How to solve number path puzzles: Number Chain rules and tips

One continuous path through every square

Number Chain is a number path logic puzzle. Fill the available squares with consecutive numbers from 1 to the final number. Numbers that differ by one must share an edge: move up, down, left or right, never diagonally.

The printed clues stay fixed. A complete solution must use every available square once, without repeating a number. Striped spaces in irregular boards are not part of the path.

A small worked example

This teaching example is a 3×3 board, not a numbered campaign level. Keep 1 in the top-left corner, 3 in the top-right, 5 in the centre, 7 in the bottom-left and 9 in the bottom-right.

The path below satisfies every clue. Read it as 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8 → 9. Notice that 3 connects down to 4, then the path travels left across the middle row.

1  2  3
6  5  4
7  8  9

Count the moves between nearby clues

The difference between two clues tells you how many moves connect them. From 4 to 7, the route must take exactly three moves, placing 5 and 6 between them.

On an unobstructed grid, count horizontal and vertical distance. If clue 4 is two columns and one row from clue 7, all three moves are already needed; the route cannot afford an extra detour. Obstacles can remove possible routes, so this distance is only a lower bound.

Check the squares your route leaves behind

Before committing to a long chain, inspect narrow corridors and corners. An interior number needs both a predecessor and a successor. If a proposed route leaves an isolated empty square, it cannot be a complete solution.

• Start with short gaps between fixed clues, where there are fewer possible paths.
• Do not change a clue to rescue a route. Undo or erase your own entries instead.
• A visually continuous line is not enough: verify the number order and that no available square is left unused.

Practise in Number Chain

Drag from an existing number through adjacent squares, then release to fill the sequence. Step back, undo or erase to try another route. There is no time limit.

The Android game includes regular and irregular boards and a daily puzzle. Campaign and daily progress are kept separately. You can play without signing in; optional Google cloud saves require an internet connection and a Google Play Games account. The game is a paid download; see Google Play for your local price.