Hidoku Puzzles
Fill the grid so that every number from 1 to the last one appears once, and each number touches the next. Tap a square, then tap a number. Sixty grids, every one solvable by deduction alone.
The same mechanic is sold under two brand names; this page uses the generic term throughout.
Related Practice
What Is A Hidoku Puzzle?
A hidoku is a single chain of numbers threaded through a grid. Every square holds a different number, running from 1 up to however many squares there are, and consecutive numbers always sit next to each other. Some of the numbers are printed for you; the rest are blank, and the puzzle is to work out where they go. Unlike sudoku there is no arithmetic and nothing to add up — the only fact you ever use is that each number must touch the one after it.
Diagonal Steps, And Why They Change Everything
Half the grids here let a number touch the next one at a corner, giving eight possible neighbours. The other half allow only up, down, left and right. That sounds like a detail and it is the biggest difference on the page, because it decides how much the setter has to give away:
| Adjacency | Neighbours per square | Numbers printed | How it feels |
|---|---|---|---|
| Diagonals allowed | up to 8 | 46–48% | Fuller grid, more freedom at each step |
| No diagonals | up to 4 | 21–28% | Emptier grid, but each number settles far more |
So a no-diagonal board looks much harder than it is. With only a fifth of its numbers showing it can seem hopeless, but a chain that cannot cut corners has so little room to wander that each printed number pins down a long stretch of it.
The move that opens almost every hidoku: find two printed numbers that are two apart, like 14 and 16. The 15 between them must touch both, and usually only one empty square manages that. Scanning for near-consecutive pairs before anything else will get you further than working methodically from 1.
Working From Both Ends
The first and last numbers are always printed here, which is the convention of the form and also what keeps a grid from having several answers. They give you two places to push from: the number after 1 can only be in a square touching 1, and the number before the last can only be in a square touching it. Growing the chain inward from both ends is often faster than growing it forward from 1 alone, because the two halves eventually have to meet and that meeting point is heavily constrained.
Why Nothing Here Needs A Guess
Every grid is proved before you see it. A solver restricted to ordinary reasoning — a number with only one square left, or a square only one number can reach — has to fill the whole grid. Because each of those steps is forced, the answer that results is the only possible one. A second program then re-walks the chain from 1 to the end by a completely different method and confirms that exactly one route exists. Every printed number beyond the two ends has also been checked to be necessary: take any one away and the puzzle stops being solvable by deduction.
Hidoku Puzzles Frequently Asked Questions
What is a hidoku puzzle?
A grid holding every number from 1 up to the number of squares, arranged so consecutive numbers always sit next to each other. Some are printed; you fill in the rest so the chain runs unbroken from 1 to the end.
What are the rules?
Two. Every number from 1 to N appears exactly once. And consecutive numbers must touch — on most boards that includes diagonals, though some grids here allow only up, down, left and right.
What is hidoku also called?
The same mechanic appears under two trademarked brand names — one for the diagonal version, one for the orthogonal one. This site uses the generic hidoku throughout, as it does for every trademarked puzzle name.
Do diagonal steps count?
It depends on the grid, and each one tells you. Diagonal boards give a number eight possible neighbours; no-diagonal boards give it four. They are different puzzles, not easier and harder versions of one.
Why do the no-diagonal grids look so empty?
Because they need far fewer. A diagonal grid prints about 46–48% of its numbers; a no-diagonal grid only about 21–28%. A chain that cannot cut corners has less room to wander, so each printed number settles more of it.
How do you start a hidoku?
Find two printed numbers close in value — 14 and 16, say. The number between must touch both, and usually only one empty square does. Scanning for pairs two or three apart is the most productive opening move.
Why are 1 and the last number always shown?
They are the two ends of the chain and are printed by convention. Without them a grid could often be numbered more than one way. Every other printed number here has been checked to be genuinely necessary.
Does every puzzle have exactly one answer?
Yes, and none needs guessing. A solver restricted to ordinary deduction must fill every square, which makes the answer unique since each step was forced — and a separate program walks the chain independently to confirm only one route exists.