Number Path Strategy: The Checkerboard Rule and Faster Paths

Updated October 2026

Number Path on this site is a race: a 5×5 grid, the numbers 1 to 25, and 150 seconds to finish as many grids as you can. Each grid has a single correct answer, so every number can be deduced rather than guessed. The players who post big scores are not cleverer, they simply carry a few fast checks that eliminate wrong cells at a glance. This guide covers how the puzzles are built, the checkerboard rule that settles half the board before you start, distance arguments, and how to spend the clock.

How the puzzles are built

Each grid begins as a hidden path that visits all 25 cells, with consecutive numbers always side by side horizontally or vertically. The generator then removes clues one at a time in random order, putting a clue back whenever its removal would allow a second solution. Finally it reveals extra cells until 11 numbers are showing. In 3,000 grids we generated with the game's own code, every one showed exactly 11 clues and every one had a unique solution.

Two more results from that simulation are useful. The number 1 was among the clues about 54 percent of the time and 25 about 64 percent of the time, so expect to locate at least one end yourself in many grids. And the ends of the path sat in a corner about 23 percent of the time, on another border cell about 30 percent and in the inner 3×3 block about 47 percent. Do not assume the path starts or finishes on the edge.

The checkerboard rule

Imagine the grid coloured like a chessboard, with the four corners dark. A 5×5 board then has 13 dark cells and 12 light ones. Every step of the path moves to a neighbouring cell, and neighbours always have opposite colours, so the path alternates dark, light, dark, light. With 25 numbers, the 13 odd numbers (1, 3, 5 … 25) must occupy the 13 dark cells and the 12 even numbers the 12 light cells. There is no other way to fit them.

This gives an instant filter. Odd numbers only ever go on cells that share a colour with the corners, which are the cells where the row and column numbers add up to an even total. Even numbers only go on the others. Before you place anything, ask whether the number's parity matches the cell's colour. Half the candidate cells disappear immediately, and so do many tempting but impossible bends in the path. As a bonus, both 1 and 25 are odd, so the ends of the path always sit on corner-coloured cells.

Distance and parity checks

If two clues differ by d, the path between them is exactly d steps long. That leads to two tests you can run in a second:

• Reach. Count the rows plus columns between the two clues. That distance can never exceed d. If it equals d, the path between them must move steadily toward the second clue, never stepping away, which usually leaves only one or two shapes.
• Slack. The difference between d and that distance is always an even number, because every detour away from the target must be paid back by a step toward it. Slack of 0 means a direct run, slack of 2 means a single bump, and larger slack is where the real thinking happens.

Example: suppose you are about to place a 9 two cells away from a 6. The difference is 3 but the distance is 2, an odd slack, so the placement is impossible before you even look at the rest of the board. This is the checkerboard rule seen from another angle. Now take a clue 6 and a clue 10 two cells apart in the same row. The slack is 2, so 7, 8 and 9 make one small detour into the row above or below. If one of those rows is off the grid, or already full, the detour has only one side to go.

Corners, edges and dead ends

Because every cell must be used, any empty cell that has only one empty neighbour left (and no clue beside it that could connect) has to be an end of the path, or the path will strand it. Corners start with only two neighbours, so they are the first places to check. If a corner is empty and one of its two neighbours is already part of a stretch that cannot turn into it, the other neighbour must lead in and out, which pins down a short chain of numbers.

Watch for cells that become isolated pockets as you fill. A single empty cell surrounded by placed numbers is only legal if its two required neighbours, the number before and the number after it, are among those placed numbers. If no pair of adjacent values around it differs by two, the pocket is a mistake and something nearby needs to move. Spotting a pocket early saves far more time than discovering it at number 24.

Working the controls quickly

Tap an empty or player-filled cell to select it, then tap a number on the pad. Tapping the selected cell again deselects it; tapping a clue clears the selection. The pad shows which numbers are already placed by dimming them, but dimmed keys still work: tapping one moves that number from wherever it was to the selected cell. That makes corrections fast. You never need to clear the old cell first. The one exception is a number that is a clue, which cannot be moved, so tapping it does nothing.

The ✕ key empties the selected cell. The game gives no warning for a wrong number; it only reacts when the whole chain from 1 to 25 connects, at which point the board flashes green and a fresh grid appears about half a second later. So if you have filled all 25 cells and nothing happens, there is an error somewhere. Scan consecutive pairs from 1 upward until you find two that are not touching.

Spending the 150 seconds

The clock starts when you press Start and counts real time, turning red in the last 20 seconds. It keeps running if you switch apps, so finish the run before looking away. Your score is the number of grids completed when time runs out, and a half-finished grid counts for nothing.

• Fill forced stretches first. Slack-zero runs and corner chains go in without thought. They also shrink the open area, which creates new forced cells.
• Work outward from the densest cluster of clues. Eleven clues are rarely spread evenly. Where several sit close together, the gaps are short and the answers come quickly.
• Leave the ends for last. If 1 or 25 is missing, it is usually easiest to place once almost everything else is filled, because it must sit next to 2 or 24 on a corner-coloured cell.
• Do not stall. If two shapes still look possible, place the one that keeps more cells reachable, and check the result quickly with the colour rule. Wrong guesses cost nothing except the moves to fix them.

A practice plan

1. Play a few runs using only the colour rule, saying "odd on dark, even on light" before each placement.
2. Add the reach and slack checks on every pair of clues before you place anything.
3. Then focus on speed: aim to finish your first grid in under 40 seconds, then two grids in a run, then three.

Your best total is kept on your device, and any score above zero can be sent to the Hall of Fame from the result card.