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Verbal Arithmetic Puzzles

Verbal Arithmetic Puzzles

Let’s do maths with letters.


What are Verbal Arithmetic Puzzles

This type of puzzles belongs to the recreational arithmetic domain and they’re basically equations in which you have to determine the value attributed to each letter. Obviously, all the number in such a puzzle will have to be a digit between 0 and 9.

Let’s have a look at one of the most famous puzzles of this type, which was published almost a century ago, in 1924, in the ‘Standard Magazine’

S E N D  +

M O R E  =


It’s not puzzling at all if you know a little math. The first clue is the M, which as a carry-over can only be 1, which indicates next that O can only be 0, S must be nine and so on.

Here’s another easy puzzle for you:

S U N +

T A N=


As you’ve seen in the first example, B can only be 1. Can you figure out the solution?


Once you have assigned a value to a character replace it wherever it appears in the puzzle and try to figure out the rest of the problem.

Most people will solve verbal arithmetic puzzles by hand, except for mathematicians who love to make everything more complicated and use terms like algorithms and integers.


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Types of Verbal Arithmetic Puzzles

The puzzles that use letters for numbers are called alphametics. These are sometimes combined with Sudoku or Kakuro puzzles, to create some fiendishly cryptic puzzles.

Puzzles in which a digit stands for another are known as digimetics.

Skeletal divisions are puzzles involving long divisions in which the numbers are replaced by symbols.


History of Verbal Arithmetic Puzzles

It’s impossible to say when arithmetic puzzles were invented, probably long ago. What we do know is that the term “cryptarithm” was coined in 1931. In 1942, this was changed to “cryptarithmetic”, which is a bit more clear.


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T Puzzle

How to solve the T Puzzle

If you like Tangram, you’ll love the T Puzzle.


What is the T Puzzle

The T puzzle is basically a tiling puzzles, in which you have only four pieces which you must arrange so as to form a capital T.

In the original version of the game you have four pieces, namely one isosceles right triangle, two right trapezoids and an irregular shaped pentagon. The game would be easy if it weren’t for the irregularly-shaped piece, which will give you quite a headache.

If you’re struggling with the puzzle, don’t worry. Studies have shown that very few people can solve it in less than five minutes, the average solving time being 30 minutes.


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History of the T Puzzle

As far as we know, the T Puzzle was invented at the beginning of the 20th century as a marketing gimmick. Many businesses took to offering pieces of the puzzle, with the company logo on it or various offers. You could collect the pieces, but some businesses gave away the whole pack. Sometimes the pieces were made of ordinary paper, but some invested a bit and made them out of cardboard. Anyway, kids and adults challenged each other to solve the T Puzzle, so it was a brilliant idea to expose people to your brand.

Later on, the T Puzzle kits contained booklets presenting more problems to solve with the same number of pieces.


T Puzzle Variants

A version of the T Puzzle is the so-called Latin Cross Puzzle, although it’s the other way around, as the cross is older, but then the T Puzzle is more popular. The Latin Cross puzzle dates from the early 19th century. Instead of four pieces, it has five pieces, three isosceles right triangles, one right trapezoids and an irregular shaped six-sized piece.

Other versions of the original Puzzle feature slightly different pieces and the resulting T has one arm longer than the other.


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Tower of Hanoi Puzzle

How to solve Tower of Hanoi puzzle

Once you get the trick, solving this puzzle will be a piece of cake!


What is the Tower of Hanoi Puzzle

You might have heard of this game as the Two Towers or the Tower of Brahma.

What you have to start with looks simple enough. A wooden board with three rods sticking out of it. On the first rod you have a number of disks, stacked in a conical shape, with the largest at the base. The aim of the game is to move all the discs to a different rod and place them in the same order.

Here are the rules:

You can only move one disc at a time.

You can place a disc on top of another, but not over a smaller one, or you can move it to an empty rod.


How to Solve the Tower of Hanoi Puzzle

The difficulty of the game depends on the number of discs in the game. The smallest version only has three discs and it has been calculated it can be solved in 7 moves.

If you’re a math head, the formula is that a Tower of Hanoi can be solved in 2n − 1, where n is the number of discs in play.

This is how you solve the 3 discs puzzle. First you move the smallest piece to the third rod and the medium one to the middle one. You now have three rods each occupied by a disc. You then move the smallest piece on top of the middle one and free up the third rod. Put the larger disc on the third rod, free up the middle piece by moving the smallest disc back to the first rod and then it’s easy.

You can use this system with larger numbers of discs, creating smaller conical shapes on the two empty rods until you free up the largest of all. All you need is to pay attention and to always calculate your next move.


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History of the Tower of Hanoi Puzzle

The puzzle was created in 1883 by the French mathematician Edouard Lucas. That’s a fact, but the legend surrounding this puzzle is quite fascinating. According to the story, there’s a temple in India where there’s a room with three rods and 64 gold discs. There, Brahmin priests following an ancient prophecy have been moving the pieces for ages and when they make the last move the world will end. No need to panic though. If you remember the formula to solve any Tower of Hanoi puzzle it has been calculated that, moving one disc per second, it would take the priests 585 billion years to finish, so we’ve got plenty of time left.


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Tangram Puzzle

How to solve Tangram Puzzles

Oldies, but goldies!


What is a Tangram Puzzle

Tangram falls into the dissection puzzles category and it’s aim it to use seven wood blocks of various shapes to create geometrical shapes.

The seven pieces of the puzzles are called tans and, in a traditional you have five triangles of various sizes, a square and a parallelogram.

A Tangram puzzle box contains a booklet with many shapes the player is challenged to recreate. Obviously, the images only offer the general outline so you have to figure out where each tan fits.


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Tangram Puzzle Paradoxes

Tangram fans refer to almost similar shapes as paradoxes. There’s for instance the famous Monks Paradox, which presents itself as two very similar shapes resembling a monk, made using the same pieces. However, one is missing a foot, something you might not even notice at first sight. Where did the foot piece go? At a careful examination you will discover that the missing piece was used to give the monk a slightly larger body.

Another example is the Clipped Square Paradox. Naturally, the Tangram pieces can be arranged in a square, that’s how they are sold, neatly placed in a square frame. However, you can also use them to create an almost identical square with a missing corner. The secret is that the second square is a bit larger, but not my much.

If you think that all you have are seven pieces, you’ll be amazed to learn that there are over 6500 Tangram problems registered to this day.


History of the Tangram Puzzle

It is believed that Tangram was invented in China in the late 18th century. It must have been brought into the Western World by sailors on merchant ships. An American shipping magnate is known to have owned a Tangram puzzle in 1802, but the puzzle only became popular after reaching England, after 1810. The Tangram puzzle soon conquered Europe and rich families had expensive sets in which the pieces were made out of glass or tortoise shell. During the First World War much of Europe went into a second Tangram craze, at least the part of Europe that was not on the battlefields.

Tangram Puzzles are still popular these days, although you can now obviously play Tangram online, both the traditional version and various other games using different pieces.


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Sudoku Puzzle

How to solve a sudoku puzzle

If you have to wait at the doctor’s or have a boring three-hour flight ahead of you, get some Sudoku Puzzles to make time fly.


What is a Sudoku Puzzle

Let’s talk about the traditional Sudoku puzzle first. What you have is a 9×9 grid which you must fill is using numbers from 1 to 9. The first rule is that each number can only appear once in every row or column. Additionally, the grid is divided in nine 3×3 squares in which again the digits must appear only once. Some of the digits have already been filled in for you.


How to Solve a Sudoku Puzzle

The complexity of the problem and the headache depend on the difficulty level. In easy mode you will have more numbers already filled in which makes it easier to guess the solution. Actually, guess is the wrong word here, because you have to use logic to solve the puzzle. The best thing to do is to find the row, column or square with the most numbers in it. For beginner levels this might mean having 7 out of the 9 numbers already locked in place, which leaves you with deciding the positions of the other two. Don’t place them at random, look at the other rows and columns and make sure they don’t clash. Say you have to place a 2 and a 3 in an almost complete row. Look at the first empty square and check the column it’s part of to see if there’s no other 2 on a different row. If there is one already, this means you must place the 3 in the first empty square and the 2 in the other one.

You must always check and double check before placing any number on the grid.

Another method is to analyze each digit, see how many 1s are there on the grid already and maybe you can find the correct spots for the others. If you have multiple possibilities, don’t make hasty decisions and wait till you get more information.


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Sudoku Puzzle Versions

Killer Sudoku is a combination between traditional Sudoku and Kakuro, which means that you not only have to place the numbers in a certain order but also make sure they add up to a target sum.

Hyper Sudoku makes your life more complicated by adding other 3×3 squares which must follow the same rule.

Twin Sudoku consists of the grids that share a 3×3 square.


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Soma Cube Puzzle

How to solve the soma cube puzzle

A 3-D puzzle with solid wood blocks some might find similar to modern Tetris pieces.

What is a Som Cube Puzzle

This puzzle falls into the category of solid dissection puzzles. As the player, you don’t have to dissect anything, but rather put the blocks back together to form a solid 3x3x3 cube, with no voids on the inside.

The game has seven blocks, six of them are made of 4 small cubes of equal size, known as cubelets, while the remaining one consists of only three little cubelets. All the blocks are of a different shape and since they resemble letters they are known as V, L, T, Z, A, B and P.


How to Solve a Soma Cube Puzzle

Many mathematicians find such problems as the Soma Puzzle fascinating and devote a lot of time to studying them and, of course, their solutions. Computers do help a lot! According to experts, there are 240 solutions to solve a Soma Puzzle, too many to list here. However, here is an essential clue. It has been discovered that in all the 240 solutions there’s only one place for the T block, that is on the bottom with its long edge along the front and the its “tongue” in the bottom center cube.


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History of the Soma Cube Puzzle

The cube was invented by Danish polymath Piet Hein in 1933, for a lecture in quantum mechanics. It’s name is a reference to the drug Soma heavily consumed in the fictitious world invented by Aldous Huxley in his famous ‘Brave New World’ novel, which had been published the year before. And yes, solving such puzzles is an addiction!

However, it was only in the 1960 that the Soma Cube was commercially produced and sold in the United States. Inevitably, some of the versions used plastic blocks instead of the old-fashioned wooden ones. In some sets, players are challenged to form other geometrical shapes after mastering the cube.

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Sokoban Puzzle

How to solve the sokoban puzzle

A sliding puzzle for the 21st century generation.


What is the Sokoban Puzzle

Actually, Sokoban was invented in Japan in 1981 and it’s puzzle video game. Remember that at the time video games were still in their infancy and they borrowed a lot of ideas from traditional games, in this case the sliding puzzles.

The term Sokoban is derived from the Japanese word for warehouse worker. You play as the warehouse employee and your job is to move crates to their designated place. Some of the squares on the screen represent the floor, while others form walls which restrict your movements. To solve the puzzle you must create paths to slide a crate to a designated space. Keep in mind that you can only push the crates, but not pull them. There are usually several crates to maneuver so you must pay attention to those as well and make sure you don’t push any of it against a wall in a position from which you won’t be able to move it later on.

The good thing about video games is that you can start all over again as many times you want and learn from your mistakes.


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Sokoban Puzzle Variations

The release of the first Sokoban puzzle was a huge success in Japan, so over the following years many variants were released. The 1982 Sokoban version featured walls you could destroy to clear a path. Another version, Hexoban is played on a hexagonal grid, rather than a square one. Multiban implemented multiple characters, so you decide who does what. Sokomind Plus introduced new restrictions – each crate has a number on it and must be placed on the empty corresponding slot.

Later versions allow the character on the screen to also pull a crate, or to use such features as holes, teleports an one-way passages.

The idea behind Sokoban has been incorporated in numerous computer games, which sometimes complicate the situation for the player by adding ice patches or holes in which the character might fall and die. However, he can sometimes use the same box or crate to cover a hole so he can move around safely.


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Sliding puzzles

How to solve sliding puzzle also called 15 puzzle

Sliding puzzles are fun toys for kids and grown-ups, but most require a lot of thinking and even some math.


What are Sliding Puzzles

Usually, a sliding puzzle consists of a frame, wood in the past and plastic nowadays, and a number of tiles you must move around to solve the puzzle. Traditional sliding puzzles have 4×4 squares, but the contain only 15 tiles, as you need an empty slot to move the tiles around. This is why many such puzzles are known as 15-Puzzles.

The simplest sliding puzzles are meant for children and the aim is to rearrange the tiles to form a picture, most often a cartoon character.

Puzzles designed for adults have numbers on tiles and they have to be solved according to the rules. The classical 15 Puzzle requires the player to place the numbers 1-15 in ascending or descending order. Other math based sliding puzzles require using a mathematical operation and the numbers on the tiles in each row or column must add up to a certain magic number.

There are also sliding puzzles with letters and the solution is a certain phrase you must write on the board.

Finally, there are sliding puzzles where the tiles bear certain symbols on them. The aim is to make sure the symbols appear only once in a row, column or maybe even diagonal line.


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Sliding Puzzles Versions

One of the most famous sliding puzzles is the so-called Klotski puzzle, name derived from the Polish term for wooden blocks. As opposed to the numerous plastic sliding puzzles, Klotski is an old-fashioned toy and it was invented in the early 20th century. The wooden sliding blocks are of various sizes and the aim of the game is to move the largest of them to a designated place on the board.

The Japanese have a similar puzzle known as Daughter in the Box, in which you have to help the girl escape from the house where she is kept a prisoner. In such puzzles the main difficulty is that you have to move around the smaller pieces to make enough room to move the larger one.

This type of puzzle is very similar to the countless online sliding puzzles in which the goal is to move a certain block towards the exit.


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Situation puzzle

Looking for something to liven up a party? Try situation puzzles!


What are Situation Puzzles

The Internet is full of them as they provide a source of endless fun for children and adults alike. A situation puzzle is usually presented by a host who reads the little story to the other players who can ask simple questions, usually Yes/No questions to explain the mystery in the puzzle. This involves both logical thinking, as well as lateral thinking, that is looking for a creative solution that is not obvious right away.

There can be more than one answer to a puzzle as very creative players can come up with perfectly valid explanation to the original mystery. It must be said that not all the situation puzzles you can find online are credible. In many cases, yes, the provided solution makes perfect sense, but for others the solution can be a little far-fetched.


How to Solve a Situation Puzzle

Sometimes you are allowed only a certain number of questions, but that depends on the rules you agree to play by. If you’re having fun you can ask questions until there’s literally nothing else you can think of. With Yes/No questions, the host is usually allowed small variations to his answer. For instance, Yope means that the full answer to that question would look something like: ‘Yes, but…’.  Not applicable or irrelevant means that the question has nothing to do with the solution. Finally, the host can answer ‘Irrelevant, but assume yes’.


Types of Situation Puzzles

Many puzzles present perfectly realistic scenarios and the solution makes perfect sense. Here is an example:

An avid birdwatcher sees an unexpected bird. Soon he’s dead.’You might try to find an obvious answer, like the guy being attacked by a bird of prey, but the point of situation puzzles is to make you look for unconventional answers.

The solution to the puzzle is that the birdwatcher was in an airplane, hence the ‘unexpected’ bird. Then, the bird gets sucked into an engine and the plane crashes.

Here is an example of puzzle which is not very realistic and involves a lot of guessing.

A man is born in 1972 and dies in 1952 at the age of 25.’

And the solution is He’s born in room number 1972 of a hospital and dies in room number 1952.

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Rubik’s Cube Puzzle

If you’ve never seen a Rubik Cube, you must have been living under a rock for the past 40 years!

What is a Rubik’s Cube

The colorful little cube is the most successful puzzle ever, with more than 350 millions items sold, and that’s probably not counting the countless ripoffs you can find at fairs all over the world.

The standard Rubik’s Cube has 9 squares on each side. A solved cube should have all the sides in a single color, that is use you should rotate the cubelets that make up the cube until all the squares of one color are grouped together. Originally, the colors were white, red, blue, orange, green, and yellow, but today you might find models in various shades. What is truly impressive about this little toy is the complex internal mechanism that allows the pieces to move against each other without the whole thing falling apart. Well, there have been many players fascinated with the concept who actually took apart a cube to see how it works.


How to Solve a Rubiks Cube

Many novices make the mistake of being overly confident when they first lay their hands on a Rubik’s cube. It can’t be that hard, you move some cubelets around and they’ll fall into place, right? Such an approach is dead wrong, as many soon discover.

The first one to come up with a method to solve this puzzle was British math teacher David Singmaster who published a book on Rubik’s Cube in 1981. According to him, you should not focus on a side, but rather concentrate on layers. Solve the top layer first, then go on with the middle and solving the bottom layer should be easy. If you take this approach, you should be able to solve the puzzle in less than a minute.

Another method is to try to solve the corners first.

Computer programs have also been used to analyze the best way to solve a Rubik’s Cube and in 2010 a team of researchers came to the conclusion that it can be rearranged in 20 moves. Well, that depends on the starting configuration so don’t beat yourself if you’ve been scrambling the little cubes for 30 minutes and you’re no way near a solution.


History of Rubiks Cube

As the name says, the puzzle was invented by this Rubik guy, whose full name is Erno Rubik, a Hungarian sculptor and architecture professor. He invented the game in 1974 and took out a patent in 1975. At first, it was only sold locally, but in 1980 it had reached the Western world where the Rubik craze began.

Today, the versions of the popular cube are produced by various companies, and sometimes it’s not even a cube anymore. There are some easy 4×4 versions, but there are some models increasingly complex, with dozens of rotating cubes. If you’re new to this game, better start with the basic model.