Number Link Puzzle

Connect matching numbers with paths that fill the entire grid. A challenging logic puzzle that tests your spatial reasoning skills.

How to Play: Click on a numbered cell to start drawing a path, then click on adjacent cells to extend the path to the matching number. Paths can only go horizontally or vertically (not diagonally) and cannot cross other paths. All cells must be filled when the puzzle is complete.

0
Moves
6×6
Grid Size
0
Connected
00:00
Time
Number pairs: 6
Puzzle Solved!

You've solved the Number Link Puzzle in 00:00 with 0 moves!

All number pairs are connected and the grid is completely filled.

Move History

Moves: 0

About Number Link Puzzle

Number Link (also known as "Arukone" or "Number Connection") is a logic puzzle where players connect pairs of numbers with paths that fill the entire grid. The puzzle was invented in Japan and has become popular worldwide for its simple rules but challenging gameplay.

Mathematical Significance: Number Link puzzles are NP-complete problems, meaning they are computationally difficult to solve in the general case. They are related to Hamiltonian path problems in graph theory.

Solving Strategies

Look for Forced Moves
Identify cells that have only one possible path direction. These often occur near edges or corners, or when a number is surrounded by other paths.
Work from Both Ends
Start paths from both numbers in a pair and work towards the middle. This helps visualize the possible routes and constraints.
Avoid Dead Ends
Make sure paths don't create isolated empty cells that cannot be reached by any number. All cells must be filled in the final solution.
Plan Multiple Paths
Consider how paths will interact. Sometimes you need to plan several paths simultaneously to avoid conflicts.

Mathematical Properties

Grid Size Number of Cells Typical Number Pairs Difficulty Level Average Solution Time
4×4 16 4-5 Easy 1-2 minutes
6×6 36 6-8 Medium 3-5 minutes
8×8 64 8-10 Hard 5-10 minutes
10×10 100 10-12 Expert 10-20 minutes

Puzzle Variations

Classic Number Link: The standard puzzle with pairs of numbers to connect. The goal is to connect all pairs with non-crossing paths that fill the entire grid.

1

Alphabet Link: Uses letters instead of numbers. Connect matching letters with paths following the same rules as Number Link.

2

Multi-Link: Some numbers appear more than twice, requiring branching paths that connect all instances of the same number.

3

Hexagonal Grid: Played on a hexagonal grid instead of a square grid, adding an extra dimension of complexity to path planning.

Frequently Asked Questions

No, paths cannot cross or overlap. Each cell in the grid can only belong to one path. This is a fundamental rule of Number Link puzzles.

Yes, a valid solution must fill every cell in the grid. This is what makes Number Link puzzles challenging - you need to plan paths that not only connect matching numbers but also cover the entire grid without gaps.

In standard Number Link puzzles, paths can only move horizontally or vertically, not diagonally. Some variations may allow diagonal moves, but these are not typical.

Well-designed Number Link puzzles have a unique solution. However, some puzzles might have multiple valid solutions, especially if they are not carefully constructed. The puzzles generated by this tool guarantee a unique solution.

The most challenging aspect is ensuring that all cells are filled while avoiding path crossings. This often requires thinking several moves ahead and considering how multiple paths will interact in the limited space of the grid.