days ago) 
Closed loop on a side length 2 cube
Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop.

The tiles to be used are equal numbers of 2 kinds of tile:
- 12 single arc tiles
- 12 double arc tiles

[![12 tiles with 2 adjacent edges joined by an arc, and 12 tiles with 2 pairs of adjacent edges joined by arcs][tiles]][tiles]

Here is a net of a cube to place the tiles on:

[![24 squares that can be folded up to give a cube][cube net]][cube net]

Both images can be opened in a separate tab if you would like to print them for experimenting or to photograph your solution to post in an answer.

[tiles]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/tiles-2.svg

[cube net]: https://raw.githubusercontent.com/trichoplax/loop-on-a-cube-puzzle/refs/heads/main/cube-net-2.svg
puzzles grid-puzzles