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Incubator Q&A Two closed loops

Grid This puzzle is played on a 5 by 5 grid of squares: Tiles There are 25 tiles to be placed on the grid, one on each square. They can each be rotated by any multiple of 90 degrees. Note ...

2 answers · posted 6mo ago by trichoplax‭ · last activity 13d ago by will.octagon.gibson‭

Question puzzles grid-puzzles

#2: Post edited by

trichoplax‭ · 2026-03-31T18:42:22Z (6 months ago)
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## Grid
This puzzle is played on a 5 by 5 grid of squares:
[![An empty grid of 25 squares in 5 rows and 5 columns](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/grid.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/grid.svg)
## Tiles
- There are 25 tiles to be placed on the grid, one on each square.
- They can each be rotated by any multiple of 90 degrees.
- Note that the first tile (the top left) is deliberately blank. This means that one of the squares in the completed grid will be blank.
[![A grid of 25 squares in 5 rows and 5 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/tiles.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/tiles.svg)
## Puzzle
Place all of the tiles on the grid such that the two different styles of line each form a single closed loop.
## Example
This shows a solution to a similar puzzle on a 3 by 3 grid.
<details><summary>Hidden example</summary>
Given the following tiles:
[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-puzzle.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-puzzle.svg)
You could arrange them like this:
[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-incorrect.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-incorrect.svg)
~~This has all of the lines of each style in a single line, but only one of them is a closed loop. The other has 2 ends, so is not a solution to the puzzle.~~
~~They can instead be arranged into 2 closed loops:~~
<details><summary>Solution to the 3 by 3 example puzzle</summary>
[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-correct.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-correct.svg)
</details>
</details>
## Printing
If you want to print the images to cut out the tiles and experiment with rearranging them, or to photograph your solution to add to your answer, you can click on the images to open them separately.

## Grid
This puzzle is played on a 5 by 5 grid of squares:
[![An empty grid of 25 squares in 5 rows and 5 columns](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/grid.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/grid.svg)
## Tiles
- There are 25 tiles to be placed on the grid, one on each square.
- They can each be rotated by any multiple of 90 degrees.
- Note that the first tile (the top left) is deliberately blank. This means that one of the squares in the completed grid will be blank.
[![A grid of 25 squares in 5 rows and 5 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/tiles.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/tiles.svg)
## Puzzle
Place all of the tiles on the grid such that the two different styles of line each form a single closed loop.
## Example
This shows a solution to a similar puzzle on a 3 by 3 grid.
<details><summary>Hidden example</summary>
Given the following tiles:
[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-puzzle.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-puzzle.svg)
You could arrange them like this:
[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-incorrect.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-incorrect.svg)
This has all of the segments of each style in a single line, but only one of them is a closed loop. The other line has 2 ends, so this is not a solution to the puzzle.
The tiles can instead be arranged into 2 closed loops:
<details><summary>Solution to the 3 by 3 example puzzle</summary>
[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-correct.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-correct.svg)
</details>
</details>
## Printing
If you want to print the images to cut out the tiles and experiment with rearranging them, or to photograph your solution to add to your answer, you can click on the images to open them separately.

#1: Initial revision by

trichoplax‭ · 2026-03-31T18:28:48Z (6 months ago)

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Two closed loops

## Grid
This puzzle is played on a 5 by 5 grid of squares:

[![An empty grid of 25 squares in 5 rows and 5 columns](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/grid.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/grid.svg)

## Tiles
- There are 25 tiles to be placed on the grid, one on each square.
- They can each be rotated by any multiple of 90 degrees.
- Note that the first tile (the top left) is deliberately blank. This means that one of the squares in the completed grid will be blank.

[![A grid of 25 squares in 5 rows and 5 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/tiles.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/tiles.svg)

## Puzzle
Place all of the tiles on the grid such that the two different styles of line each form a single closed loop.

## Example
This shows a solution to a similar puzzle on a 3 by 3 grid.

<details><summary>Hidden example</summary>

Given the following tiles:

[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-puzzle.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-puzzle.svg)

You could arrange them like this:

[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-incorrect.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-incorrect.svg)

This has all of the lines of each style in a single line, but only one of them is a closed loop. The other has 2 ends, so is not a solution to the puzzle.

They can instead be arranged into 2 closed loops:

<details><summary>Solution to the 3 by 3 example puzzle</summary>

[![A grid of 9 squares in 3 rows and 3 columns each showing a tile with 0, 1, or 2 lines in one of 2 different styles](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-correct.svg)](https://raw.githubusercontent.com/trichoplax/loops-puzzle/refs/heads/main/mini-tiles-correct.svg)
</details>
</details>

## Printing
If you want to print the images to cut out the tiles and experiment with rearranging them, or to photograph your solution to add to your answer, you can click on the images to open them separately.

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