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| − | Background on puzzles.
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| − | Puzzles have existed since the times of the ancient Greeks and Romans. Mathematical puzzles by the Greek mathematician Euclid, Pythagorous, or the Vedic scholar Bodhayana eventually evolved into accepted mathematical facts.
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| − | Puzzles are found in all schools; only there they are called quizzes or tests.
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| − | For example: How to measure out one litre of liquid using only three containers, each of different a size. (size varies from test to test and is immaterial. It is the math that counts; pardon the pun.).
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| − | Or the many variation of "How many" puzzles, such as: "If there were as many of us again and fifty percent as many more there would be 30 of us. How many are we?
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| − | Another example is: Every widget is a giget. One-half of all gigets are widgets. One-half of all zigets are gigets. There are 30 zigets and 20 gigets. All widgets are zigets. How many gigets are not widgets or zigets.
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| − | Here is a variation on number game puzzles:
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| − | Think of a number, triple it, divide result by two, triple the answer and take one-half of the result. Now divided that by nine and the result will always be one-quarter of the original number.
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| − | Mathematical challenges of ancient and more recent times can be found in puzzles such as ticktacktoe, sliding square games, or find a number games.
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| − | Puzzles have been, and are today, created to pose a challenge and/or provide intellectual joy; that mental pat on the back one receives after solving a puzzle.
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| − | == Puzzles published by [http://www.punzhu.com Punzhu Puzzles] ==
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| − | Free [http://www.magazine.punzhu.com/index.php puzzle magazines] published in Adobe PDF format by Punzhu Puzzles include crosswords, word finds, anagrams, cryptics, sudoku, pathways (connect-the-dot), and cross sum (kakuro) puzzles.
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| − | '''Crosswords'''
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| − | An Englishman named Arthur Wynne in 1913 invented crossword puzzles. The first crossword puzzles didn't have any black squares and the very first printed and published crossword was diamond shaped.
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| − | Crosswords are perfect puzzles for improving your vocabulary and knowledge of words. They are created using a grid, usually rectangular, containing black squares to indicate the end or beginning of a word or word sequence, and white squares for letters.
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| − | Words in a crossword grid may be written horizontally (Across) or vertically (Down). Numbers are assigned to the horizontal and vertical squares and correspond to the clue definitions provided for that puzzle grid.
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| − | Example:
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| − | [[Image:Crossword.jpg]]
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| − | Crossword clues may be a synonym, an antonym, a type of thing the solution is, a hint like in 4 Across in example, a partial definition, a cryptic clue, or an anagram to name just a few clue examples.
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| − | ''Crossword variations''
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| − | Variations on the standard crossword include:
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| − | 1) a diagramless puzzle in which some or all of the black squares are removed;
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| − | 2) a diagramless puzzle with anagram clues;
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| − | 3) a jigsaw style of crossword in which a puzzle is broken into pieces like a jigsaw and you place the pieces back in the correct order to match the solution;
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| − | 4) a zigzag crossword where a word in the grid bends 90 degrees once or twice and continues onward to the next black square;
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| − | 5) a pick-one crossword game where the puzzle has two letters in a square and you must pick one to form the correct word in the solution;
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| − | 6) a code word crossword in which each blank square contains a number corresponding to a letter in the alphabet.
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| − | These and other crossword puzzle variations are available for free from [http://www.punzhu.com Punzhu Puzzles].
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| − | Punzhu has produced commercial crossword puzzles for the automotive industry, adult education and English as a Second Language education, and governments. For more information on our commercial crosswords contact our [http://www.punzhu.com/forums/sendmessage.php sales] department.
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| − | '''Word Find puzzles.'''
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| − | Word find puzzles, sometimes called word search puzzles, are also perfect for improving your vocabulary. Most word find games have difficulty levels ranging from easy to hard.
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| − | Word find puzzles have letters filling a square or rectangular puzzle box, with some of the letters in the square or rectangle forming words that are provided to you in a word list for that puzzle.
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| − | To solve a word find game you match a word in the word list to the letters in the puzzle box and circle only the found word. You then cross out the found word in the word list.
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| − | One easy way to solve a word find is to start looking for words beginning on the left of the puzzle and following the letters to the right. Another is to look for groups of identical letters, like "tt" in letters, "oo" in looking, "zz" in puzzle.
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| − | There are different levels of difficulty in most word finds, such as easy, medium or hard. Easy word finds have the words going Across or Down like a crossword puzzle. Medium difficulty word finds may have words going Across, Down, forward angle down, forward angle up, backward across, backward down, backward angle up, or backward angle down. Hard word finds will have all possible combinations of word directions.
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| − | Level of difficulty also depends upon how many garbage letters surround the actual word in a grid and whether those garbage letters form partial words or not.
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| − | In many medium or hard puzzles the words may overlay other words or intersect on the first or last letter of a word.
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| − | Some word finds will use a special sentence or phrase as fill-in letters surround the words in a puzzle grid. The special sentence or phrase replaces the random letters or random partial words that usually act as filler in standard word finds. This style of word find is often called a Hidden Phrase, Secret Message, or simply Hidden Message.
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| − | Example of an easy word find, with words going Across and Down only.
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| − | [[Image:Wordfind.jpg]]
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| − | Word finds are often used in education as a language-learning tool. Punzhu Puzzles publishes [http://www.magazine.punzhu.com/index.php free] word finds in a variety of languages, and are thus suitable for schools, businesses, travel, or challenging yourself or friends to a foreign language game.
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| − | Punzhu has produced commercial word find puzzles for the automotive industry, adult education and English as a Second Language education, and governments. For more information on our commercial word find puzzles contact our [http://www.punzhu.com/forums/sendmessage.php sales] department.
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| − | '''Anagram puzzles.'''
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| − | An anagram is a word written backward or scrambled. For example, "anagram" can be scrambled to "a ragman", "ram a nag", "arm a nag", and many other variations of the word.
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| − | Anagrams can be used in crosswords and other word puzzles. When used in crosswords as clues the anagram usually includes the number of letters in a word to help solvers when the solution is two or more words. See 1 and 4 Down in example.
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| − | [[Image:Anagram.jpg]]
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| − | Punzhu publishes a variety of anagram style of puzzles and makes them available as [http://www.magazine.punzhu.com/index.php free] downloads or as special commercial use puzzles for businesses, other publishers, governments, and educators. For more information on commercial use anagram puzzles contact our [http://www.punzhu.com/forums/sendmessage.php sales] department.
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| − | '''Cryptic puzzles.'''
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| − | Cryptic puzzles are code word puzzles. Code puzzles originally began as a form of messaging for the military and governments... the secret message or cipher.
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| − | Ancient Greeks reportedly employed the first cipher method around 400 BC as a message method between military leaders.
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| − | They employed a tapered wooden stick with a piece of parchment wrapped around it, making sure the ends of the parchment didn't overlap. A message was then inscribed on the parchment, which when unwrapped was just a bunch of meaningless letters; unless you knew which size stick was used to create the original message. To decode the message you simply placed the cipher parchment on the correct size of tapered rod. This was called a "scytale".
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| − | In the early 1400's the Arabs devised and used both substitution and transposition ciphers. About 1412 al-Kalka-shandY included in his encyclopaedia explicit instructions on how to cryptanalize cipher text and provided lengthy examples to illustrate this technique.
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| − | Around the late 1400's some European governments used two rotating concentric circles containing a sequence of 26 letters. One disk was used for the plain text and the other was for the corresponding coded letter. Punzhu Puzzles uses this form for its cryptic puzzles.
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| − | The Vatican houses a manual produced in 1379 by Gabriele de Lavinde, who served Pope Clement VII, which contains brief code called vocabularies, or nomenclators, that were then expanded and used by nearly all European governments.
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| − | All modern ciphers, password generators, encryption devices and other code systems are but advances based upon the basic letter substitution created in the thirteen and fourteen hundreds.
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| − | Example:
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| − | X D D I V M C P Z J T L B C P W, L X W W N V P M
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| − | K C Z C P X O V P W, C Z J P A L O T V Z M C F T J C W X Z M
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| − | V O B C P J V M C W A W O C I W X P C Q G O X M F X Z J C W
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| − | Q X W C M G L V Z O B C Q X W T J D C O O C P
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| − | W G Q W O T O G O T V Z J P C X O C M T Z O B C O B T P O C C Z
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| − | X Z M H V G P O C C Z B G Z M P C M W.
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| − | Plain: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
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| − | Cipher: X Q J M C H K B T S U D I Z V L R P W O G F N E A Y
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| − | Solution is the sentence before this example.
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| − | Punzhu Puzzle cryptic puzzles usually contain three letters in both the Plain and Cipher, but sometimes for a really hard puzzle we include fewer or no code help. Some of our puzzles will have code hints for the letters A, B, or C in the solution. Sometimes our puzzles will have other combinations.
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| − | To help solvers we provide an extra amount of space between the lines of coded letters in our cryptic puzzles, for the placement of possible solution letters under the cryptic letters.
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| − | Cryptic puzzles are both challenging and entertaining. Punzhu Puzzles publishes [http://www.magazine.punzhu.com/index.php free] cryptic games and has produced commercial cryptic puzzles for businesses, other publishers, and educators. For more information on our commercial cryptic puzzles contact our [http://www.punzhu.com/forums/sendmessage.php sales] department.
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| − | '''Sudoku'''
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| − | The word Sudoku simply means "single number" in Japanese. A sudoku grid contains 9 large squares; each large square contains 9 squares for the placement of a single number.
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| − | The numbers used are between one and nine, including one and nine, and there is no mathematical relationship between the numbers.
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| − | In 1979 freelance puzzle constructor Howard Garnes introduced the game, which he called Number Place.
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| − | In 1986 in Japan two important changes were made that led the popular game as we know it today. First, no more than 30 numbers were given in any puzzle grid to help a solver. Second, the puzzles were symmetrical.
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| − | [[Image:Sudoku.jpg]]
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| − | Symbol sudoku puzzles created by Punzhu Puzzles add an extra degree of challenge for solvers. Instead of the numbers 1-9, Punzhu uses various symbols. Many of our symbol sudoku puzzles have a common theme to their symbols.
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| − | Here is one example of the various symbols used by Punzhu Puzzles in creating our symbol sudoku puzzles using Unicode box drawing style of symbols:
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| − | [[Image:Symbol.jpg]]
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| − | Both sudoku and symbol sudoku puzzles are available for free on our [http://www.magazine.punzhu.com/index.php web site]. Punzhu Puzzles has also created special symbol sudoku puzzles for businesses and educators. For more information on our commercial sudoku puzzles contact our [http://www.punzhu.com/forums/sendmessage.php sales] department.
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| − | '''Pathway Puzzles''' (Connect-the-dot)
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| − | Pathway puzzles, or connect-the-dot puzzles, are variations on a maze game. These puzzles are "simply connected" mazes, meaning these puzzles have no breaks or detached walls.
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| − | Most mazes have parallel sides in which a solver travels until a block is met. The solver must retrace his steps at this point until the solver ultimately reaches the end of the maze.
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| − | The first mazes, or labyrinths as the Greeks and Romans called them, were blind alleys and passageways that made exiting difficult. Later, mazes were integrated into gardens using high hedges as walls for the pathways. Modern mazes in Japan use movable wooden walls so that the configuration can be easily, and ever so often, changed.
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| − | A computer chip, motherboard, software, and other computer devices also work on a maze principle. An electron A travels along path B until it reaches end C or wall D. If it reaches wall D it is diverted to another path until it ultimately reaches end C.
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| − | Rush hour traffic and trying to find the quickest, shortest route to your destination is another style of maze.
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| − | Our Pathway puzzles don't use the typical "walled" maze but instead are based upon the wall-less connect-the-dot puzzle in which a shape is constructed when a solver connects the dots properly.
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| − | To direct a solver along the pathway we use the numbers 0 to 3 as guides along a square. Each Pathway puzzle contains a series of squares, like a diagramless crossword puzzle, and a solver chooses one of the four sides as the Pathway using the numbers as guides.
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| − | A zero means there are zero points along the square, one means one of the four sides is a pathway, two means two of the four sides are pathways, and three means three of the four sides are pathways.
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| − | No Pathway line may cross over another Pathway line, nor may a Pathway line cross back upon itself.
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| − | To design a Pathway puzzle we first set the number of squares we want across and down. Then we create the line that becomes the Pathway. Finally, the number guides are entered and the existing line removed so that only the numbers and the squares remain.
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| − | Here is an example of a completed Pathway puzzle with an easy level of difficulty:
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| − | [[Image:Pathway.jpg]]
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| − | Not all corners of the solution have numbers. As you can see from the example above there is no number three for the left corner of the letter T. This is where your deductive abilities come into play and is a function of designing interesting (and challenging) Pathway puzzles.
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| − | Punzhu makes this style of puzzle available for [http://www.magazine.punzhu.com/index.php free] on our web site. Custom commercial puzzles for businesses, educators, and other publishers are available by contacting our [http://www.punzhu.com/forums/sendmessage.php sales] department.
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| − | '''Cross sum (kakuro)''' puzzles
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| − | Kakuro puzzles are a combination of crosswords and sudoku. Whereas in a crossword puzzle the black square represents a block, in kakuro puzzles the black square contains a diagonal line with a number above the line representing the sum (or product) of the numbers across from it and below the diagonal line the number there represents the sum (or product) of the numbers below it.
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| − | Kakuro puzzles have a grid similar to crosswords and, like sudoku, use only the numbers 1-9.
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| − | Kakuro, and sudoku, may have had their origins in magic squares. A magic square is a square array of integers in which the rows, columns, and diagonals have the same sum. Magic squares are one of the oldest mathematical puzzles and have been known since at least medieval times.
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| − | Both sudoku and kakuro may share some history as first put forth by Leonard Eular, a Swiss physicist, in a paper in 1783 showing how to construct magic squares with a certain number of cells. He referred to this as a Latin square because he used Roman numerals.
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| − | Sudoku and kakuro puzzles differ from magic squares in that the same sum is not shared across the rows, columns, and diagonals. However, it is not a major leap to consider that both sudoku and kakuro puzzles have some link in history to magic squares due the extensive time period in which magic squares have been known and used.
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| − | As with our crossword grids, a kakuro puzzle grid is first created then tested to determine if the grid design is successful or needs revision. A kakuro grid may be square, rectangular, triangular, round, or any shape that lends itself to be an interesting (and solvable) puzzle.
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| − | The level of difficulty within a grid is determined during its construction. Some kakuro puzzles may seem difficult when one first looks at the grid, but in reality the puzzle may be quite easy. And vice versa.
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| − | Here is an example of an easy kakuro puzzle:
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| − | [[Image:Kakuro.jpg]]
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| − | Kakuro puzzles are available for free download from our [http://www.magazine.punzhu.com/index.php web site]. Please contact our [http://www.punzhu.com/forums/sendmessage.php sales] department for commercial kakuro puzzles.
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