You do not Have To Be Good At Maths to Play Sudoku

YOU DO NOT HAVE TO BE GOOD AT MATHS

TO PLAY SUDOKU

and if you Worry about

EXERCISING YOUR BRAIN.

IT'S A HUGE HELP.

You've probably ventured into a bookstore and saw a table overflowing with partially grid numbers pictured on the covers of numerous books titled 'Sudoku' and assumed you have to be good at math to play this game.

The good news is you don't have to be good at maths.

Sudoku is a great mental workout. Keeps your mind sharp and makes you think.

It's a great fun, addictive and an inexpensive hobby.

When I first became interested in Sudoku Val found me a book full of the ways and wherefores by Carol Vorderman.

www. Carol Vorderman..com

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A sudoku puzzle...

...and its solution numbers marked in red

Sudoku is a logic-based number placement puzzle. The objective is to fill a 9×9 grid so that each column, each row, and each of the nine 3×3 boxes (also called blocks or regions) contains the digits from 1 to 9, only one time each (that is, exclusively). The puzzle setter provides a partially completed grid.

Completed Sudoku puzzles are a type of Latin square, with an additional constraint on the contents of individual regions. Leonhard Euler is sometimes incorrectly cited as the source of the puzzle, based on his work with Latin squares.[1]

The modern puzzle was invented by an American architect, Howard Garns, in 1979 and published by Dell Magazines under the name "Number Place".[2] It became popular in Japan in 1986, after it was published by Nikoli and given the name Sudoku, meaning single number. [3] It became an international hit in 2005.

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The name Sudoku means "single digits". The name is a trademark of puzzle publisher Nikoli Co. Ltd. in Japan. The word sudoku derives from the Japanese phrase "Sūji wa dokushin ni kagiru," meaning "the numbers must be single," or "the numbers must occur only once. Other Japanese publishers refer to the puzzle as Number Place, the original U.S. title, or as "Nanpure" for short Some publishers spell the title as "Su Doku". The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are irrelevant. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules. In fact, ESPN published Sudoku puzzles substituting the positions on a baseball field for the numbers 1 through 9; and Viz magazine published a Doctor Who version of the game, using images of the television series' first nine leading actors in place of the numerals. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979

Strategies

The strategy for solving a puzzle may be regarded as comprising a combination of three processes: scanning, marking up, and analyzing. The approach to analysis may vary according to the concepts and the representations on which it is based.

The top right region must contain a 5. By hatching across and up from 5s elsewhere, the solver can eliminate all the empty cells in the region which cannot contain a 5. This leaves only one possibility (shaded green).

Doubles and triples

Finding pairs or doubles can be helpful in finding a solution. If a pair is found in a row where those 2 squares aren't the only open squares, those numbers can be cancelled out of that row. The same goes for triples.

Scanning

Scanning is performed at the outset and throughout the solution. Scans need be performed only once between analyses. Scanning consists of two techniques:

• Cross-hatching: The scanning of rows to identify which line in a region may contain a certain numeral by a process of elimination. The process is repeated with the columns. It is important to perform this process systematically, checking all of the digits 1–9.
• Counting 1–9 in regions, rows, and columns to identify missing numerals. Counting based upon the last numeral discovered may speed up the search. It also can be the case, particularly in tougher puzzles, that the best way to ascertain the value of a cell is to count in reverse—that is, by scanning the cell's region, row, and column for values it cannot be, in order to see what remains.

Advanced solvers look for "contingencies" while scanning, narrowing a numeral's location within a row, column, or region to two or three cells. When those cells lie within the same row and region, they can be used for elimination during cross-hatching and counting. Puzzles solved by scanning alone without requiring the detection of contingencies are classified as "easy"; more difficult puzzles are not readily solved by basic scanning alone.

Logically, every sudoku puzzle, regardless of difficulty, is solved via scanning heuristics. In a true sudoku puzzle, every number has a necessary position in each part of the grid which can be deduced from the description or if you prefer definition of what a "true" sudoku is. The only difference between solving advanced puzzles and simpler puzzles is not the techniques used to solve the puzzle but recognizing the logical implications of the scanning heuristic. One such implication would be recognizing logical "contingencies" which just basically means narrowing down the possibilities of a given square via the relations between every other square.

A method for marking likely numerals in a single cell by the placing of pencil dots. To reduce the number of dots used in each cell, the marking would only be done after as many numbers as possible have been added to the puzzle by scanning. Dots are erased as their corresponding numerals are eliminated as candidates.

The partially filled sub-square determines that 3,5, and 6 must go in the top row. These create a contingency for the far right hatched cell based on the complete row across. It must be a 4.

Marking up

Scanning stops when no further numerals can be discovered, making it necessary to engage in logical analysis. One method to guide the analysis is to mark candidate numerals in the blank cells.

Subscript notation

In subscript notation, the candidate numerals are written in subscript in the cells. Because puzzles printed in a newspaper are too small to accommodate more than a few subscript digits of normal handwriting, solvers may create a larger copy of the puzzle. Using two colours, or mixing pencil and pen marks can be helpful.

Better still use a magnetic board and tabs

Dot notation

The dot notation uses a pattern of dots in each square, where the dot position indicates a number from 1 to 9. The dot notation can be used on the original puzzle. Dexterity is required in placing the dots, since misplaced dots or inadvertent marks inevitably lead to confusion and may not be easily erased.

Analysis

The two main approaches to analysis are "candidate elimination" and "what-if". In "candidate elimination", progress is made by successively eliminating candidate numerals from cells to leave one choice. After each answer has been achieved, another scan may be performed—usually checking to see the effect of the contingencies. In general, if entering a particular numeral prevents completion of the other necessary placements, then the numeral in question can be eliminated as a candidate. One method works by identifying "matched cell groups". For instance, if precisely two cells within a scope (a particular row, column, or region) contain the same two candidate numerals, or if precisely three cells within a scope contain the same three candidate numerals, these cells are said to be matched. The placement of those candidate numerals anywhere else within that same scope would make a solution impossible; therefore, those candidate numerals can be deleted from all other cells in the scope.

BETTER IDEA A MAGNETIC BOARD AND TAGS.

Difficulty ratings

The difficulty of a puzzle is based on the relevance and the positioning of the given numbers rather than their quantity. Surprisingly, most of the time the number of givens does not reflect a puzzle's difficulty. Computer solvers can estimate the difficulty for a human to find the solution, based on the complexity of the solving techniques required. Some online versions offer several difficulty levels.

Most publications sort their Sudoku puzzles into four or five rating levels, although the actual cut-off points and the names of the levels themselves can vary widely. Typically, however, the titles are synonyms of "easy", "intermediate", "hard", and "challenging" (also known as "diabolical" or "evil"). An easy puzzle can be solved using only scanning; an intermediate puzzle may take markup to solve; a hard or challenging puzzle will usually take analysis.

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History

Page from La France newspaper, July 6, 1895

Number puzzles first appeared in newspapers in the late 19th century, when French puzzle setters began experimenting with removing numbers from magic squares. Le Siècle, a Paris-based daily, published a partially completed 9×9 magic square with 3×3 sub-squares in 1892.[22] It was not a Sudoku because it contained double-digit numbers and required arithmetic rather than logic to solve, but it shared key characteristics: each row, column and sub-square added up to the same number.

Within three years Le Siècle's rival, La France, refined the puzzle so that it was almost a modern Sudoku. It simplified the 9×9 magic square puzzle so that each row and column contained only the numbers 1–9, but did not mark the sub-squares. Although they are unmarked, each 3×3 sub-square does indeed comprise the numbers 1–9. However, the puzzle cannot be considered the first Sudoku because, under modern rules, it has two solutions. The puzzle setter ensured a unique solution by requiring 1–9 to appear in both diagonals.

These weekly puzzles were a feature of newspaper titles including L'Echo de Paris for about a decade but disappeared about the time of the First World War. According to Will Shortz, the modern Sudoku was most likely designed anonymously by Howard Garns, a 74-year-old retired architect and freelance puzzle constructor from Indiana, and first published in 1979 by Dell Magazines as Number Place (the earliest known examples of modern Sudoku). Garns's name was always present on the list of contributors in issues of Dell Pencil Puzzles and Word Games that included Number Place, and was always absent from issues that did not.[11] He died in 1989 before getting a chance to see his creation as a worldwide phenomenon.[11] It is unclear if Garns was familiar with any of the French newspapers listed above.

The puzzle was introduced in Japan by Nikoli in the paper Monthly Nikolist in April 1984 as Suuji wa dokushin ni kagiru which can be translated as "the digits must be single" or "the digits are limited to one occurrence." At a later date, the name was abbreviated to Sudoku by Maki Kaji, taking only the first kanji of compound words to form a shorter version. In 1986, Nikoli introduced two innovations: the number of givens was restricted to no more than 32, and puzzles became "symmetrical" (meaning the givens were distributed in rotationally symmetric cells).[10] It is now published in mainstream Japanese periodicals, such as the Asahi Shimbun.

Popularity in the media

In 1997, retired Hong Kong judge Wayne Gould, 59, a New Zealander, saw a partly completed puzzle in a Japanese bookshop. Over six years he developed a computer program to produce puzzles quickly.[24] Knowing that British newspapers have a long history of publishing crosswords and other puzzles, he promoted Sudoku to The Times in Britain, which launched it on 12 November 2004 (calling it Su Doku).

The rapid rise of Sudoku in Britain from relative obscurity to a front-page feature in national newspapers attracted commentary in the media and parody (such as when The Guardian's G2 section advertised itself as the first newspaper supplement with a Sudoku grid on every page). Recognizing the different psychological appeals of easy and difficult puzzles, The Times introduced both side by side on 20 June 2005. From July 2005, Channel 4 included a daily Sudoku game in their Teletext service. On 2 August, the BBC's programme guide Radio Times featured a weekly Super Sudoku.

Even the Greeks owe the publication of their first Sudoku magazine to British influence. It was at Heathrow airport in the summer of 2005 that a Greek computer magazine publisher first laid eyes on a British Sudoku magazine and - realising the opportunity - proceeded to purchase the necessary software and quickly launch the first local Sudoku magazine that became an instant success.

In the United States, the first newspaper to publish a Sudoku puzzle by Wayne Gould was The Conway Daily Sun (New Hampshire), in 2004.

REMEMBER its FUN and

LIKELY TO BECOME HABITUAL

Comments

cpa says:

I love Sudoku, though as a CPA you might think I have an affinity for maths. In this case I agree with MrMarmalade that it has nothing to do with maths. It is an excellent way to work the brain.

Zsuzsy Bee says:

MrMarmalade! Our local Alzheimer society published an article not very long ago where it stated that Sudoku and crossword puzzles are a great preventive excercise that will keep the mind active. I can't remember how exactly they worded the write-up but it went something like this: ...our muscles and bones need exercise to stay nimble and so does the brain, these puzzles are Pilates for the brain...I just love Sudoku I try to do one a day along with my crossword puzzle in the newspaper with my morning coffee...

Great HUB

regards Zsuzsy

cgull8m says:

I love Sudoku; here is a good site I play online and very useful. It definitely helps our mind for sure. Great Hub.

http://www.menneske.no/sudoku/eng/

Isabella Snow says:

I've yet to try this - you've made me curious!

MrMarmalade says:

Thank you cgull8m, Isabella Snow

I thank you both. A friend has both told me this morning that if your mind is forgetting how to tie your shoe laces, Sudoku may help prolong the absence of memory. Here I was thinking it was just me making a reason up to puzzle at Sudoku

mqjeffrey says:

Great Hub... as a personal enemy of Math, I was surprised how much I love Sudoku!

MrMarmalade says:

Can I tag this real live hub to the bottom of the Sudoku hub please?

It is just the atmosphere that Sudoku would love to have behind.

Thank you

sukritha says:

Max is my permanent Enemy. Bit after reading this I think I have to change my decition. Good one Again

Sukritha

vishnuprk says:

Its simply logic. But beware, u may get addicted to it

Marisa Wright says:

27 hours ago

I'm a "subscript notation" girl myself. Mind you, I had to buy a book to work out how to play it.

Experts now say the best thing to ward off Alzheimer’s is physical exercise that requires mental coordination (dancing, playing an instrument, racquet sports), but then again I can hardly do those on the train to work, can I?