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Nurikabe Puzzle

Nurikabe is a Japanese term which means ‘invisible walls’ and you will see why the puzzle bears this name.


How to Solve a Nurikabe Puzzle

Like many other puzzles, Nurikabe starts with a grid of various dimensions and all the cells are white. Some of the cells also have numbers on them and this indicated they are part of an island, hence the alternative name for the game Islands in the stream. The number indicates how many cells are in an island, but you don’t know its shape.

You need to use logical deductions to figure out the shape of each island and pencil in the surrounding cells, and these will be the river. The islands can only touch each other at the corners. Sometimes the puzzle is referred to as ‘Structured Cells’ walled in by the black cells.

The easiest way is to look at the smallest numbers on the grid. A 1 means that the island only has one cell, that with the the number on it so you can immediately color the surrounding cells black. Another thing to look for is adiacent islands. If you have a cluster of numbers of the grid, the cells between any two of them must be black since the islands cannot touch each other. Also keep in mind that the river must be continuous, to flow, so to speak, so you cannot have a group of black cells fully surrounded by white cells, as this would form a ‘pool’ rather than a river.

Finally, an experienced player can usually spot unreachable cells, those that are too far away from any numbered cell. This means they simply cannot be part of an island and can be colored black right from the start.


History of the Nurikabe Puzzle

The Nurikabe Puzzle was created by the Japanese company Nikoli, which published the first grid of this type in 1991. The company also released a variants of this binary determination puzzle and the idea was used to create many computer and mobile games. Those who remember the old Minesweeper game on Windows must have noticed the Nurikabe puzzle is based on the same principle.

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Morpion Solitaire Puzzle

You might have heard of this game as Join 5 or simply the Line Game. Morpion Solitaire is a bit of a misnomer, as they game can be played by two players and is actually more fun like that.


How to Play Morpion Solitaire Puzzle

The first thing you need to do is draw the grid of dots or crosses and it’s best to use a piece of paper from a math notebook, which allows you to trace the pattern much easier. The standard version of the starting grid is that of a cross which consists of a square of 4×4 dots plus four 4×3 dots rectangles on each side of the square. The aim of the game is to draw lines connecting 5 dots. The game ends when it becomes impossible to draw another line.

If you play the game on your own, at the end you can count the number of lines and see if you’ve managed to beat your personal record. If there are two players, the one who manages to draw more lines or the one to connect the last remaining dots wins.

The most important rule of the game is that no new line can overlap with parts of a previously drawn line.

Another rule says that if you have four aligned dots or crosses in the pattern you can draw a fifth dot outside the initial cross outline. This extra dot can be used to draw a five dots line or, if you don’t actually needed you can save it for later.


Morpion Solitaire Puzzle Variants

One version of the puzzle starts with cross-shaped pattern made of 36 crosses. Unlike the standard version, there are no crosses or dots inside the pattern. You still need to connect 5 crosses, but you are allowed to draw new ones as long as they are in line with other 4 crosses. The winner is the player who manages to place more extra crosses.


History of the Morpion Solitaire Puzzle

Some says this puzzle might have originated in Northern Europe, but there are many elements pointing to it being of French origin. The term morpion comes from the French phrase ‘mords pion’ which means bite pawn, while solitaire is the French term for alone or loner. Also, the first known references to this puzzle appeared in French papers during the 1970s. As far as anyone can tell, before becoming famous, this was just a game used to play in school.

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Maze Puzzles

A maze puzzle challenges the player to try the different paths in the image to find the way to a goal.


Types of Maze Puzzles

A classical maze puzzle is typically a square in which many different paths have been drawn. There is one entrance and then you have to follow a certain path to make it to the goal. The paths can be blocked by walls which force the player to make a detour to escape a dead end. More complex maze puzzles have one-way doors, which means that once you use a door you cannot go back if you discover you’ve entered a trap you cannot escape. The only thing you can do is start all over again.

Round puzzles typically challenge the player to make it to the center of the maze.

In loops and traps mazes the player has to follow the directions indicated by the arrows printed on the board or paper. Sometimes the goal can be to find the exit or, more commonly to return to the starting point.

Block mazes present themselves as grid with black and white cells in an apparently random pattern. There are two starred cells on opposite corners of the grid. The goal is to pencil in four of the white cells and create a route linking the two stars. You can only go up and down, left or right. You cannot move following diagonal lines, which would be the easiest way to go from one corner to the opposite one.

Number mazes do not have paths. You move around by jumping over a number of squares as indicated by the number in each cell. The player starts from the star typically placed in the left upper corner and can only move horizontally or vertically. The goal is to make your way back to the star.


Real Life Maze Puzzles

Fans of this type of puzzles can test their observation skills by trying to find their way out of the many real life mazes built as tourist attractions around the world. Most of them are created with hedges, but there are also some indoor mazes, like the one at the Gardens Shopping Mall in Dubai, which is considered the world’s largest indoor maze.

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Mahjong Solitaire Puzzles

One of the most addictive games known to man, especially since you can find tons of Mahjong Solitaire puzzles online.


How to Play Mahjong Solitaire Puzzles

If you’ve never heard of Mahjong Solitaire before let us give you a few quick explanations. Mahjong Solitare is a single-player game in which you have to match two tiles with the same image or symbol in them and remove them from the board. Sounds pretty easy, right?

Well, the problem is that you need a keen eye as traditional puzzles use all sorts of Chinese symbols which can be deceptively similar. A traditional Mahjong puzzles has 144 tiles displayed on four tiers. The ones on the upper tiles or the edges can be entirely seen and are called exposed or open tiles. You can only match exposed tiles. Once tiles are removed from the board, those immediately below become exposed.

One big problem with this puzzle is that some of the tiles appear more than two times in a set and this is where many players mess up. In many cases, players tend to remove pair of exposed tiles only to discover that at some point they cannot uncover all the tiles and cannot form new matches. Basically, you’re stuck and the only solution is to restart again trying to avoid making the same mistake. The point of the game is to try to expose as many tiles as possible rather than go for the more obvious choices.


Mahjong Solitaire Puzzle Variants

The game can be played with a traditional board and wooden pieces, but millions of people only know online Mahjong. On some website, when they cannot see any more matches players can use features like reshuffle, which means rearranging the remaining tiles on the board in a different pattern. Some games feature wildcard tiles or special tiles that give you additional points if you manage to match them.

If Chinese symbols are too difficult to distinguish from one another, you can play the game with tiles decorated with flowers, jewels and other symbols more easily recognizable.


History of Mahjong Solitaire Puzzles

The original Mahjong is a board game developed in China in the 17th century. The game has 144 tiles with Chinese symbols on them and is usually played by four persons. Each player receives 13 tiles at the start of the game, then they all take turns drawing and discarding tiles until one of the them can make five of the many combinations possible using all the tiles on his board.

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Magic Square Puzzle

How to solve a magic square puzzle

Not everybody likes math, but recreational math that’s different, that’s fun and this is what a magic square puzzle is about.

How to Solve Magic Square Puzzles

Magic square puzzles are simple grids of various sizes which must be filled with numbers, making sure the numbers on each row, column or diagonal line add up to a magic number. The smallest possible magic square is a 3×3 grid using the digits 1-9, with 15 as the target number. In such a small square the numbers appear only once, although in more complex puzzles of this type it is sometimes allowed to use the same number twice.


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Watch Video on How to Solve


Magic Square Variants

One of the most common variant is that of the bordered magic square. What you have there is a normal magic square of whatever dimension, bordered by a row of  empty cells. The numbers in the cells above and below each column must add up to a target number as well. The same goes for the numbers added to each horizontal and diagonal line.


History of the Magic Square Puzzle


The first evidence of people, presumably mathematicians, playing with magic square puzzles was found in China and dates from the year 190 BCE. And yes, such puzzles have been associated with magic and studies of the occult. For instance the 190 BCE manuscript calledMemoir on Some Traditions of Mathematical Art, presents a magic square that was allegedly used for divination and astrology.

If filling in one square seems complicated to you, think that Chinese mathematicians had fun creating meta-puzzles containing several smaller magic squares and the whole grid also followed the same principle of all the numbers in a row, column or diagonal adding to the same target number. Now, that’s a major headache!

Magic squares were very popular all over Asia and you can find some depicted on temple walls in India. The magic square puzzle traveled through the Middle East reaching Europe as early as the 12th century. At the time, magic squares of different orders (number of cells) were ascribed to various planets. It was only in the 18th century that magic squares lost their mystic allure and became simple recreational math puzzles.


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Knights and Knaves Puzzle

Knights and Knaves puzzles all fall into the category of logic puzzles and can easily solved by making the right deductions.


What is a Knights and Knaves Puzzle

All the puzzles in this category take place on an island where the inhabitants are either knights who always tell the truth or knaves who only lie. The puzzles revolve around one visitor to the island who meets a small group of locals and has to determine whether their knights or knaves. In some cases, the visitor can ask a local directly what he is or he can use simple Yes/No questions.


How to Solve a Knights and Knaves Puzzle

There are many types of puzzles in this category, so let’s focus on one of the most popular. Let’s say the visitor meets three inhabitants of the island named A, B and C. He asks the first one, A, what he is, but unfortunately does not hear the answer so he has to rely on the other two locals. B says A’s answer was ‘I’m a knave’, while C jumps in ‘Don’t believe him, B is a liar’. Who’s telling the truth and who’s what?

If you’re at all familiar with logic you’ll notice that what B says cannot possibly be true. A couldn’t have said ‘I’m a knave’ as this falls under the liar’s paradox. If a liar says he’s a liar than he’s telling the truth, which is impossible.

Therefore, it is easy for the visitor to assume that A said ‘I’m a knight’ (which might be or not be true), B is definitely a liar, while C is certainly telling the truth. As far as A is concerned there is not enough information to determine whether he’s a liar or not.


Knights and Knaves Puzzle Versions

There are many variations to this popular puzzle. For instance the visitor must determine the identity of a local by using one question. It cannot be a direct question like ‘Are you a knave’ as both the knight and the liar would say No. The trick is to use a question for which the answer is already known. One solution for this puzzle would be asking the local something like ‘Are you a tree frog?’ The knight would obviously say No, while the liar would be forced to say Yes, which the visitor knows it’s a lie.

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Kendoku Puzzle

Kendoku is just another type of Sudoku. Sudoku with a twist!


How to Solve a Kendoku Puzzle

Kendoku or KenKen looks like a basic Sudoku grid, its dimensions ranging from 3×3 to 9×9 cells. The aim of the game is to fill the cells with numbers, making sure the same digit does not appear twice in the same row or column. For a 4×4 grid you have to work with numbers from 1 to 4, while for a 9×9 you will have to use all the digits from 1 to 9. So far, so good, your basic Sudoku puzzle. However, here comes the twist.


What are Kendoku Puzzle Cages?

Every grid contains a number of so-called cages, that is heavily outlined groups of cells and the numbers in each of them must produce a certain magic numbers. The first cell in a cage will have inscribed in the upper left corner the target number and the mathematical operation to be used to reach that number. Most magic number puzzles only use addition, but in Kendoku you might have to use subtraction, multiplication or division to reach that target number. Each cage has its own mathematical operation so it’s quite possible to have to use all four of them while solving a grid. More advanced Kendoku puzzles may include other types of  complex operations or use negative numbers.

You can have a number repeated in a cell, as long as they are not on the same row or column.

In some cases, no operation is specified so the player is free to reach the target number anyway he can.


History of the Kendoku Puzzle

Kendoku was invented in 2004  by a Japanese math teacher named Tetsuya Miyamoto, who was trying to develop a fun educational game. The name of the game comes from the Japanese term for cleverness. The new Japanese puzzle gained international fame in 2008 when British newspaper ‘The Times’ first published a Kendoku grid. At present, hundreds of papers in the US and Europe regularly publish Kendoku, and, of course, such puzzles can be found on many websites.

Since its a puzzle with an outstanding educational value, starting 2010 there have been national Kendoku championships, usually held in New York, as well as international competitions open to students of all levels.

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Jigsaw Puzzle

Everybody knows jigsaw puzzles, but how much do you know about this extremely popular game?


History of the Jigsaw Puzzle

Ever wonder why they are called jigsaw puzzle? The term refers to the first such puzzle ever created, in 1760, by an English engraver and cartographer named John Spilsbury. Legend has it he made a puzzle by cutting a drawing, most probably a map set on a hardwood board with a small saw. At the time, children were taught geography by cutting up maps along the border lines and having the pupils put the continent back together. Even today such puzzles remain a very useful educational game, and it can also be played online.

The cardboard jigsaw puzzles only appeared in the late 1800s.


How to Solve Jigsaw Puzzles

People have devised many methods to tackle a jigsaw puzzle. Many try to separate the pieces depending on their color and by looking at the picture they can get a rough idea where they should go. Another popular method is to start with the margins, separating all the pieces with a straight part which must be part of the frame. Finding the four corners also helps as you can use them to put together the edges. Some puzzles have even the edge pieces cut out in irregular shapes to make it harder to put together the margins.

The most difficult to solve are the so-called Japanese style puzzle, in which the pieces are very similar in shape.


Jigsaw Puzzle Variants

Puzzles for children have larger pieces and vibrant colors to make them easier to solve. A typical puzzles aimed at adults has 1000 pieces, and they can be extremely difficult is large parts of the reference image are of the same color – depicting the sea or a forest for instance. Jigsaw puzzle aficionados can test their skills on sets with up to 32,000 or 40,000 pieces.

Globe puzzles are a relatively modern invention and some are made of steel and the pieces are magnetic so they stick to the sphere.

If you think you’re good at Jigsaw Puzzles you should try the ultimate challenge, Ravensburger’s Krypt puzzle, which is does not have any image. All 736 pieces in a set are of the same color black, silver, or gold and the manufacturer promises all the pieces have a unique shape.

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Induction puzzles

These puzzles are examples of applied logic which use the induction principle to determine the solution to a complex problem by solving the simpler problems in contains.

Examples of Induction Puzzles – The Muddy Children Problem

The Muddy Children puzzle presents a situation in which a group of nice little children are informed that at least one of them has a dirty face. No fingers are pointed so the children have no way of knowing if it’s about them or not. The problem assumes all the children have the same reasoning capacities so they will be able to make the same deductions. You’ve probably noticed they do not receive information as to the specific number of children with a muddy face – at least one might mean just one, two, three or indeed all of them. Since they cannot look in a mirror how do they find out if the problem concerns them or not?


How to Solve an Induction Puzzle

The children are standing in a circle so they can see each other and they are told to take a step forward when they hear a stroke if they believe they are dirty.

To understand how the induction principle works it’s easier to start with just two children Jane and John. They know one of them must have mud on her face. If Jane is the dirty one she will see that John is squeaky clean and will step forward rightly concluding that she is at fault. If both kids have mud on their faces, neither will move forward at the first stroke, each assuming that it’s the other who should do so. When none of them moves, they will both realize the other has seen the mud on their face and will understand they are also dirty.As a result, at the second stroke, both kids will move forward. Puzzles involving a larger number of participants can be solved using the same logical step.


Versions of the Muddy Children Induction Puzzle

A well-known version of this puzzle is the King’s Wise Man Hat, in which the rules gathers three of the most brilliant minds in his kingdom and announces that the one who will solve a riddle will be his new adviser. The king places a hat on each man’s head and tells them that at least one of them wears a blue hat, while the rest have white hats. There are other variants with other characters and up to ten participants, but the way to solve them is basically the same.

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Geometric Magic Square Puzzle

How to solve geometric magic square puzzles

Magic square puzzles usually have numbered tiled which have to add up to a certain number. Geometric magic square puzzles do the same thing with shapes which put together must form a square.


Watch This 40-Second Short Video That Explains It



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How to Solve Geometric Magic Square Puzzles

All magic square puzzles consist of a square frame with tiles in it. In the Geomag version, each tile has a geometrical shape painted on it. They’re not your traditional triangles or pentagons, but some very odd-looking shapes. What you need to do is figure out how you can use these shapes to form a the target shape, usually a square. As if this wasn’t complicated enough, you need to make sure that the tiles in every row, column or diagonal line also make up the same shape.

The traditional frame is a 3×3 grid and has 9 tiles or images you need to fit in. Like in the classical magic squares using numbers, the pieces used in a Geomag puzzle must have distinct shapes.

For the time being, the only existing Geomag puzzles are in 2D, as no one has figured out how to come up with a 3D version.


History of the Geometric Magic Square Puzzle

This type of puzzle was invented in 2001 by British electronics engineer Lee Sallows, who is well-know for his interest in recreational mathematics. Besides the geometric puzzle, he also came up with the idea of alphamagic squares, which remain magic when you replace each number with the number of letters in its name. Later on he presented an even more devilish idea, the geometric alphamagic squares, combining the two principles.

Perhaps the most surprising thing about Geomag puzzles is that creating such a puzzle is even more complicated than solving one. You have to first decide upon a target shape, than design the pieces that could be fitted together to create it. Usually this requires a lot of math and testing of shape designs.


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