Hidato

Hidato is a logic puzzle invented by Gyora Benedek, a scuba-enthusiast mathematician who says he was inspired by watching the complex paths of fish while diving. There are numbers, but don’t worry – like Sudoku, they’re just symbols – there’s no mathematics involved!

The goal of Hidato is to fill the grid with consecutive numbers that connect horizontally, vertically, or diagonally. Here is a small sample Hidato puzzle:

Rules of Hidato

The rules of Hidato are very simple: fill in all the missing numbers in the grid such that they connect consecutively from smallest to largest, touching horizontally, vertically, or diagonally. In other words, starting at 1, it must be possible to travel to 2, then 3, then 4 and so on, by moving between touching squares.

Here’s what our small sample puzzle looks like once it’s solved. We’ve overlaid the arrow to make it easier to see the path from 1 to 16:

The solution to the earlier small example Hidato puzzle.

Solving Hidato Puzzles

Every puzzle has a single and unique solution. They are solved using a process of elimination. Here are some tips to help you, and then we’ll look at a worked example.

Start with placements that you are certain of. In the example above, the first number we need to place is the 4. There are four empty cells touching the 3, but only one of them also touches the 5, so that must be where the 4 goes.
When you reach a number with more than one possible placement option, skip ahead. On your first pass through the puzzle, complete all the sections where placement is in no doubt. You can then return to the beginning and will find some earlier areas you could not complete now have a single solution.
Sometimes you can skip ahead a few numbers, find a placement, then return to to where you skipped from and you can fill in the blanks.
If you’ve skipped ahead more than a few numbers, once you have placed a number it can be helpful to then work backwards. Often you can get all the way back to where you left your initial gap.
Keep an eye out for potential dead-ends. If filling in a number will isolate an empty cell that can’t be connected to any of those surrounding it (a dead end), you’re making an error.
When faced with two or more cells a number could go in, look at the pre-filled numbers in the surrounding area. You may find that one or more of your candidate cells must be used to connect them, thus giving you your answer. This technique works well in easier to intermediate level puzzles.
In harder level puzzles, work out likely routes between pre-filled numbers. Even if you don’t know the exact cells the numbers go in, you can work out the rough route they must take based on how many cells they must traverse. When you work out two or three such routes, you’ll see places where they cannot go (because they would cut off other routes) – this can give you further placements.
If you have two paths open to you, consider writing in candidates (small numbers), like with Sudoku. That way, when you fill in one of those two cells with a definitive placement, you can erase the small candidates and immediately fill in the other cell as well.

Worked Example

Here’s a bigger puzzle, though still an easy one. We'll work through step by step. If you want to print it out to play along, it's part of our Taster PDF you can download at the bottom of this page.

Hidato puzzle, worked example - possible placements

We’ll start at number 1, because starting at the beginning is as good a place as any for easy level puzzles. We know we need to place the 2 and the 3 somewhere (the next pre-filled number being 4). Starting from the 1, there are three cells available for the 2.

Although cell A touches the 1, we cannot possibly put the 2 in there, because we can’t get from there to the 4 in one cell. So the 1 goes in either B or C.

Hidato puzzle, worked example - potential placement of two numbers

We could put the 2 in B and the 3 in C like this. At first glance this looks good. But there’s a problem. Can you spot it?

The problem is that to get from the 9 to the 11 we know we will have to put the 10 in cell B. So the 2 cannot go there.

Hidato puzzle, worked example - definitive placement of a number

It has to go in cell C, like this.

Hidato puzzle, worked example - filling in part of the puzzle

Now we have an easy run, using the same logic to fill in numbers all the way up to 19. You may notice that the 12 appears to have two possible placements, but only one is valid because we cannot block the path between 27 and 29.

We are faced with a choice for where we put the 20: cell A and cell B. It’s very easy to work out which must be the answer. The next printed number is 24, so that’s where we are headed. If we put the 20 in cell B, it won’t be possible to reach 24, it’s too far. So the 20 must go in cell A

Hidato puzzle, worked example - another definitive placement

There’s another choice here. 21 could conceivably go in A or B – both let us get to 24. We don’t know which it is yet, so we’ll have to skip ahead.

Hidato puzzle, worked example - filling in everything up to number 33

Counting up from the 24, we can get all the way to 33 with no decisions to make.

After the 33, we are faced with a choice, where to put the 34, in A or B? Again, the answer is simple because cell A is the only possible path between the 41 and the 43, so we must put the 34 in cell B, leaving A free for the 42.

Hidato puzzle, worked example - filling in everything to 49

Once we’ve done that, we’ve got a clear run all the way to 49. We’ve already completed more than half the puzzle!

It’s not immediately clear whether we should place the 50 in cell A or B – either would work. Instead of worrying about that, let’s skip ahead.

Hidato puzzle, worked example - skipping ahead a few numbers

Counting from the 53, we can add in numbers taking us all the way to 67. The 68 could go in cell B or C. Looking around that area, we can see that we need to put the 73 somewhere, and maybe that goes in cell C, but it doesn’t have to, so we cannot use that to determine where the 68 goes.

Hidato puzzle, worked example - spotting an easy placement

Let’s look and see if there are any other numbers we can definitely place. 79 is easy to spot.

Hidato puzzle, worked example - counting backwards

From there, we can keep counting backwards, placing the 76, 75, all the way down to 71.

Now we know that cell C must contain 70...

Hidato puzzle, worked example - filling in previously skipped numbers

That means cell B must contain 68, which means A must be the 50 we couldn’t decide about earlier.

Now we can go back and fill in the rest of the cells – they are all easy. Can you do it? If you want to check your answers, have a look at the Hidato Taster PDF below – it’s got a few puzzles for you to try including this one, along with the solutions.

Try Hidato Yourself

Ready to have a go yourself? We’ve put together a taster of four puzzles for you, including the example above. You can download and print the PDF below. Solutions are included, but no cheating!

Download Our Hidato Taster

Where To Play

We publish Hidato puzzles in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazine – find out more, and get your copy, here.