Category: How to Solve

What would happen if you had not two, but eight queens on a chess board?

 

How to Solve the Eight Queens Puzzle

Solving this puzzle requires not only basic knowledge of chess rules but also mathematics.

The original Eight Queens Puzzle refers to placing the eight chess pieces on a 8×8 board, making sure that no queen threatens another one. As you probably know the queen can move any numbers of unoccupied squares in any direction – horizontally, vertically or diagonally. It is obvious that, in order to solve the puzzle, no two queens can occupy the same row, column or diagonal.

In theory, the number of ways you can place the eight pieces on an 8×8 board is huge, 4,426,165,368, to be exact. You don’t have to go through all of them to find one of the 92 solutions to the puzzle.

 

Since such puzzles are meant to be fun, better forget about math and just look at the board. One thing you know from start is that there has to be only one queen to each row or column and you work your way to a solution from here.

 

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History of the Eight Queens Puzzle

This fiendish puzzle was invented in 1848 by Max Bezzel, a German chess enthusiast who created many chess problems. Two years later, Franz Nauck came up with several solutions and also invented the n queens problem. This refers to placing an n number of queens on an nxn board, thus offering the possibility of playing the same game on a larger or smaller board.

 

Chess Puzzle Variants

If you like this brain-racking puzzle, you should try one of its variants that use other chess pieces, knights, bishops, kings and even rooks. The easiest to solve is the version with knights. Since knights move in an L shape they always land on a square of the opposite color. A simple solution to prevent them from attacking each other is to place all the knights on squares of the same color and it doesn’t even matter where you place them.

Other versions allow for two different types of pieces to be used, like queens and pawns or knights, the goal being the same – keeping the peace on the board.

 

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Also known as entanglement puzzles, these are more than simple toys (How to solve video below).

 

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Types of Disentanglement Puzzles

There are many version of this popular toy and all have a common goal, trying to disentangle an element, like a ring, from the loops or plate it seems firmly attached to.

Wire and string puzzles

The string can be made of a string or a ribbon and there are various elements attached to it. The toy also has at least one stiff wire, but some also have a ball though which the string is threaded.

You usually have to detach the string from the wire. The loop the string makes can be closed, which makes the puzzle seem impossible to solve, or the loop can be open, but the string has balls or wooden elements to prevent it from slipping.

One famous example in this category is the Boomhower puzzle, notoriously difficult to solve. Subsequent variants use the Boomhower idea and consist of one or two vertical beams on a wood support with various elements attached to them.

Plate and rings puzzles

All the pieces are usually made of metal and the goal is to detach the ring from the plate. Typically, the plate will have holes or indentations, some meant to help you, some to make your task more challenging.

Wire puzzles

Sometimes referred to as nail puzzles, these puzzles are made from stiff pieces of wire in various shapes, forming closed or open loops, that you need to disentangle.

As complicated as disentangling such crazily linked pieces, putting it back together can be even harder, but that is also part of the game.

Possibly Impossible

While most disentanglement puzzles take some time and a lot of effort to solve, there are some that are actually unsolvable. Should anyone ever challenge you to solve the “Notorious Figure Eight Puzzle” stay away from it. The puzzle created by Stewart Coffin in 1974 looks deceptively simple, like the figure 8 with a loop string attached to it. Many people have tried in vain to solve it, mathematicians have also looked into it and came up with the conclusion it is unsolvable, which is why it is sometimes referred to as the Possibly Impossibly puzzle.

 

Watch Video Below

 

 

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Good for sending secret messages to your loved one as well as to encrypt sensitive military information.

 

How to Solve Cryptogram Puzzles

A Cryptogram is basically a row made up of lines of empty cells that stand for words. Under each cell there is a certain letter or number. The aim of the puzzle is to understand what letter each of the letters or numbers in the printed cryptogram stands for. These are called substitution cryptograms, meaning that a letter (or number) substitutes for another letter. If you want to use cryptograms to communicate with someone both of you will have the key, but as a puzzle you have to use logic to find the key.

The first step in solving a cryptogram is looking at one letter words, if any. In English, only I and A form one letter words, so you already have an important clue. Also, you need to check for double letters (OO, SS, etc) and spot id there are any apostrophes. Another important part is looking at three-letter words, as in English the most common are AND and THE. No letter can substitute for itself.

 

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History of Cryptogram Puzzles

Using a cypher to encode a message dates back many centuries, if not more. It is believed cryptograms were invented by monks for entertainment purposes. The oldest known reference to the use of cryptograms can be found in a manuscript dating from the 9^th century.  A manuscript discovered at Bamberg, in modern Germany,  mentions the fact that that Irish visitors to the court of Merfyn Frych ap Gwriad (died 844), who reigned over Gwynedd in Wales were presented with a cryptogram which could only be solved by transposing the letters from Latin into Greek.

In modern times, Edgar Allan Poe used cryptograms in some of his works and as a magazine editor he often asked readers to submit their own cyphers, which he would then publish, challenging the public to come up with the solution.

The infamous Zodiac Killer also used cryptograms in messages meant to taunt the police. Only one of the four messages has been solved to this day.

A version of this traditional puzzle very popular today is the CryptoQuiz which is a themed puzzle, and all the words fall in the same category.

 

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One of the most popular puzzles of all times to test your knowledge and skill at guessing words.

 

How to Solve Crossword Puzzles

A crossword puzzle is a square or rectangular grid you must fill in with words or sometimes phrases, based on the clues you are given for the horizontal and vertical lines. The end to a word is marked by a black cell. When you think you know the answer to a clue, let’s say in a vertical line, check how each letter affects the solutions to the horizontal lines it crosses.

Many crosswords are themed so most of the clues refer to a certain topic – music, literature, geography, TV shows, sports etc.

 

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Versions of Crossword Puzzles

Straight Clues

The most basic, and most popular, variant of crossword puzzle is that in which the clues are straightforward. An example of straight clue reads like ‘The capital of France’, with the obvious solution – PARIS. The clues must be consistent with the time of the verb, distinguishing between present and past, and must indicate if a noun is in the single or plural form.

Indirect clues

Indirect clues involve lateral thinking rather than a direct answer. For instance, ‘Start of spring’ could mean MAR (as in March) or ESS the way you spell S, the first letter in the word spring.

Cryptic clues

Puzzles for crossword aficionados tend to have very challenging cryptic clues, Basically, the clue itself is a puzzle you must figure out before filling in the solution to the crossword puzzles. Anagrams are sometimes used as clues, and the rule is to indicate that in the clue, but they are easier to understand than other cryptic clues.

One type of cryptic clues refers to words that can have more than one meaning. The solution to a cryptic clue like‘Cat’s tongue’ is PERSIAN, as it’s a type of cat, but also a language or tongue.

Sometimes, the list of clues includes cross-referencing, which means that the clue for a certain word points to another clue you need to guess.

If the solution to a clue is a hyphenated word, the clue might indicate the number of letters in the two words linked together.

 

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Crossword puzzle meets Sudoku, that’s the easiest way to explain Kakuro.

 

How to Solve Kakuro Puzzles

First, let’s have a look at what Kakuro puzzles look like. The traditional version is a 16×16 grid, filled with white cells divided by black cells. A line of white cells is called an entry.

In a crossword puzzle you have the cues listed on the side, but in Cross Sums your clues are numbers and are printed on the black cells that form the top row and the the leftmost column. If the clue is, say, 7 the numbers in the solution must add up to 7. You can use any number from 1 to 9 to arrive at a sum, which represents the solution to an entry. You are not allowed to use the same digit twice in the same line.

Each line or entry has to contain at least two digits, while the longest possible line has nine cells, so you have to use all the numbers from 1 to 9.

Some version have an added constraint, the rule being that you cannot have the same combination used twice in a grid. For instance, if you have 7 as a clue twice, you cannot use 4+3 in both cases.

 

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Tricks to help you with the Kakuro Puzzle

Guessing is not a good strategy to solve a Cross Sums puzzle, you have to use logic, make deductions as to the digits you should input by considering their position both in the horizontal and the vertical clues.

Start by looking at the shortest entries, preferably those with two cells. Also, see if there are any 3 or 4 clues. If you have 3 as a clue, the only possible answer is 1 plus 2. When the clue is 4, the answer can only be 1+3, as you cannot duplicate the twos in 2+2. Even higher sums can be easy to solve. If you have to use two digits to add up to 17, those two digits can only be 8 and 9, and you have to decide where each of them fits best.

 

History of Kakuro Puzzles

In Japan, these puzzles are almost as popular as Sudoku and the name Kakuro means addition cross. In the Western part of the world, the term Cross Sums was coined in 1966 by Canadian Jacob Funk, but today most publications use the term Kakuro.

 

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Playing with sliding wood blocks, what could be more fun? Well, if it’s a Burr puzzle you’re in for so

me head-scratching.

 

How to Solve Burr Puzzles

This popular game belongs in the interlocking puzzles category and they all use the same basic idea. The set consists of six (or more) notched sticks, or little pieces of wood which the player must use to recreate a certain shape.

 

The most popular interlocking puzzle is the 6-piece burr, also known as “Puzzle Knot” or “Chinese Cross”. The aim is to slide and lock the 6 sticks into position to form some sort of a cross. Some variants of the game have a so-called key, an unnotched piece which can easily slide in and out.

No matter what shape you need to replicate, the notches on the pieces fall on the inside, where they cannot be seen, leaving the outer surface smooth and quite puzzling as it is impossible to tell how the sticks fit together. In fact, taking apart such puzzles is as challenging as creating the required shape.

There are two main types of such puzzles – Solid Burr puzzles which don’t have any voids or empty spaces inside, and Holey Burrs which have at least one empty space inside, usually not visible from the outside.

 

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Burr Puzzle Variants

The Altekruse puzzle consists of 12 identical pieces and in order to take it apart the two halves of the puzzle have to be moved in opposite directions. Versions of the Altekruse puzzle can have 6, 24, or 36 pieces.

The Chuck puzzle differs from other Burr puzzles because it consists mostly of U-shaped pieces of various lengths. Some of the sticks have an extra notch ande are used as key pieces.

Another version of the classical Burr puzzle is the Pagoda, also known as “Japanese Crystal”. The smallest version, Pagoda 1, has only three sticks and does not even require notches to be assembled or taken apart. A Pagoda of size 2 has 9 pieces, while bigger variants come in sets with 19, 33, 51 or even more pieces. This might seem a bit complicated but, the truth is once you understand how the pieces fit together it’s easy to assemble the puzzle.

Diagonal Burr puzzles present an interesting variation. The notches on the pieces are not square as in the classical Burr puzzles, but diagonal, which changes the way the pieces slide against each other.

 

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Back from the Klondike is the brainchild of a famous American chess player and puzzle author Sam Loyd, and it was first published back in 1889.

 

How to Solve Back from the Klondike Puzzle

The puzzle looks like a grid filled with numbers from 1 to 9. You need to start from the square right in the middle, marked with a heart, and find your way out of the maze. The number on that cell says 3. You can move in a straight line in all directions – horizontal, vertical and diagonal. As the number is 3 it indicates you can move three squares. The cell you land on will have another number indicating how many squares you can jump in your next move. Repeat this process, moving in straight line in any direction, until you land on a cell whose number will allow you to make just one step over the borders of the puzzle. This means you got out of the maze and won the game.

Sam Loyd offered a solution to his puzzle and it has to do with favoring the South West route to liberty.

 

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Back from the Klondike Variants

Mathematicians are typically fascinated by this type of puzzles and in 1976 two graduate students from the University of Washington developed a Fortran computer program dedicated to analyzing all the possible solutions to the Back from the Klondike puzzle and they came up with hundreds of ways to get out of the puzzle. The most interesting thing they discovered was that all the escape routes passed through a cell that was part of Loyd’s original solution, but also through one that did appear in his solution. This indicated there was actually an error in the famous puzzle, which has been since corrected.

Modern variants of the puzzle will have the 16^th row comprised of the following numbers 81112, while in the original form it was 81212. The good news, at least for math lovers, is that the corrected version has only one solution. For regular people just looking for some fun activity this might not be such a good news! Good luck anyway!

How to Solve Anagram Puzzles

You can play anagram with pen and paper, online or without anything, which is a bit challenging as you have to keep track of the letters in your mind.

Let’s see a few examples: study – dusty, night – thing, below – elbow, act – cat.

 

The original word, the word you start the game with is called the subject. To create an anagram you must rearrange the letters to form another word.

For instance, if the subject is listen, its anagram will be silent. Or enlist. It doesn’t matter if change the part of speech. If the subject is a verb, the anagram can be another verb, adjective or noun, unless you want to make it more challenging and have the players stick to one part of speech.

The solution to the puzzle may be a synonym of the subject. For instance: evil – vile.

Skilled players can play the variant called antigram, which means the solution must be an antonym of the subject or close enough.

The pair funeral – real fun counts as an antigram.

Moving on to the next level – phrases. Debit card – bad credit.

 

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Anagram Puzzle Variants

Sometimes anagrams can be used to poke fun at someone or something by rearranging the the letters in their name, a tradition that dates back centuries ago.

One modern example is George Bush – He bugs Gore.

Sometimes anagrams were used by authors who wanted to publish something controversial under a pen name, but still one easily recognizable by the discerning mind. One of the most memorable anagram in modern times can be found in the Harry Potter series, where the name of the mysterious character Tom Marvolo Riddle spells out I am Lord Voldemort!

If you search around a bit you can find various anagram solvers online, but, of course, that would be cheating…

 

History of Anagram Puzzles

Anagram puzzles can be traced back to ancient times, the first recorded examples being in Latin. Anagrams remained so popular through the times that King Louis XIII of France had a Royal Anagrammatist and the job paid well enough.

 

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It’s all about the clues. The original version had only two word clues, but in online versions you might start with multiple clues.

 

How to Solve Acrostic Puzzles

First of all you are given a set of word clues, usually two. The traditional variant that still follows the rules set by the game’s creator Elizabeth Kingsley in 1934 starts with clues for two words you have to guess. The solution to each clue is presented as a series of numbered blanks, indicating how many letters are there in the answer. Each of the letters has a corresponding number.

A player has to use those numbers to start solving the quotation. If you know that 1 stands for A and 4 stands for D, you can easily decipher the sequence of numbers 1-9-4 to be AND, which tells you 9 was N. And so on.

 

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Rules for Online Acrostic Puzzles

However, online acrostics are more complex than that and look more like a crossword puzzle, a layered puzzle in which you need to guess not only a quote but also the name of the author and the source.

You start by looking at the lettered clues A, B, C etc. Chances are you’ll know a couple of them. Fill in the words in the blank spaces.

Just as in any crossword, each time you fill in a word you will have uncovered some letters that are part of the answers to other clues. Maybe you still don’t know the answer to the next clue but at least you have a hint.

Go back to the set of clues and see if you can guess the next one. If not, move to the next one, there must be something you can figure out.

Guessing the first two or three clues is the hardest part. To solve the rest of the puzzle go back and forth between clues and grid and you will slowly start to decipher the quote that is basically the prize for solving the puzzle.

History of Acrostic Puzzles

Originally, the term acrostic comes from a form of poem in which the first letter of each line read from top to bottom spells out a name. For acrostic puzzles, those letters will reveal the name of the author whose quote you have just uncovered.

 

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