Puzzle Genius

Yagit is a (severe!) contraction of Yagi to ookami which is Japanese for goat and wolf. It’s a spatial awareness puzzle played on a square grid divided into cells. The grid represents a field. In some cells are goats, and in others are wolves. Your goal is to erect fences to divide up the field in such a way that goats and wolves never find themselves in the same area. There are some fence posts dotted around the field to help you. Here’s what a small Yagit puzzle looks like:

Yagit small example puzzle

Rules of Yagit

The rules of Yagit are as follows:

  • Fences must begin and end on the borders of the field (grid).
  • Fences can turn ninety degrees at a fence post (but they don’t have to).
  • Fences can cross other fences, but never at a fence post.
  • Every area must contain one or more goats, or one or more wolves, but never a mix of both.
  • No fenced off area can be empty, it must contain at least one animal.
  • You don’t have to use all the fence posts.

This is what the example puzzle looks like once it has been completed:

The solution to the small example Yagit puzzle

Solving Yagit Puzzles

Yagit is solved through a combination of logical deduction and elimination. There is always a logical solution and never any need to guess, but as puzzles get harder you will need to make longer chains of deduction to work out where fences must be placed. Here are some tips to help you get started, and then we will work through an example puzzle from start to finish.

Begin by separating goats and wolves in adjacent squares. Since they cannot be in the same field, there must be a fence between them. You can extend these fences to the boundaries or fence posts, whichever comes first, because fences cannot exist in isolation.

Eliminate routes from fence posts that already have two lengths of fence attached (because fences cannot cross at posts). This reduces the options for where fences can go.

You can also eliminate routes where placing a fence would create an empty area. 

When you eliminate a route (cell dividing line), you can continue to eliminate it in both directions until you reach a border or a fence post.

Worked Example

The best way to understand how a puzzle works is to solve one. We’ll work through an example from start to finish, which will give you a good idea of the basics. Remember, though there is only one valid solution, there are many ways of reaching it. This is not the way to solve this puzzle, just one possible path to do so.

Yagit worked example 1

This is the puzzle we are going to solve. It’s an easy Level 1 grid that provides an overview of the basic techniques necessary.


Yagit worked example 2

We’ll begin by separating goats and wolves that are in adjacent cells. There are four such cases on this board, so we start by drawing in sections of fence to separate them.


Yagit worked example 3

Because we know that fences must originate and terminate at the borders of the field, and that they can only turn at a fence post, we can extend our fence sections to the borders or posts, whichever come first.


Yagit worked example 4

To work out where we must go next, we can start to eliminate some possible routes for fences. Consider the fence at the top left corner. From the fence post, it could turn ninety degrees and go to the top of the field, or it could turn ninety degrees the other way and go to the post three rows further down the field, or it could continue straight on and go to the right-hand edge of the field (as shown here). However, were it to go straight on like that, we would be creating an empty area (yellow) which is not allowed.


Yagit worked example 5

Therefore we know the fence cannot go straight on. That means we can strike through those borders to remind ourselves that no fence can run there. This will help us see options as we progress.


Yagit worked example 6

We can also strike through a potential route one row further down for the same reason – any fence to run along it would create an empty area in the yellow highlighted cell.


Yagit worked example 7

In fact, we can cross off quite a few possible fence routes. All these red strike marks show us where we can’t put a fence because we’d be creating empty areas. This helps us see where we must run fences.

Now, let’s look at the wolf highlighted in yellow. We need to separate it from the two goats to its right. There’s only one place we can possibly put a fence that will do that, so we can draw it in…


Yagit worked example 8

…like this.

This new fence gives us a new clue. Because it’s connected to a fence post that already has a fence attached to it, we know that no more fences can ever connect to that post (because fences cannot cross at posts). That means we can strike off the two remaining paths to that post.


Yagit worked example 9

Now consider the (highlighted) fence post in the bottom right corner. It’s only got one possible path it can take – it has to connect to the post to its left.


Yagit worked example 10

Having drawn it in, it’s easy to see that it must now go upwards. We’ve eliminated the path to the left, and if we were to go down, we would be creating a large empty area. Up to the top of the field is the only route possible…


Yagit worked example 11

…like this.

We’re making good progress. There are a couple of ways we could continue, but let’s look at the goat and wolf highlighted here. We need to separate them, and there’s only one fence we can put in which will achieve that.


Yagit worked example 12

We run the fence from the border up to the first post we encounter. Now we have a choice to make. Do we continue that fence up to the next post above, or do we turn left? See if you can work it out…

Did you do it? To see the answer, let’s consider what would happen if we ran the fence up towards the top of the field.


Yagit worked example 13

At first glance, it looks like it might work. But we’d still have to separate the two enemies highlighted in yellow, and there would be no way of doing that without creating an empty area – it’s just not possible.

So that means it’s not a valid option. We have to run that fence to the left instead.


Yagit worked example 14

Now we just have the top corner to worry about. There are two fence posts in the yellow box, and each one has two possible directions in which a fence can be run to reach the border or another fence post. You can think through all the permutations, but there’s only one way to complete the two fences that does not leave us with an empty area…


Yagit worked example 15

…and this is how it’s done.

That’s it, the puzzle is solved. Every area contains at least one animal, and there are no goats and wolves within the same area. No fences cross at posts. Simple! Ready to try one yourself? Read on…


Try Yagit 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 Yagit Taster

Where To Play

Puzzle Weekly Presents: Yagit - front cover

Finished the taster and want more great Yagit puzzles? No problem! Get 120 carefully crafted puzzles set over seven levels in Puzzle Weekly Presents: Yagit– it's great value!

We include Yagit in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here.

Yakazu is a logic puzzle in the same vein as Sudoku. The rules are simpler, but don’t let that fool you into thinking the puzzle is too! Harder level puzzles require some extended logical reasoning to complete.

Here’s an example of a small Yakazu puzzle:

A small example of a Yakazu puzzle

Rules of Yakazu

The aim of the puzzle is to complete the grid such that every region of consecutive cells contains the numbers 1 to x, where x is the size of the region. So a run of cells that’s four cells wide must contain the numbers 1, 2, 3, and 4. Numbers can be in any order. Sounds simple, right?

Here’s what our small example puzzle looks like once it’s been solved:

The solution to the small example Yakazu puzzle

Solving Yakazu Puzzles

Solving these puzzles requires a combination of elimination and logical reasoning. Here are some tips to help you get started, then we’ll work through an example puzzle.

  • Begin with easy wins. Regions only two cells high or wide are the simplest to fill in.
  • Next look for three-cell regions. Even if they don’t already contain a clue number, you can often fill them in by looking at the regions they intersect with.
  • Generally speaking, it’s usually easier to work on smaller regions first, as they have fewer candidates.
  • Use crossing rows (or columns) to eliminate candidate numbers. For example, in a row nine cells wide, any intersecting column smaller than eight cells cannot contain the 8 or 9. Looking for tall or wide regions that are crossed by short ones is a good way to find easy placements.
  • In harder level puzzles, it may be necessary to write in small candidate numbers like in Sudoku. This can help you eliminate placements and reveal hidden opportunities.
  • Always check for consequences after filling in a cell. Often filling in just one number can set off a chain reaction.

Worked Example

We’re going to work through an example puzzle from beginning to end. Whilst every puzzle only has a single valid solution, there are lots of ways of reaching that solution. So please do bear in mind that this in not the way to solve this puzzle, just one possible way to solve it.

Yakazu Worked Example 1

This is the puzzle we are going to solve. It’s a Level 1 puzzle, an easy 6x6 grid, which will provide an overview of the basic techniques for approaching Yakazu.


Yakazu Worked Example 2

We’ll begin with the easiest of easy wins. There are a couple of two-cell regions we can fill in without a second thought (both of them taking a 2). We’ve also got a three-cell region missing just the 1. That cell also happens to complete a row. 


Yakazu Worked Example 3

We can fill in this three-cell region. The middle cell cannot contain the 3 because it’s in a column that already has a 3. So the 3 has to go in the last cell, leaving the middle cell for the 1.


Yakazu Worked Example 4

Column three is now easy to fill in. The 1 cannot go in the bottom cell because that’s in a row that already has one, so we put it in the top. That leaves the bottom cell for the 2.


Yakazu Worked Example 5

Let’s look at another technique. Consider the row highlighted in yellow; it is missing a 3, 4, and a 5. Ignoring any other way of working out what goes where (because we’re demonstrating a method!), we can focus on the 5. There’s only one place in the row it can go, and we can work it out by looking at the three intersecting columns, which happen to correspond to the three available empty cells. 

Looking from right to left: the orange column is four cells high, so cannot take a 5. The blue column is three cells high, so also cannot possibly have a 5 in it. That leaves the green column, which is six cells high, and therefore can take the 5. Indeed it’s the only cell in that row which can do so…


Yakazu Worked Example 6

…and so we can write it in. Where next?

Well, the blue column should be easy enough to fill in, based on the two rows that cross it.


Yakazu Worked Example 7

The bottom cell can only be a 3 (because it’s in a row that already has a 1 and a 2), and the 2 can only go in the middle cell, leaving the top cell as having to be the 1.

Now we can complete the third row down, because there’s only one free cell…


Yakazu Worked Example 8

Putting a 4 in that last free cell means there’s only one place to put the 3 in the intersecting column, and that in turn leaves just the 4 for the top row. This can happen a lot in Yakazu – filling in one cell can lead to a chain-reaction, which is why it’s always worth checking for consequences when you complete a cell.

There are only three cells left to fill in, and they are simple to work out.


Yakazu Worked Example 9

It doesn’t really matter whether you look at the six-cell row first or the six-cell column first, their intersections mean there’s only one way to complete them.

All done! Of course, that was the easiest level…the puzzles can get much tougher than this, requiring some deeper logical thinking. Ready to have a go yourself? Read on…


Try Yakazu 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 Yakazu Taster

Where To Play

Puzzle Weekly Presents Yakazu

Finished the taster and want more great Yakazu puzzles? No problem! Get 120 carefully crafted puzzles set over seven levels in Puzzle Weekly Presents: Yakazu– it's great value!

We also include Yakazu in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here.

Aquarium (sometimes also called Water Fun) is a spatial awareness logic puzzle. It shares some similarities with Thermometers, but make no mistake, this puzzle is its own thing with some unique challenges. Here’s what a small example puzzle looks like:

Aquarium small example puzzle

Rules of Aquarium

The aim of the puzzle is to fill the aquariums (regions delimited by bold lines) such that the number of filled cells matches the clue numbers shown outside the grid. Water always finds its level, so the water level in connected regions must match.

Here’s what our small example puzzle looks like once it’s been solved:

aquarium small example - solution

Solving Aquarium Puzzles

Solving Aquarium puzzles is, much like Thermometers, about exclusion and forced placement. Here are some tips to help you get started, and then we’ll work through an example puzzle from start to finish.

  • As always, begin with easy wins. Look for aquariums (regions) that are wider horizontally than the clue number for a row. They cannot be filled so can be excluded. For example: A row has a clue number of 3, and a tank is four cells wide in that row. None of those cells can contain water (if any one was full, they’d all have to be full), so they can be excluded.
  • When excluding cells horizontally, you can automatically exclude cells in the same tank that are above them – but look out for water breaks that could hold water into some areas.
  • Look for horizontal combination constraints. Tanks cannot be partially filled horizontally – either the whole width of the tank is filled or none at all. Therefore some tanks must be empty because they cannot be combined with other tanks in a row to arrive at the clue number. This same constraint can sometimes show you tanks that must be filled as part of the row.
  • Keep an eye out for rows and columns that are already sufficiently filled; any remaining cells can be excluded.
  • Look at columns that are partially filled. If a tank has more empty cells than the number necessary to complete the column, you can exclude the top cells. For example, if a column has a clue number of 6 and you already have four cells filled, and there’s a vertical tank three cells high, you know you can exclude the top cell of that tank – which may in turn lead to other cells being excluded as the tank extends into other columns.
  • Look for forced fills. If a row or column only has as many cells available as a clue number, they must all be filled.
  • Don’t restrict yourself to working in any particular direction (such as from the bottom up), or on any particular row, column, or tank at a time. Partial fills can be very useful and will open up paths through the rest of the puzzle.
  • In harder puzzles, consider whether clue numbers for a row are odd or even and look at whether the tanks in that row contain an odd or even number of cells. This can help you exclude or include certain combinations of tank to reach the target number of filled cells.
  • As with most of these kinds of puzzles, it helps to mark off cells as you exclude them, and to strike out clue numbers as you complete rows and columns.

Worked Example

Now you know how Aquarium works, we can put it into practice and work through a full size puzzle. There is rarely a single path to solving a given puzzle, so this is not the only way to solve this one, only a single possible way to do so. Indeed, I’m going to deliberately bypass some obvious steps in order to demonstrate some techniques.

Aquarium Worked Example 1

This is the grid we are going to work through. It’s a Level 1 puzzle which is easy enough to solve but should give you a grasp of the basics. There are lots of places to begin, but we’ll start with the easiest of all, which is probably the two rows labelled with the clue number of 2.


Aquarium Worked Example 2

Both of those ‘2’ rows have horizontal sections of aquarium that are considerably larger than two cells, therefore they cannot be filled. We can mark them with Xs to exclude them.

By implication, we can also exclude the cell highlighted in yellow – there’s no way that could contain water if those below it are empty.

Now we know how to complete the top row of the puzzle…


Aquarium Worked Example 3

…as there are only two cells remaining. That completes the row, so we strike out the clue number.

Of course, that cell in the top right corner can’t be filled on its own – the water cannot simply float there! We have to fill the rest of the aquarium beneath it....


Aquarium Worked Example 4

...like so.

Moving on, we know we can fill all the other empty cells in the ‘8’ row.


Aquarium Worked Example 5

That’s completed the row. And because we had to back-fill the aquarium at the far left, it’s also meant we’ve completed the ‘2’ row beneath it.

Where next? We have a few options, but let’s go and exclude some more cells.


Aquarium Worked Example 6

 Excluding the two yellow areas for the two ‘3’ rows (because they are wider than three cells) lets us knock out a whole load of other cells by implication.

That’s going to let us complete some more rows…


Aquarium Worked Example 7

…specifically, the two ‘4’ rows in the middle.

Now, let’s have a look at the ‘6’ row.


Aquarium Worked Example 8

Although we don’t know all the cells that need to be populated to complete that row, we do know that the 2-cell region must be filled. There’s no way to complete that row without filling it. So we can fill it, which incidentally lets us strike off the end column as being complete. That means we can also put an X in the bottom-right cell.


Aquarium Worked Example 9

That lets us complete the bottom ‘8’ row, which in turn means we complete the first column (and can strike out the two remaining cells in it). We can also strike out the ‘3’ column as complete.

Finishing the puzzle now is easy, as it’s just a case of filling in the last few cells to meet the column and row targets.


Aquarium Worked Example 10

And that’s it – all done. Ready to have a go yourself? Read on!


Try Aquarium 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 Aquarium Taster

Where To Play

Aquarium Cover

Finished the taster and want more Aquarium in your life? No problem! Get 120 carefully crafted puzzles set over seven levels in Puzzle Weekly Presents: Aquarium – it's great value!

We also include Aquarium in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here.

Snake (sometimes also called Tunnel) is a spatial awareness path-finding logic puzzle. The aim is to connect the snake’s head with its tail by filling in grid cells following certain rules. Here’s what a very easy Snake puzzle looks like:

A small example of a Snake puzzle

Rules of Snake

The rules of Snake are easy to remember:

  • The snake’s body can be filled in horizontally and vertically
  • The body must never touch itself, not even diagonally
  • The numbers outside the playing grid tell you how many cells must be filled in for a row or column

In easier level puzzles, every row and column is labelled. As the difficulty ramps up, some rows and columns are blank, making it harder to determine the snake’s path.

Here’s what our earlier example puzzle looks like once solved:

The solution to the small example puzzle

Solving Snake Puzzles

Solving these puzzles requires a combination of elimination and forced placement based on logical deduction. There is no single ‘correct’ way to solve a Snake puzzle, rather, you need to have a variety of techniques available to you.

Although the goal is to connect the snake’s head to its tail, there is no particular need to start at either the head or the tail; sometimes it makes more sense to start somewhere in the middle, solving different sections at a time until eventually they all link up.

Here are some tips to help you tackle Snake puzzles, then we’ll look at a worked example below.

  • As you find cells that you know cannot contain part of the snake, it is useful to mark them off. As you narrow your options in this way, you will find places where the snake must go. 
  • Check for extremes. If a row or column is marked as 0, you can eliminate all the cells within it. Similarly, a row or column labelled with a number that matches the dimension of the grid (eg: labelled 6 in a 6x6 grid) can be fully filled in. However, both these scenarios are very rare and unlikely to appear in anything but the simplest puzzles.
  • Look for rows and columns labelled as 1. It is useful to highlight these because they effectively split the grid into unique sections. You can think of these rows and columns as one-way crossings – once the snake crosses one, it cannot return. Thus it becomes necessary to complete each side of a ‘1’ column or row before crossing it.
  • Bear in mind that crossing a ‘1’ column or row requires at least three consecutive cells to be filled in. This further narrows your possible crossing places.
  • Rows or columns labelled 2 are also constrained. You cannot perform a ‘U-turn’ within them, because that would require at least 3 cells due to the fact the snake cannot touch its own body. This can reduce potential crossing places.
  • If you locate three or more filled cells in a row, you can block out the middle cells to either side. Again, the rule about the snake not touching its own body means the snake cannot return to those cells.
  • Remember that as soon as the snake body touches the head or tail, it cannot go any further. So be careful not to run into either too soon.
  • Cross out clue numbers outside the grid as you complete rows and columns; it helps to remind you where you can no longer go.

Worked Example

We will work through a sample puzzle from beginning to end. As with all examples, remember that there’s no single path to the solution. This is just one way to get to the end.

Snake Worked Example 1

This is the Snake puzzle we are going to solve. At 8x8, and with every row and column labelled, it’s quite easy.


Snake Worked Example 2

There are no extreme values on this 8x8 grid (no rows or columns labelled with a 0 or an 8). 

We do however, have a ‘1’ row and a ‘1’ column. Because these are one-way crossings, it’s useful to highlight them. Once the snake’s body crosses each of these, there’s no turning back.

This allows us to immediately cross off three cells. The two to the right of the tail cannot be used, because it takes three cells to cross a ‘1’ column, and that would violate the 2 for that row. We can also eliminate the cell to the left of the head, for the same reason. That means the body extends from the head either up or down. Either way will allow us to fulfil the 2 clue for the column containing the head. Which way to go?


Snake Worked Example 3

We have to go down. Why? Because the row above the head requires three cells to be filled in. Crossing the ‘1’ column would use our full complement. We would have to get back down to the bottom row to fill in the six cells that must be filled there, and that would violate the ‘2’ row, and the ‘3’ row on our way back. The only way to fill in the ‘6’ row is to go there directly from the head. 

Once on the bottom row, we know we fill three cells to cross the one-way ‘1’ column. In fact, we can also deduce that we must place all six required cells in that row because there’s no valid way to leave the row and return. In other words, we couldn’t go across three cells, up a couple, across again, and back down, because that would violate the rows above.

This one move has completed a row and two columns for us. Where do we move next?


Snake Worked Example 4

We know we have to move up the ‘7’ column, because we’ve filled the ‘6’ row. Going up one cell completes the ‘2’ row (with the head), so we must go up another cell – there’s no choice.


Snake Worked Example 5

Now we do have a choice though. Because we have a one-way barrier ahead of us (the highlighted ‘1’ row), we know we must complete the ‘3’ row before moving upwards. So do we go left or right?

The one-way barrier means that once we turn upwards, we will have to continue for at least another two cells. Going right would violate the rules in two ways. Firstly, we would be filling three cells in a ‘2’ column. Secondly, we would end up touching the snake’s tail (diagonally). As the snake cannot touch itself, this would be an invalid move. 

So we have to go left…


Snake Worked Example 6

…then we have to cross our one-way barrier row by going up three cells, completing another column.

We can’t go up any more, so we have to go right…


Snake Worked Example 7

…and then upwards, because we’ve completed the three cells allowed in this row, and also because we have to complete our ‘7’ column. We’ve knocked off quite a few rows and columns now. 

It’s a clear run to the end. We have to fill four cells in the top row, and there’s only one way to do that…


Snake Worked Example 8

…which means we can drop down to the tail, completing the puzzle. Easy! Ready to have a go yourself? Read on!


Try Snake Yourself

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

Download Our Snake Taster

Where To Play

Puzzle Weekly Presents: Snake - Front Cover

Finished the taster and want more Snake in your life? No problem! Get 120 carefully crafted puzzles set over seven levels in Puzzle Weekly Presents: Snake – it's great value!

We publish Snake puzzles in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here

Pipelink is a spatial awareness puzzle from Japan. There are no numbers, there’s no complex mathematics, and no fancy formulas. The objective is very simple: to link all the cells in the grid with a single, continuous pipeline. Here’s what a very easy Pipelink puzzle looks like:

Example of a Pipelink puzzle

Rules of Pipelink

The rules are straightforward:

  • The pipe must pass through every cell in the grid.
  • It must use all the sections that are provided.
  • You cannot add to given cells.
  • The pipe may cross itself, i.e. create an intersection of perpendicular segments, but it cannot turn at an intersection.

Here’s what our earlier example puzzle looks like once solved:

What the example puzzle looks like once solved.

Solving Pipelink Puzzles

These puzzles are solved through logical deduction and spatial reasoning. We begin with what we know — the given pipe segments – and using that knowledge we work out where we can and cannot extend them. As we grow the pipeline a segment at a time, we slowly reduce the options for where subsequent segments can be placed.

Here are some tips to help you get started.

  • Begin by ruling out routes the pipeline cannot take. Because we must not add to given segments, we can use them to block certain paths.
  • Next, extend all the given segments. Every given segment must extend to the middle of the next cell. For example, a horizontal segment extends at least to the middle of the cell to its left, and to the middle of the cell to its right.
  • Then look for forced placements – places where your extensions must connect because there’s no other valid option.
  • Look for incomplete crossings. If you have a cell with three entries/exits, you know you must add a fourth for it to be a valid crossing.
  • Keep an eye out for dead ends. If extending a pipe in a certain direction is going to create a dead end with no possible way to connect back to the main pipe, you’re making a mistake.
  • If you get stuck, consider lightly pencilling in a candidate segment (or use a different colour if playing on screen) to make it easy to go back and erase it if it turns out to be wrong.

Worked Example

We will work through a sample puzzle from beginning to end. As with most puzzles, remember that there’s no single way to solve it. The larger the puzzle, the more possible paths to reach the final solution.

Pipelink Worked Example 1

This is the puzzle we will be working on. It’s an easy grid, but sufficient to demonstrate the techniques used to solve Pipelink puzzles.


Pipelink Worked Example 2

We can begin by marking out routes we know the pipe cannot take. This will be helpful later when we come to start extending it. Because we cannot add to the given segments, we know our pipe can’t go anywhere we’ve marked with a red cross.


Pipelink Worked Example 3

Next we can extend all the given segments into the middle of the adjoining cells. Doing so has connected some sections of the pipeline together – we’re making progress already!


Pipelink Worked Example 4

We can continue extending the pipe. The segments in the highlighted cells can only be extended in a single direction…


Pipelink Worked Example 5

…so we can extend those.
Where next? Let’s examine the grid further…


Pipelink Worked Example 6

The two highlighted cells have only one possible direction to extend. We have to extend them both downwards.


Pipelink Worked Example 7

But this leaves us with a problem. We’ve got two ‘islands’ that are isolated from the rest of the pipeline below. We’ll deal with the smaller one first. If we are to connect it to the rest of the pipeline, we can only do so from the highlighted cell. There’s simply no other option. Do we go down, or to the left? The answer, of course, is both! We cannot have a cell with three segments entering/exiting, it’s either two or four (because either the pipeline traverses the cell, or it crosses itself within the cell). So we can draw those extensions in now.


Pipelink Worked Example 8

That’s connected the top right-hand island, but it’s given us a two new problems – the highlighted cells are invalid because they have three entries/exits. Of course, these aren’t really problems, they’re opportunities, because we know we have to add a fourth segment to both of them. They must be crossings.


Pipelink Worked Example 9

We’re almost done. We just have one gap, and it’s an easy one to connect up…


Pipelink Worked Example 10

…which completes the puzzle. It’s fairly easy to see that this solution is valid just by looking. With larger puzzles, it can be harder to be sure your solution is valid. To check a solution, it can be worth tracing the entire pipeline with a different colour to make sure you can cover off the whole thing, and every cell, without lifting the pencil or stylus.


Try Pipelink 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 Pipelink Taster

Where To Play

We publish Pipelink puzzles in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here

Binairo, which is sometimes also called Takuzu, is a pure logic puzzle played on a variable sized grid. Using just 1s and 0s, it might be quick to learn but it can be a real challenge to solve! Here’s a small example puzzle:

Binairo Small Example puzzle

The goal is to fill the grid with 1s and 0s, following certain rules.

Rules of Binairo

There are only three rules to remember:

  1. No number can appear more than twice consecutively in a row or column.
  2. Each row and column contains the same number of 1s as 0s.
  3. No row or column can be duplicated within the puzzle.

Here is what the example puzzle looks like once completed:

The solution to the example puzzle above.

Solving Binairo Puzzles

Every puzzle has a single valid solution, though of course there may be lots of ways to reach that solution.

Unlike many kinds of logic puzzle, Binairo is not necessarily easier to solve from the outside in; even the corners aren’t helpful. On the contrary, the easiest wins come from clusters of numbers.

Here are some tips on how to approach solving a puzzle. Below, we will work through an example from beginning to end.

  • As with any puzzle, look for ‘easy wins’ first. There are three kinds of easy placement in Binairo:
    1. Doubles – i.e. two 1s or two 0s adjacent within a row or column. You can immediately place the opposite number either side of a double (otherwise you’d be putting three in a row, which violates rule 1).
    2. Empty cells with the same number either side of them. As with doubles, you can immediately fill the cell with the opposite number.
    3. Single remaining cells within a row or column. You’re unlikely to find these off the bat, except in very easiest puzzles. As you progress through a puzzle though, they crop up a lot. Simply count up the 1s and 0s already present in the row or column to work out what the final missing number must be. 
  • When you’re out of easy wins, look for forced placements based on the number of 0s and 1s you know you must put in a row or column. For example, if you know you have to place three 0s and you have four cells remaining, if three of them are in a row, the three 0s cannot all go in there together. Therefore one of them must go in the other free cell.
  • Remember after filling a cell to check for any consequences. Often placing even just one number will have a ripple effect, giving you an easy win which leads on to more easy wins. 

Worked Example

As with all puzzles, there’s not a single correct way to solve a Binairo. The example presented here is just one way, and is a demonstration of the general techniques used.

Binairo Worked Example 1

Here is the grid we are going to work through. This is a level 2 puzzle, so though it’s easy to complete, it still presents enough of a challenge to give an overview of the techniques used to solve these puzzles.

We’ll begin by looking for all the easy wins. Remember there are three kinds of easy win. First up, doubles (two adjacent numbers the same).


Binairo Worked Example 2

There are six doubles. We know that the numbers either side of them must be the opposite of the numbers forming the doubles, otherwise we’d be trying to put three numbers in a row, which isn’t allowed. So between them, these doubles allow us to solve seven cells. We’ll put those numbers in now.


Binairo Worked Example 3

Filling those in gave us three new doubles. We’ve also got an almost completed column (another easy win). We can fill in the yellow cell straight away; we know we must have an even number of 0s and 1s in each row and column. That column already has four 0s, but only three 1s. Therefore the yellow cell must be a 1.


Binairo Worked Example 4

Now the top row is almost complete, so we can figure out what the one remaining (yellow) cell must be. We’ve got all the 1s, so it must be a 0. 

We can also work out the two remaining cells in the second column must both be 0s, for the same reason.


Binairo Worked Example 5

We’ve used up all the easy doubles for now, so let’s check on another kind of easy win - empty cells with the same number either side. There are two such opportunities available here, so we can fill out those cells.


Binairo Worked Example 6

That’s opened up two new opportunities: there’s a single remaining cell in column three (yellow), and a new double in column five (green). Even without the double, we could complete that column just based on the count of 0s and 1s.


Binairo Worked Example 7

The penultimate row has a new double (which is also a single cell surrounded by two numbers the same).
Row five has a full complement of 1s, so we know the last two cells must both be 0.


Binairo Worked Example 8

We’ve got one more easy win for now (the green highlight). There are a couple more cells we can solve here too.

First, the blue column. It’s already got three 0s, and as this is an 8x8 grid we know we need one more. Although there are three empty cells, there’s only one into which we can place the missing 0 – the bottom cell marked with the blue X. If we put it in either of the others, we’d be making a row of three.

Next, the yellow row. We know that one needs three more zeros. We can’t put all of them in the last three cells, so one of them must go in the cell with the purple X.


Binairo Worked Example 9

Now we’ve got a double and a single cell, although we don’t need them anyway because as there are four 0s already, both remaining cells in that column must be 1s.


Binairo Worked Example 10

Here’s another single we can fill in.


Binairo Worked Example 11

That gives us a row with one empty cell.


Binairo Worked Example 12

Here’s an easy double.


Binairo Worked Example 13

That gives us an almost complete row.


Binairo Worked Example 14

We’re out of doubles, and empty singles. In fact, we’re left with several pairs of cells and no obvious answers as to which way around to fill them.

But we do have a way to move forward. We can use several pieces of logic to solve the blue and green cells. We can combine our knowledge of what numbers we still need to place, along with the fact that no two columns can be the same. The column with the blue cells is shaping up to look a lot like column two. And the column with the green cells is looking like its neighbour to the left so far. These facts limit our placement options.

Let’s consider, for example, the end column. We must place three 0s somewhere. If we put them both in the top two free cells, that would make the two blue cells at the top of column six both 1s. But that would make it impossible to fill in the remaining free cells in rows two and three correctly:


Binairo Worked Example 14b

This is wrong! Clearly that cannot be the solution...


Binairo Worked Example 15

In fact, if we work through the options, there’s only one way we can fill in the blue and green cells in such a way that the columns don’t duplicate others, and that allows us to complete the last two cells correctly. And that’s it – we’ve completed the puzzle.


Try Binairo 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 Binairo Taster

Where To Play

Puzzle Weekly Presents: Binairo - Front cover

Finished the taster and want more Binairo in your life? No problem! Get 120 carefully crafted puzzles set over seven levels in Puzzle Weekly Presents: Binairo – it's great value!

We publish Binairo puzzles in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here

Thermometers is a logic puzzle played on a square or rectangular grid filled with thermometer shapes. Each thermometer has a base (the bulbous end) and a top. In easy to intermediate level puzzles, thermometers may be placed horizontally and / or vertically. In more difficult levels, the thermometers may be ‘broken’ such that they span more than one column or row.

The objective of the game is to fill the thermometers sufficiently that the number of cells filled in a row and column of the grid corresponds to the numbers on the outside of the grid.

Here’s a small example Thermometers puzzle:

Thermometers small sample puzzle

Rules of Thermometers

The thermometers are filled (or not) according to the following rules:

  • Thermometers can be entirely unfilled, partially filled, or completely filled.
  • Thermometers always fill from the bulb toward the top. This is irrespective of the thermometer's actual orientation on the grid.
  • Each filled segment of a thermometer counts as one filled cell.

Here is what the example puzzle looks like when it has been solved:

Thermometers small sample puzzle - solution

Solving Thermometers Puzzles

These puzzles are solved through a combination of forced positioning and elimination. Here are some tips to get you started.

  • Look for rows or columns with a 0 written outside. This means no cell in that row or column is filled, so all thermometers crossing it remain unfilled beyond that cell. Zeros are rare in all but the easiest puzzles though.
  • Look for total fills. For example, a clue of 5 for a row of five cells would mean every cell in that row or column is filled. Again, such clues are rare outside of easy puzzles.
  • Look for forced fills. If a thermometer segment in a row or column is filled, then all segments below it (toward the bulb) must also be filled.
  • Check for forced ‘empties’. If you know for sure a segment is unfilled, then all segments above it (away from the bulb) must be unfilled too.
  • Partially fill where you can. Often you can work out that at least a certain number of cells must be filled, so fill them. Even if it doesn’t complete the row or column, having filled part of the thermometer can help solve rows or columns crossed by it.
  • Cross out cells you have determined cannot be filled. Eliminating places you cannot fill is just as important as determining those you can. It reduces options for filling other rows and columns.
  • It can also be helpful to cross off the numbers outside the grid as you complete columns and rows.
  • Highlighter pens work well for filling thermometers quickly if you are solving on paper.

Worked Example

We are going to work through a sample puzzle from beginning to end. This is a level 2 puzzle, so easy to complete but a good demonstration of the techniques required. Remember that there’s no single path to a solution; this is just an example of one way to solve this puzzle.

Thermometers worked example 1

This is the grid we are starting with. As a level 2 it’s fairly small, and the thermometers only run horizontally and vertically. We’ll start off by looking for the easiest fills. Being a 7x7 grid, those 6s look promising.


Thermometers worked example 2

The final column is an easy win. Out of seven cells, six need to be filled. It’s easy enough to work out the one that cannot be filled – it’s in a row labelled 2, at the end of a thermometer four cells long. Obviously the end two cells of that thermometer can never be filled. To make life easier, we can cross them out. We know all the other cells in the column are filled. We can strike through the 6 at the top of the grid too, so we know we’ve done that column.

Let’s look at the first row, which is also a 6.


Thermometers worked example 3

Because we’ve already got one cell filled in that row, we have to fill the whole of the other thermometer. We cannot possibly fill the cell in 1-column, because, well, that column can only contain one filled segment and that thermometer is four cells high! In fact, while we are at it, we will strike out the top three cells of that thermometer because we know they can never be filled. That row is done, so we can strike out its label, too.

Now we know how to complete the first column.


Thermometers worked example 4

We can fill up the first five cells of the thermometer, reaching our target of 6. We strike out the bottom cell as it can’t be used, and strike out the label because that column is complete.

Now we’ve done the easy ones, let’s do some elimination. We’ll see if there’s anything we know we definitely cannot fill.


Thermometers worked example 5

We can take out four more cells. Now, consider the row highlighted in yellow. We need to fill five cells, and have already filled two. There are four cells remaining. We know we’ll have to fill the bulbs of the two thermometers that start in that row, even if we don’t yet know where the fifth cell will be.


Thermometers worked example 6

Putting those in completes the 1-column. Striking out the cell at the bottom of that column leaves us only one place to put our second cell in the 2-row (bottom row), so we can fill that in as well. These last placements have more knock-on effects: we can strike out cells in both the 3-columns because they are impossible to reach now.

Where next? Well, that second row (5) is looking promising.


Thermometers worked example 7

We needed to fill three cells, and there were only three left. We’ve completed that row. We’ve also completed the 3-column, so we can cross out the last two cells in that one.

The cell we filled in the 4-column is useful, because it’s at the top of a thermometer. We must fill the cells below it.


Thermometers worked example 8

That’s completed the 4-column, so we cross out the remaining cell. That leaves us only one place to fill in the last cell in the 5-row highlighted...


Thermometers worked example 9

…and because that’s the top of a thermometer (even if it’s upside down), we have to fill the cells below it. That completes a whole bunch of columns and rows! In fact, we only have one cell left to fill in to complete the puzzle…


Thermometers worked example 10

That last cell completes the remaining 2-row and 3-column. All done!


That was easy, wasn’t it? Of course it was, it was a level 2 puzzle! We publish seven levels of difficulty, with bigger grids, longer thermometers, and even thermometers that go around corners. Harder grids also have rows or columns without labels. Plenty to give your brain a proper workout. Read on to find out more.

Try Thermometers 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 Thermometers Taster

Where to Play

Fancy filling some thermometers? We publish this puzzle occasionally in our free Puzzle Weekly magazine. You should totally sign up for that if you haven’t already, as it puts at least 28 brand new puzzles in your inbox every week.

You can also find lots of Thermometers puzzles in our Jumbo Adult Puzzle Book – which happens to include more than 500 puzzles of 20 different varieties.

Line segment is a spatial awareness logic puzzle invented in the USA. Whilst it can look a little daunting at first, it’s actually very straightforward to learn. Here’s a very small example puzzle:

Simple example of a Line Segment puzzle

The aim of the puzzle is to fill every cell with lines that can run either horizontally, vertically, or diagonally. Naturally, there are some rules.

Rules of Line Segment

  • Every cell containing an H must have a horizontal line passing through it.
  • Every cell containing a V must have a vertical line passing through it.
  • Every cell containing a D must have a diagonal line passing through it.
  • Lines must pass through either three or four consecutive cells.
  • Every cell must be traversed by one (and only one) line.

Solving Line Segment Puzzles

Here’s what the earlier example looks like once it’s been solved:

Solution to the example Line Segment puzzle

This very small puzzle is particularly easy because there are no diagonals. Most puzzles are larger and include diagonal lines. 

Solving Line Segment puzzles is largely a process of elimination. Here are some tips that should help you get started. Below, we’ll work through a larger puzzle from start to finish.

  • Begin by putting vertical and horizontal bars through the Vs and Hs in the puzzle. As you do so, you’ll find that some of them must be connected.
  • Work inwards from the outside. It can be useful to start from the top, then when you are about halfway down, move to the bottom row and work up from there. A V in the top or bottom row only has one direction a line can be drawn from. Similarly, an H in the first or last column is an easy win as you know you can draw a line at least three cells wide (unless constrained by another letter).
  • As you eliminate cells by putting lines through them, look for further constraints that have been created.
  • If you get stuck, look for cells where there are only one or two possible directions of travel.
  • Work through all the Hs and Vs before attacking the Ds. Diagonals have twice as many directional options so they are harder to constrain!
  • Keep an eye out for ‘landlocked’ cells. If drawing a line is going to cut of a cell and make it impossible to connect to another line, you’re making a mistake.

Worked Example

Let’s put everything into practice and work through a real puzzle. 

Line Segment worked example 1

Here’s the grid we are going to solve. We’ll begin at the top left and work across, marking out horizontal and vertical cells. As we do, we are bound to pick up some ‘quick wins’ - sections we know we can complete. We’ll ignore diagonals for now because they are more complicated.


Line Segment worked example - 2

You can see we’ve worked across the top row, and that’s already allowed us to eliminate several cells. The first cell is a V, and we know it must descend at least 3 cells vertically. Maybe it connects to the next V below it, maybe not, we don’t know. The same thing goes for the V in the second cell.
When we get to the H, we know we must go at least 3 cells to the right (can’t go left), so that knocks out the next H.
The final H in the top row is an interesting one; we don’t know whether it incorporates the right-most cell or not, but as it must be at least three cells wide, it must include the cell to its left. So we can bar those two.
Let’s continue along the next row.


Line Segment worked example - 3

We can bar three cells with the first H (can’t go left so it has to go right). We don’t yet know if the second H connects to the first or not, but either way we can bar it.
The V at the end must connect to the others below it.
At this time, we still cannot determine what goes in the two empty cells in the top row. Maybe they connect to the Hs, or maybe they are part of diagonals. We’ll have to wait and see. In the meantime, we’ll continue working down the puzzle. Let’s do the next three rows, still looking at Hs and Vs, and leaving the Ds alone for now.


Line Segment worked example - 4

The H is easy – it’s hemmed in by Ds on either side so it’s a no-brainer. The three Vs can be marked out, but we don’t yet know whether they connect to the others below them. We’ll find out later.
Before we move to the bottom of the puzzle, let’s look at the D which I’ve highlighted. I know I said we aren’t looking at diagonals yet, but this one’s interesting because it’s hemmed in on all sides except two, and one of those is not a valid move. Can you see which? The only possible place we can put a valid line (ie one at least 3 cells long) is to the bottom right. So we might as well put that in now...


Line Segment worked example - 5

Having that diagonal is going to help us by eliminating other possible placements later. For now though, we’ve moved more than halfway into this puzzle, so let’s switch to the bottom and work up from there. By working from outside in, we are making the constraints of the puzzle work in our favour. We’ll just do the bottom row for now.


Line Segment worked example - 6

The first V must go up at least three cells. At this point we can see that the only way to make a valid vertical line with the two remaining Vs in that column is to connect them together plus a cell below, so we can draw that in too.
The first H in that bottom row must be at least three cells wide, but we don’t yet know if it connects to the second, so we’ll just put a bar through that.
The stacked Vs in the penultimate column are connected and must include at least one more cell. The final V is a no-brainer because it’s hemmed in above by the D.
Now we can look at the last H and the four remaining Vs.


Line Segment worked example - 7

The first two Vs must be connected. If we draw in the H, which has to be three cells wide because it’s hemmed in on both sides, then we can see that the V in the third column up must connect to the one above it we already drew in - there’s nowhere else for it to go.
That leaves one V in the fourth column, and because of the diagonal we put in earlier, we know it must be three cells high.
We can go back and look at the two cells I’ve highlighted in blue. These cells are now cut off from the rest of the puzzle – they can’t be reached by any possible diagonals. There are only two of them, so they can’t form an independent vertical either. The only way we can fill them is to connect them to the verticals above and below, so we’ll do that now.


Line Segment worked example - 8

At this stage we have marked off all the H and V cells, and filled in all our quick wins. We even managed to sneak a diagonal in there. Where next? Well, if we examine the remaining empty cells, we can see that almost all of them could be part of several different lines. For example, the top-right cell could form part of the horizontal line to its left, or it could be a diagonal. There’s a block of six empty cells near the middle towards the right – they are full of potential. They could be two horizontal lines, or parts of diagonals, or possibly even part of a vertical in one case.
The cell highlighted in blue is a different case though. It can’t be a horizontal because it’s hemmed in that way, and it can’t be a vertical because it’s only got one free cell below it. It must be a diagonal, and there’s only one direction we can draw a valid line from it. Let’s draw that in.


Line Segment worked example - 9

There are a few ways we can advance from here, but we’ll stick close to the edges because of the built-in constraints. The highlighted D could be drawn in two ways – from its top-left to bottom right, or it could form the bottom of a diagonal going up and to the right (both possibilities highlighted). Can you work out which is the correct line? It has to be the one going up and to the right, because if we went the other way, we would be locking off the cell immediately below the D. So we can draw in the correct diagonal, and complete the H on the bottom row as well.


Line Segment worked example - 10

This gives us another constrained cell (highlighted). There’s only one way we can draw a line on that, and that’s by going up and to the right diagonally.


Line Segment worked example - 11

We don’t know if that diagonal is three or four cells long, so we’ll just draw three for now. (Note: If we think about two moves ahead, it’s pretty easy to see it must be four cells long. The fourth cell could potentially be part of a horizontal line, but that would cut off a cell below it. We’re keeping things simple here and not thinking too far ahead, so we’ll just draw it three cells long for now.)
Working methodically back up the puzzle, we have a D (highlighted) on the right that can only go one way, so we’ll add that next.


Line Segment worked example - 12

There’s a pair of Ds that only have one place to go, so we’ll draw that line in.


Line Segment worked example - 13

Still working our way up, we’ve got another highlighted cell with only one way to go – another diagonal. We’ll draw that one in too.


Line Segment worked example - 14

If we draw our attention to the cell highlighted in blue, we can see that with this latest diagonal in place, it can no longer form part of a horizontal line with the cell to its left, because it would only be two cells wide. So that cell must be a diagonal, no other option. We can draw that in, and at the same time connect that orphaned H to the existing 3-cell horizontal to its left.


Line Segment worked example - 15

Phew, nearly there! We only have two cells remaining. The very top right must be part of the horizontal line to its left, because that line isn’t long enough yet (all lines must be three or four cells long).

The final cell on row four must be an extension of the diagonal - no other option.


Line Segment worked example - 16 - final solution

That’s it - we've solve the puzzle!

Try Line Segment 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 Line Segment Taster

Where To Play

We include Line Segment in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here.

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:

Small example 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

Hidato puzzle, worked example - starting position.

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.


Hidato puzzle, worked example - another definitive placement

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 magazinefind out more, and get your copy, here.

Tents is a logic puzzle hailing from the Netherlands. It’s a nifty little spacial awareness teaser that’s quick to learn and great fun to solve. Here’s an example puzzle – a very small one:

Small sample Tents puzzle

We are playing on a grid with numbers on the outside, and circles in some of the cells. These circles represent trees, and our objective is to place tents such that every tree has a tent associated with it. There are, of course, some rules to follow.

Rules of Tents

  • Every tree must have a a tent placed next to it, either above or below, or to the side of it.
  • No tent can touch another tent, even diagonally (but trees can have multiple tents touching them).
  • The numbers on the outside of the grid tell you how many tents there are in that column or row. 

Solving Tents Puzzles

Here’s what our example puzzle looks like once it’s been solved:

Solution to the small sample Tents puzzle

This small example is made particularly easy because of the five 0s on the outside. These reduce the possible positions of the tents to almost one for each tree:

Eliminating zero rows and columns in a Tents puzzle

Not every puzzle is this simple! Most have fewer 0s. Indeed, as the puzzles get harder, some rows and columns are not labelled at all. 

Solving a Tents puzzle is all about eliminating places that the tents cannot be placed. Here are some tips to get you started, then we’ll work through an example of a full-size puzzle (below).

  • Begin with 0 rows and columns. Striking them out immediately reduces the possible placements of the tents.
  • Look for places where there are three or more trees in a line. These limit the possible placement of tents for the trees in the middle of the formation.
  • When you have found a place where a tent must go and have drawn it in, strike out all the cells around that tent (including the diagonals) – we know none of them can contain another tent.
  • When you have “completed” a row or column, which is to say it has its full complement of tents, strike out the rest of the cells in that row or column. This further reduces placement options.
  • It can be helpful to cross out trees once you have placed their associated tent, and to cross out the numbers outside the grid when you have complete a row or column. This helps focus on where any remaining tents must be placed.

Worked Example

Tents full size tutorial puzzle.

Here’s a full-size puzzle. If you want to download and print a copy to play along, this puzzle is included in our Tents Taster PDF that you can download here.


Tents tutorial puzzle - step 1

Let’s begin by blocking out the 0 row, as we know it cannot contain any tents.

Straight away, that gives us the position of our first tent (marked by the blue box). The tree in that box only has one available cell adjacent to it into which we can place a tent. Let’s draw that in, then block out the cells around the tent.


Tents tutorial puzzle - step 2

Now we have two more places to put tents (the blue boxes again). With the blocked out cells, these trees only have one remaining adjacent cell each. Let’s fill in the tents and block out the cells around them.


Tents tutorial puzzle - step 3

To make it easier to see what we’re doing, we can put crosses through the trees that have their tent in position. We can also cross out completed rows and columns. One of the tents we’ve just placed has complete a column, so we can cross it off and block out the rest of its cells.

We’ve got a new place to put a tent, right in the bottom corner. We’ll draw that in, and block off that completed column.


Tents tutorial puzzle - step 4

This gives us two more positions. The 2 halfway up the right hand side is easy to spot because there’s only one adjacent cell next to it. But what about the 1 in the bottom left? That has a cell above and one to the left. How do we know in which one to place our tent? Simple: the row above the tree is labelled with a 4, and there’s only one valid place we can put a tent to complete that row.


Tents tutorial puzzle - step 5

Those placements let us block off lots more cells, complete a column, and gives us a whopping five more positions (all marked with blue boxes above)! Filling those in gets us a long way...


Tents tutorial puzzle - step 6

You now know everything necessary to complete the rest of the puzzle – can you do it? To give you a head start, I’ve marked the next known tent position with a blue box again. To check your solution, have a look at the Taster PDF (linked below).

Try Tents 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 Tents Taster

Where To Play

Puzzle Weekly Presents: Tents - Front Cover

Want some top-quality Tents puzzles? We have you covered! Puzzle Weekly Presents: Tents is a collection of 120 puzzles set over seven levels. 

We include Tents in Puzzle Weekly from time to time. Puzzle Weekly is our free weekly puzzle magazinefind out more, and get your copy, here.

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