Category: How to Solve

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 17^th 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.

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.

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.

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.

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.

This is probably one of the most famous riddle in the so-called river-crossing category.

What is the Wolf, Goat and Cabbage Puzzle

When you listen to the riddle it sounds a bit childish. Basically, it’s a little story about a farmer who went to the market and bought a wolf, a goat and one cabbage. Don’t bother asking why on Earth would someone buy a wolf, maybe he just liked wolves, OK? Now, the man gets to a river and hires a boat to cross it. The problem is he can only take one thing or animal with him, which puts him in a terrible dilema. If he first takes the cabbage across, he will have to leave the goat and the wolf behind and you can guess what happens next.

How to Solve the Wolf, Goat and Cabbage Puzzle

Maybe if he hadn’t bought the wolf, the poor guy wouldn’t be in such a pickle, but that’s a different story. The farmer needs to play it safe which means taking the goat across, leaving the wolf to stare at the cabbage. When he gets back for the second crossing he can choose either the cabbage or the wolf. In both cases he is faced with the same problem. If he takes the cabbage across the goat will surely eat it and if he takes the wolf it will probably feast on the goat as soon as the farmer leaves for the third crossing. The trick is to take the goat back. It seems like a lot of trouble but it’s the only way to keep all the purchases safe.

Let’s say the second trip he leaves the cabbage on the other side and takes the goat back. Then he can move the wolf to the other side, leaving the goat to wait for its turn.

History of the Wolf Goat and Cabbage Problem

The first documented reference to this puzzle can be traced to the 9^th centuries and variants involving different animals can be found in the folklore of many people, especially in Europe and Africa.

This type of river crosing puzzle has appeared in many video games and even TV shows, including ‘The Simpsons’.

Variants of the Wolf, Goat and Cabbage Puzzle

One of the most funny version is the one with the Cannibals and the Missionaries. You have to figure out how to cross 3 cannibals and 3 missionaries. The rule is that if the missionaries are outnumbered by cannibals they will be eaten.

Another version refers to three married couples and the problem is you cannot leave one woman with another man if her husband is not present.

It’s not even about math, although it’s not as simple as it might seem.

How to play 15 Puzzle

The name of this puzzle comes from the fact that there are 15 sliding tiles set in a 4×4 square and also because you must arrange them in ascending or descending order. Since there are 16 slots and only 15 tiles, that leaves you with an empty slot so you can slide the pieces around.

The numbers on the tiles go from 1 to 15. You can start by placing the the target number, 15, in the upper left corner and place the tiles in descending order or you can start with 1 and work your way up.

You might think it’s child’s play, but the fact is that many mathematicians have analyzed the puzzle. They came up with the startling conclusion that depending on the way the tiles are arranged at the beginning half of the initial positions are impossible to solve no matter how many moves you make. This has to do with terms like invariant, parity of the permutation of the 16 tiles, which sure don’t sound like much fun. If you ever find such a toy in a shop it will probably be solved, just as Rubik cubes are sold, which means that no matter how much you scramble the tiles you will always be able to arrange the tiles in order. So don’t try to excuse yourself by saying it’s probably one of the unsolvable configurations.

History of the 15 Puzzle

Today, a Canadian postmaster named Noyes Palmer Chapman is credited with inventing the 15 puzzle in 1874. His original design was passed from hand to hand until it reached Boston, where the first commercial 15 puzzles were manufactured in 1879. The odd thing is that following the 1880s craze with the 15 puzzle, the famous American chess player and puzzle inventor Sam Loyd claimed that he had created the popular toy.

Another famous American chess player, world champion Bobby Fischer was a fan of the 15 puzzle and his personal record was solving the puzzle in 25 seconds, a feat he demonstrated on a popular TV show.