Category: How to Solve

One of the most popular games to test your wit, played by children as well as by serious grown-ups who love a challenge.

 

What are Riddle Puzzles

There are two types of riddles – the so-called engimas who use metaphorical language and conundra, which are basically puns. They’re both solved the same way, by furiously scratching your head until you guess! To be fair, creators of good riddles deserve as much credit as those who can guess the answer, if not even more. And they’re much more than a fun pastime, as many linguists and folklorists have spent their whole lives collecting, categorizing and studying riddles, which can be found in every culture.

 

Famous Riddle Puzzles

Some riddles only make sense to a certain people or part of the world, but others can easily be translated in any language as they refer to universal values.

For instance, a riddle like “This woman has not been to the riverside for water, but there is water in her tank” would make no sense to people who don’t understand African culture and have never seen a coconut in their lives, for that is the answer.

On the other hand, the famous Riddle of the Sphinx can easily be guessed by anyone.

‘It goes in the morning on four feet, at lunch-time on two, at evening on three.’ That’s a man (or woman), of course, who crawls as a baby, then walk on two feet, and ends up using a cane in old age.

History of Riddles

The oldest riddles in the world were discovered in Babylonian manuscripts, but unfortunately they did not contain the answers so they are hard to guess since we don’t know that much of their culture. Who can say what ‘my knees hasten, my feet do not rest, a shepherd without pity drives me to pasture’ meant for them?

In Ancient Greece, riddles were a form of entertainment at public meetings and they were usually in verse.

In modern times, riddles tend to be more humorous, being frequently referred to as jokes. Here’s an example. ‘Why is 6 afraid of 7? Because 7 8 (ate) 9.’

Riddles are sometimes featured in game shows as well as in books or movies. Perhaps the most famous example is the riddle contest between Bilbo Baggins and Gollum in Tolkien’s ‘The Hobbit’

Creating a rebus puzzle is the art of combining images, letters and symbols to form words or phrases.

 

What are Rebus Puzzles

What would you understand if someone put in front of you a piece of paper with the picture of a bee, followed by the cryptic message + N on it? Why, that’s a rebus of the easiest type and the answer is been? What about H+ the picture of an ear? This has two possible answers, equally easy – hear or here. You get the idea.

We use rebuses in our modern messaging systems, CU is such an example, and so is K9 for canine.

The basic principle behind rebuses is the use of pictograms and symbols to transform them into phonograms, to create new words. If you see the picture of an eye in a rebus it has nothing to do with seeing, it stands for I.

Want an example of a sentence fully made of images? ‘eye—can—sea—ewe’ reads I can see you.

 

The history of Rebus Puzzles

Rebuses are so old nobody knows when they first appeared. However, many linguists believe that this process of using drawings to represent sounds was fundamental to the development of language. They say the Chinese alphabet was probably derived from this picture to sound technique, which is also evident when you look at Ancient Egyptian hieroglyphs. If you’ve ever seen one of those memes saying we’re reinventing hieroglyphs, know that’s not accurate – emojis are ideograms, not pictograms.

Rebuses were frequently used in the Middle Ages in heraldry, knights and noblemen paying handsome prices to those who could come up with clever ideas to represent their name or the name of their estate using pictograms.

Rebuses were sometimes used to teach the Holy Bible to children who were to young to read, while missionaries in Latin America made use of pictograms to teach the Lord’s Prayer to the natives, in Latin, nonetheless.

Rebuses were also very popular in Japan and even today they are still used, most notably on corporate logos.

The ancient rebus has adapted well to modern times, such puzzles being featured in many TV game shows. Also, you can find on the Internet so-called guessing games that use pictures to represent in a visual manner common phrases, book or movie titles etc.

This puzzle has some pretty high stakes – One wrong guess and all the prisoners die!

 

What is the Prisoners and Hats Puzzle

This is one of the most famous riddle in the Hat Puzzle category. It’s a story about four prisoners accused of some crime, but the problem is the jail is full so the warden comes up with an idea. He’ll have the prisoners solve a puzzle. If they win, they go free, if they fail they will be executed. Three of the prisoners are made to stand in a line – B is facing a wall, C has B in front of him, while D is last and can see both B and C. Poor A is placed is an another room so he cannot see anyone or be seen. The warden explains he will give them 4 party hats, two white and two black. The prisoners can not see the hats on their own heads. If any of them feels confident that he knows the color of his own hat, he only has to say it out loud and they all walk. Can they save their lives?

 

How to Solve the Prisoners and Hats Puzzle

Poor A is pretty much useless since he is isolated, so it’s up to the other three to find a solution. B is staring at a wall, so he doesn’t know anything either. Their lives depend on C and D. There are two possible solutions. Remember that D has a vantage point as he can see the heads of both B and C. If their hats are both black, it’s obvious that D must be wearing a white hat so he can cry out the answer and save everybody. The game assumes that all prisoners are smart and have the same reasoning skills, so they will wait to see if D has the answer. If they don’t hear anything, C will realize that he and B must be wearing hats of different colors, which explains why D wasn’t able to figure out the color of his hat. Now, all that C has to do is look at B’s hat. If it’s black, this means that he is wearing a white one and he gets to save their skins.

 

Prisoners and Hats Puzzle Variants

There are variants in which there are more or less prisoners and the number of hats of each color vary accordingly, but they generally follow the same logic. The most interesting is that with 10 prisoners and 10 hats, either red or blue, but they don’t know how many of each color are there. They are lined single file and they can see all the hats in front of them, but not behind, obviously. It’s an each for his own game and there is a simple solution for 9 of them to survive, while the other one will have to guess so he has a 50/50 chance to survive. Can you figure it out?

You wouldn’t believe how many animated debates this puzzle has generated.

 

What is the Pirate Loot Puzzle

It’s a situation game that requires logic to find the answer. The idea is that there are five pirates, A, B, C, D, and E, and they found 100 gold coins. In order to divide the loot they decide that each pirate will propose a plan and the other will vote on it. In case of a tie, the proposer has the deciding vote. Now, don’t think they should agree to each getting 20 coins, because the pirates have other laws. First of all, they don’t trust each other so there can be no alliance between any of them. Then, they’re all interested in surviving and, if possible, throwing some of their mates overboard. The proposals will be presented by order of seniority, starting with A, so they can also figure out how the negotiations might go.

 

How to Solve the Pirate Loot Puzzle

Now, the logical deductions are a bit difficult to follow so it’s best to start with the official solution to this puzzle, which is A proposes to keep 98 coins for himself and offer one each to pirates C and E. Unfortunately, B and D don’t get anything. Why would the others accept? Because that’s the most they can get.

To understand the logic behind this you have to work your way backwards. If A,B, and C are thrown overboard, and only D and E remain, it’s obvious D will keep all the loot as he has the deciding vote. If there are three pirates left, C, D and E, pirate C can figure it out that D won’t give E anything, so he can propose giving E one coin. If there were four pirates left B, C, D and E, pirate B is smart enough to understand he only had to give one coin to D and leave C and E empty handed. Basically, knowing their mates, C and E they won’t get anything if they don’t agree to A’s plan.

However, this elegant solution has generated a lot of discussions among puzzle lovers, with many believing there’s not enough information to reach a conclusion on how the pirates will divide the loot. What do you think?

This puzzle started as a recreational math game and kept people entertained as they waited for someone to invent Tetris

 

How to Solve a Pentomino Puzzle

The term Pentomino comes from the shape of the 12 tiles in the game which are made of five squares of the same size. The 12 tiles resemble letters from the Latin Alphabet and are sometimes referred to as the L, the Y or the X tile.

The starting board, the rectangular frame you need to fill in using the tiles, has exactly 60 squares, the same number as in 12×5, the total number of squares in the tile. This means you must find a way to fit all the tiles inside the frame with no gaps or overlaps. Obviously, you are allowed to rotate the tiles as you see fit, just like in

Tetris.

 

Pentomino Puzzle Versions

Since the frame for the traditional version needs to have exactly 60 squares, there’s little room for variation. You can play a bit with the height and width of the rectangle, but that’s about it

There is also a 3D version of the Pentomino Puzzle and the goal there is to create a cube.

 

The Pentomino Puzzle Board Game

The board game version is called Golomb’s Game, in reference to the game’s inventor. The game is played on an 8×8 board and there can be 2 or 3 players who take turns placing tiles on the board so they fit in with the others without gaps or overlaps. The last player who manages to place a tile on the board wins the game. The French have created a board game called Blokus, which incorporates all the 12 pentominoes in Golomb’s Game and added other tiles made of 1, 2, 3, or 4 squares.

 

History of the Pentomino Puzzle

The Pentomino Puzzle was invented by American professor Solomon W. Golomb who presented it in a 1965 book on polyominoes. In Math speak, a Pentomino tile is a polyomino of order 5. The puzzle became popular in the US after Scientific American published an article on it in October 1965.

Something to do when you’re feeling bored and computer games have not bee invented yet.

 

How to Solve Peg Solitaire Puzzle

Peg Solitaire is a game played on a wooden board with lines of holes that have pegs in them. In the classical version of the game the 32 pegs are placed in a cross pattern, leaving the hole in the middle of the board empty. The player is allowed to move up and down, left and right, jumping over a peg, which is then removed from the board. You can start with any peg you want, but the rule is that you need to land on an empty space, which doesn’t leave you many options. Since at the beginning the only empty space is that in the middle you will have to start with a peg in that area.

You can, of course, try to solve this puzzle by using random moves, but this might give you quite a headache as you’ll soon find it impossible to make a new move.

The best solution is to start by focusing on the areas that are further from the centre and try to clear all the pegs there before moving to another part of the board. For instance, focus on eliminating the pegs in the lower part of the board, calculating each move to empty some spaces to be able to do your jumps.

 

Peg Solitaire Puzzle Version

The puzzle with the cross-shaped pattern is also known as the English version, while in the European variant the holes and pegs are displayed in an oval shape. Other popular versions of the starting pattern shape are triangle, hexagon and diamond. Obviously, you can find Peg Solitaire Puzzle online and, even better, there are many tutorials offering the winning strategy.

 

History of the Peg Solitaire Puzzle

It’s hard to say when this game was invented, but the oldest reference to it can be traced to the times of King Louis XIV of France. An engraving dated 1687 presents a princess at the court with a Peg Solitaire puzzle on the table beside her. That’s probably why the game is also known as Solo Noble, as it was a pastime for noble people.

How many balls can you fit in one sphere?

 

What are Packing Puzzles

Packing puzzles are part of what is known as recreational math, but they are also called optimization problems. Indeed, some regular people might consider this types of problems fun, but for manufacturers they can bea real problem. A company that produces tennis balls actually needs a solution to fit as many as possible in one container to cut costs. Did you know that a Japanese company once invented square watermelons, not as a novelty to impress the public with, but to solve a simple packing problem. (The public did not appreciate the odd-looking melons and the idea was dropped!)

All packing puzzles have basically the same goal, finding a way to fit as many identical items in as few containers as possible.

 

Types of Packing Puzzles

Puzzles in two dimensions are just for fun as they have no practical utility. One example refers to packing sand, specifically grains of sand wasting as little space as possible. The grains are represented as circles and the idea is to find a compact way of stacking them.

Most packing puzzles in three dimensions concern spheres, as cubes are way easier to stack, not much of a puzzle there, you only need basic geometry.

Since most real-life packaging problems revolve around boxes, many puzzles ask the players to find the highest number of spheres that can be crammed into a cuboid. Unlike many other puzzles that require logical deductions or lateral thinking, to solve packing puzzles you have to use what you learned in school.

 

Famous Packing Puzzles

One of the best-known packing puzzle is the so-called Slothouber–Graatsma puzzle which challenges the player to pack six 1 x 2 x 2 blocks and three 1 x 1 x 1 blocks into a 3 x 3 x 3 box. Unlike other puzzle, this one has only one solution.

Another example is the Conway puzzle, in which you have to pack rectangular blocks of various dimensions into a cubic

box.

The Knapsack problem is a more complex packing puzzle as it adds another element, which is value. What you have is a set of items with different weights and value. The goal of the puzzle is to determine the number of items to put in a knapsack so that the total weight is less than or equal to a given limit and the total value is as large as possible.

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.

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.

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.