Hidato vs Numbrix vs Trail: Number Path Puzzles Compared
Hidato allows diagonal steps, Numbrix does not, and Trail numbers are checkpoints. Their origins, the rules side by side, and one 4x4 path solved three ways.
Hidato, Numbrix and Trail are three versions of the same idea: one path through every square of a grid, visiting the numbers in order. The differences are in two rules. Hidato, invented by Gyora Benedek, lets the path step diagonally; Numbrix, Marilyn vos Savant's puzzle in Parade magazine, allows only up, down, left and right. In both, every square gets a number. Trail also moves only in straight lines, but its numbers are checkpoints, you draw a line instead of writing numbers, and harder grids add walls.
This post is for players who know one of the three and want to understand the others. It covers where each came from, the rules side by side, one small grid set as all three puzzles, and how the solving techniques change.
The three puzzles side by side
All three are Hamiltonian path puzzles: the answer is a route that visits every square exactly once. What changes is how you may move and what the printed numbers tell you.
| Hidato | Numbrix | Trail | |
|---|---|---|---|
| Created by | Gyora M. Benedek | Marilyn vos Savant, for Parade | Puzzle Picnic's version of the genre |
| Moves | Up, down, left, right and diagonal | Up, down, left, right | Up, down, left, right |
| What a printed number means | Its step in the path | Its step in the path | A checkpoint; only the order matters |
| What you fill in | A number in every square | A number in every square | A line through every square |
| Grid shapes | Square, hexagonal or irregular | Square (7x7 and 9x9) | Square, 5x5 to 8x8 |
| Walls | No | No | On Hard and Expert |
LinkedIn's Zip, launched in March 2025, follows the same rules as Trail. Grandmaster Puzzles, which helps design it, describes a path through all cells that moves "horizontally or vertically", cannot cross itself or a wall, starts on 1, passes the numbers "in ascending order" and ends on the highest number.
Hidato: Gyora Benedek's puzzle with diagonal steps
Hidato is the puzzle where consecutive numbers may touch in any of eight directions. Its inventor is Dr. Gyora M. Benedek, an Israeli mathematician, and the name comes from the Hebrew word hida, meaning riddle. It is also known as Hidoku, and the name Hidato is a registered trademark.
You are given a grid with some numbers already in place, including the first and the last, and you fill the rest so that each number touches the next one horizontally, vertically or diagonally. The grid is usually square, but Hidato also comes on hexagonal grids and on irregular shapes with holes in them.
Andrews McMeel Syndication, which syndicates Hidato and carries it in The Puzzle Society, quotes Benedek on what he wanted from it: "a good puzzle ... must have a unique solution and ... solving it should not require any trial and error." The same page says he came up with the idea while scuba diving, wondering whether he could "connect the dots and reconstruct the fishes' crazy swimming pattern".
Numbrix: Marilyn vos Savant's straight-line version
Numbrix is the same puzzle with diagonal steps taken away. It was introduced in Parade magazine in July 2008 by Marilyn vos Savant, who writes the magazine's "Ask Marilyn" column. It started as a 7x7 puzzle; the weekly print version asks you to place the numbers 1 to 81 in a continuous path on a 9x9 grid, and vos Savant also makes daily Numbrix puzzles for Parade's website. Wikipedia notes that vos Savant has used only 7x7 and 9x9 grids.
Since 2014 Parade's website has also published a much harder variant, Jadium (formerly Snakepit), by Jeff Marchant.
Taking away diagonals changes more than it seems. Each square has at most four neighbours instead of eight, so there are fewer routes to consider. And the path alternates colours on a chessboard pattern, which gives Numbrix a check that Hidato does not have (see the technique table below).
Trail: the numbers are checkpoints
In Trail you draw one line from 1 through every square, passing the numbers in order and ending on the highest one. The line moves up, down, left or right, never crosses itself, and cannot pass through a thick wall. The Trail rules guide covers them in full.
The big difference from Hidato and Numbrix is what a number tells you. In Numbrix, a 10 means "this is the tenth square of the path". In Trail, a 3 only means "the third checkpoint". Between checkpoint 3 and checkpoint 4 there could be one blank square or fifteen. You lose the counting that Numbrix players rely on, and you gain other information instead: there are far fewer numbers, so every one of them matters, and on Hard and Expert the walls take away routes.
The other difference is physical. In Hidato and Numbrix you write numbers into squares, so a mistake means erasing a run of numbers. In Trail you drag a line, drag back to undo, or tap a square on the line to cut it there.
One path, three puzzles
The clearest way to see the differences is to set the same answer as all three puzzles. Here is a path through a 4x4 grid, written as step numbers. Squares are named by row and column from the top left: r3c4 is row 3, column 4.
As a Numbrix
Five givens are enough to make this a Numbrix with exactly one answer.
- Counting from 10 to 13. They are three steps apart and three squares apart in a straight line down column 1. With no room for detours, 11 and 12 go straight down: r2c1 and r3c1.
- Counting from 13 to 16. The same reasoning along row 4 puts 14 and 15 on r4c2 and r4c3.
- Where 9 goes. 9 must touch 10, and the only free square beside 10 is r1c2. So 9 is r1c2.
- Where 3 goes. 3 must touch 2, so it is r3c2 or r2c3. If it were r2c3, then r3c2 would be left with a single free neighbour, r2c2. A square with one way in has to be an end of the run from 3 to 9, and both ends are already placed (3 on r2c3, 9 on r1c2). So 3 is r3c2, and 4 is r2c2, its only free neighbour.
- The run from 4 to 9. The four squares left, r2c3, r2c4, r1c4 and r1c3, must take 5 to 8 in a chain from r2c2 to r1c2. Only one order works: 5 on r2c3, 6 on r2c4, 7 on r1c4 and 8 on r1c3.
Steps 1 and 2 are the Numbrix move that Trail does not have: when two givens are exactly as many squares apart as their numbers differ, the path between them is a straight run.
As a Hidato
Keep the same five givens but allow diagonal steps, and the puzzle falls apart. A computer search finds 20 different answers. Here is one of them.
Even the straight run from 10 to 13 is no longer forced: with diagonals, 11 can sit on r2c2 and 12 step back to r3c1, because a diagonal step covers a row and a column at once. Five of the 20 answers do exactly that. A Hidato setter has to give more numbers, or numbers in different places, to pin the path down.
As a Trail
In Trail the clues are checkpoints, so the same path needs a different set of numbers. Four checkpoints are enough here.
The opening uses Trail's own tools rather than counting. The end, 4, sits beside 1, but the line cannot step straight from 1 to 4 because it would skip 2 and 3. It cannot step from 1 to 3 either. So 1 leaves through r3c3, and the line reaches 4 last, from r4c3. The corners do the rest: r1c1 must link r1c2 and r2c1, r4c1 must link r3c1 and r4c2, and r1c4 must link r1c3 and the 3.
How the solving techniques differ
The core ideas are shared, but each puzzle leans on a different one. This table compares the main techniques.
| Technique | Hidato | Numbrix | Trail |
|---|---|---|---|
| Distance check: are two numbers close enough? | Yes, counting king moves (a diagonal step covers a row and a column) | Yes, counting rows plus columns | No, checkpoints carry no step count |
| Exact distance forces a straight run | Rarely, because diagonals allow detours | Often | No |
| Chessboard colour check | No, a diagonal step keeps the same colour | Yes, odd and even numbers sit on opposite colours | Only for the whole line, not number by number |
| Corners force links | Weakly, a corner has three neighbours | Yes, a corner has two neighbours | Yes, and walls make more corner-like squares |
| Dead ends | Yes | Yes | Yes, the main tool |
| Numbers out of order | Built into the counting | Built into the counting | A key rule: never link two non-consecutive checkpoints |
The chessboard check is worth spelling out. Colour the grid like a chessboard. Every straight step moves to the other colour, so in Numbrix all odd numbers sit on one colour and all even numbers on the other. So a given 7 and a given 12 must sit on opposite colours, and any square you consider for 9 must share 7's colour, which rules out half the grid at a glance. In Hidato a diagonal step stays on the same colour, so the check does not work. In Trail it still holds for the line itself, which matters on odd-sized grids like 5x5 and 7x7, where the line must start and end on the more common colour. The path puzzle strategies guide uses this in detail.
Which one to play
The three puzzles reward slightly different habits, so the best choice depends on what you enjoy.
- Numbrix suits players who like counting. The givens are step numbers, distances are easy to check, and the chessboard rule gives a quick test. It is the most arithmetic of the three, though it never needs more than counting.
- Hidato suits players who enjoy a looser, more visual search. Diagonal steps mean many more routes to rule out, and the grids come in more shapes.
- Trail suits players who like drawing and seeing the whole route form. With fewer numbers, the reasoning shifts to corners, dead ends and walls. In Puzzle Picnic it comes at four levels: Easy 5x5, Medium 6x6, Hard 7x7 with walls, and Expert 8x8 with more walls and fewer numbers.
If you are new to all three, Trail and Numbrix are the gentler start, because straight moves leave fewer options per square.
Frequently asked questions
What is the difference between Hidato and Numbrix?
The only rule difference is diagonals. In Hidato consecutive numbers may touch horizontally, vertically or diagonally; in Numbrix they must touch horizontally or vertically. That one change matters a lot: Numbrix gains a chessboard colour check and straight-run deductions that Hidato does not have.
Who invented Numbrix?
Marilyn vos Savant, the Parade magazine columnist behind "Ask Marilyn", introduced Numbrix in Parade in July 2008. It started on a 7x7 grid, and the weekly print puzzle uses a 9x9 grid with the numbers 1 to 81.
Is Trail the same as Numbrix?
No, though both move only up, down, left and right and visit every square. In Numbrix each given number is a step count and you fill in all the missing numbers. In Trail the numbers are checkpoints that only set the order, you draw a line rather than writing numbers, and harder grids add walls.
Is LinkedIn's Zip a Hidato or a Numbrix?
Neither, strictly. Zip's numbers are checkpoints passed in ascending order, its path moves only horizontally and vertically, and some grids have walls. Those are Trail's rules, not Hidato's or Numbrix's.
Where to go next
If you came from Numbrix or Hidato, the quickest way into Trail is to stop counting and start looking at corners: how to play Trail walks through a first puzzle that way. For the shared maths behind all three, Hamiltonian paths and one-line puzzles explains why finding such a path is hard in general but friendly on a small grid. When walls start to appear, walls in path puzzles shows how to read them. You can try a Trail grid in your browser on the Trail page.