Nonograms are simple and fun because they have the added bonus of producing a picture!  They were first invented in the 1980’s in Japan, published under the name “Window Art Puzzles.”  From there they migrated to the UK in the 1990’s, where they were renamed “nonograms,” and Games magazine began publishing them in the US under the name “paint by numbers,” which is how I first discovered them.  Perhaps these puzzles are most famous for the various Nintendo spinoff games for the GameBoy and DS, namely Mario Picross and Pokemon Picross (picross being short for “picture crossword”).

Like all the other puzzles discussed in this blog, the rules for nonograms are simple.  The picture is supposed to be drawn in a grid of no specific dimensions (though usually at least 10×10).  Along the sides of the grid there are a bunch of numbers, indicating how many squares should be filled in consecutively in that row or column; column numbers are listed along the top of the grid, row numbers are listed on the left.  That is, a 4 along row 2 in Figure 2 means that the picture has exactly four boxes shaded in in that row, consecutively.  The (2 2) in row 4 means that the picture has two boxes shaded, then at least one space, then another two boxes shaded.  The goal is to create a picture which matches the numbers on the sides of the puzzle.  While this sounds easy, it can actually become very challenging, very fast, and require quite a bit of guesswork depending on the difficulty level of the puzzle.  Here are a few tips to help you get started!

 

One easy trick to look for rows or columns with a number that is more than half the length of the grid. For instance, in Figure 2 there are 11 column boxes.  Looking at the second column, we can see that we need to fit nine boxes in a row.  No matter how we orient those boxes, there will be a certain region that must be covered: namely, from row 3 to row 9.  Thus we can shade those 7 boxes in, without exactly knowing where the other two will land.

 

Once we know that, we can use another technique which involves looking at numbers that are close to the edges of the grid.  Consider, for example, the 4 in row 7.  We know that the second column square in that row is shaded in, so that limits our possibilities for which boxes can be shaded in that row.  In fact, there’s only one square available to the left of the second column, so we know there’s only two orientations for that block of squares: either its right up against the edge, or it starts in the second column.  Either way, the third column and fourth column would both have to be shaded.

 

Nonograms are a lot of fun and I encourage you all to try them!  There is a link below to online nonogram puzzles.  Happy puzzling!

http://www.nonograms.org/nonograms/size/small

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Sources:

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/pic-a-pix/history

 

My roommate’s best friend Bryce doesn’t appreciate nonograms.  People are always asking him, “Bryce, why don’t you like nonograms?” and he says, “If they can’t all be pictures of clowns, then what’s the point?”

We’ve now arrived at my favorite Japanese logic puzzle, Kakuro.  Like Sudoku, Kakuro is not Japanese in origin.  Dell Puzzles in America is credited with the first Kakuro puzzles in the 1960’s, which they called Cross Sums.  While Cross Sums were somewhat popular in America, they didn’t truly catch on until the Japanese puzzle company Nikoli rebranded Cross Sums as Kakuro in the 1980’s and its popularity exploded in Japan.  Today Kakuro’s popularity in Japan is second only to Sudoku, and while it is not as popular in America, it is one of the more well-known Japanese logic puzzles.

The rules of Kakuro combine Sudoku with arithmetic.  Black boxes, much as in crosswords, separate rows and columns into smaller subrows, or sub columns.  Like Sudoku, it uses only the numbers 1 through 9, and numbers cannot be repeated in subrows or sub columns.  You might notice that the black boxes are sometimes separated by diagonal lines.  The numbers in a subrow must add up to the number above the diagonal in the black box on left of the subrow; the numbers in a sub column must add up to the number below the diagonal in the black box on top of the sub column.

Unique number combinations are very important in Kakuro.  Consider the number 4 over 2 squares: the only combination permitted in Kakuro would be 1 and 3, since 2 and 2 would be repeating a number.  In the bottom righthand corner of the puzzle in Figure 1, for instance, we know that a 1 must go in the bottom, righthand-most box since the column has to add up to 3 (with the unique combination 1 and 2) and the row has to add up to 4 (with the unique combination 1 and 3).

The single digit rule is also very important.  Consider the square below the 5 in the rightmost column of Figure 1, in the same row with the 13.  Now, 5 can be either 2 and 3 or 1 and 4, but whatever goes in the square also has to work with 13.  If we put 1, 2, or 3 in that box, we would have to put a double-digit number in the other box to make 13.  Thus only a 4 can go there.

One last trick is to consider the minimum and maximum numbers that can be made over a series of squares.  For instance, the highest number we can make over 4 squares is 30 (9 + 8 + 7 + 6).  If we’re trying to make the number 33 over 5 squares, we know we can’t use 2 or 1, because then we would have to be able to make 32 or 31 over 4 squares.  Minimums works in a similar way: if we’re trying to make 11 over 3 squares, we can’t use 9, because then we’d have to make 2 over 2 squares, which is impossible.  The smallest number we can make over 2 squares is 3 (1 + 2).

Kakuro is much more complex than Sudoku, and, if I may say so, much more interesting.  I hope you will give it a try.  Below is a link to online puzzles.  Happy puzzling!

http://www.kakuroconquest.com

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Sources:

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/kakuro/history

 

My roommate’s best friend Bryce enjoys Kakuro on a daily basis.  People are always asking him, “Bryce, why do you love Kakuro so much?” and he says, “Oh, I don’t know, I’m just clowning around.”

 

 

 

 

 

 

 

 

Hashi, short for hashi o kakero (“build bridges”) is another logic puzzle invented by the Japanese puzzle company Nikoli. It first appeared in Nikoli’s magazine in December of 1989.  Like Sudoku, it is simple in construct, but can be very difficult to solve. There is no standard size for hashi, but typically the larger the puzzle, the trickier it is. The puzzle starts out with just the “islands” – numbers from 1 to 8 enclosed in little circles. The objective of hashi is to draw bridges to connect all the islands to one another following five rules:

1. A bridge is a straight line which connects two islands, and must emanate horizontally or vertically from an island (no diagonal lines allowed).

2. The number of bridges connected to an island must match the number on the island.

3. A pair of islands can be connected by one or two bridges, but not more. This is why the maximum number for an island is 8: there are four possible ports, which can each host two bridges.

4. Bridges cannot cross other bridges or islands.

5. All the islands have to be connected to each other in the end, through some series of bridges.

This may seem overwhelming, but considering the rules there are a few techniques that immediately present themselves as good starting places when doing this puzzle.

First, look for islands whose bridge placement possibilities are limited by their quantity of neighbors. For example, if an island only has one other island it can possibly connect to (see Figure 1), all of its bridges must connect to that island. Another instance might be if an island with 4 bridges is in the corner of the puzzle; then it must have two neighbors, with two bridges connecting it to each neighbor (Figure 2).  Finally, you might have a case where an island with 3 bridges has two neighbors (Figure 3).  In all the possibilities for bridge placement, you must have at least one bridge between the 3 island and each of its neighbors.

 

 

 

 

 

 

Next, look for cases which might violate the rule that all the islands must be connected.  For instance, if two 1 islands are next to one another, they cannot be connected without cutting them off from the rest of islands (Figure 4).  This can help cut down on bridge placement options.  In Figure 4, the 1 island must connect to island A since that’s its only other neighbor.

 

 

 

 

 

These are the basics to solving hashi puzzles.  They can be tricky to get the hang of, but with a little practice, one can start picking out the patterns pretty quickly.  I first learned of hashi puzzles through Games magazine, which was a monthly puzzle magazine.  Some of the puzzles cycled in and out of the magazine, but hashi appeared in almost every issue, and I was quickly addicted.  There is a great sense of completion in connecting the scattered islands, which, at first glance, seem patternless.  Below is a link to a website with free printable hashi puzzles.  Happy puzzling!

http://www.websudoku.com/?hashi

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Sources:

http://www.conceptispuzzles.com/index.aspx?uri=puzzle/hashi/rules

 

 

The creation of Sudoku was truly an international effort. Its origins date back to ancient China, two thousand years ago, with the creation of magic square puzzles. Magic squares were grid puzzles in which all the rows and columns had to add up to the same number, with no numbers being repeated in the grid. During the 19^th century the French began printing magic square puzzles in the newspapers, only giving the reader a few of the digits so he or she could fill in the rest. One paper in particular, Le Siècle, made a puzzle that was 9×9, composed of 3×3 smaller squares (much like Sudoku), in which all the rows and columns of the smaller squares, as well as of the larger 9×9 square, had to add up the same number. This puzzle, however, allowed double-digit numbers, which are not permitted in Sudoku. A rival paper, Le France, eliminated the smaller 3×3 sub-squares, but added the constraint that each row and column had to have the digits 1-9.

These puzzles largely disappeared after World War I, only to be revitalized in 1979 by Howard Garns in America for Dell magazines. Garns created a puzzle called Number Place, which is essentially modern-day Sudoku. Number Place did not catch on America, but it did end becoming very popular in Japan. The puzzle company Nikoli is credited with being the first to print Sudoku in Japan, adding two final touches to the puzzle: each puzzle would start out with at most 32 digits already printed, and those digits would be printed in a rotationally symmetrical pattern (much like crosswords). Nikoli also gave Sudoku its name, which literally translates to “single number,” which comes from the rule that Sudoku only uses single-digit numbers.

Then, in 1997, a man named Wayne Gould discovered Sudoku and had in printed in a British newspaper called The Times, right next to the crosswords. Sudoku was an instant success in Britain, spreading rapidly to other newspapers, magazines, and even TV guides. American newspapers began printing Sudoku in 2004, and soon after the rest of the world was swept up in Sudoku. British channels launched live Sudoku game shows in 2005, and in 2006 the first World Sudoku Championship was held in Italy. Since then the World Championships have been held in countries such as Czech Republic, India, Slovakia, China, Croatia, Bulgaria, and the US. Historically, top contenders in these championships have been teams from Germany, the US, China, Poland, and Japan. Thus Sudoku is a worldwide phenomenon.

For those unfamiliar with Sudoku, it consists of a 9×9 grid, with 9 3×3 sub-squares, with some boxes already containing digits. The objective is to fill in the rest of the boxes so that each sub-square, row, and column has the digits 1-9. Common tactics involve focusing on specific sub-squares, rows, and columns and eliminating possible positions for each number 1-9. There are lots (LOTS) of variants of Sudoku, with additional rules or alternative grid sizes, but this original version is still the one that most people love best. Below is a link to a sudoku website to get you started! Happy puzzling!

http://wpc.puzzles.com/sudoku/

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Sources:

http://www.sudokudragon.com/sudokuhistory.htm

http://wpc.puzzles.com/history/index.htm

 

My roommate’s best friend Bryce feels nothing but disdain for Sudoku.  People are always asking him, “Bryce, why didn’t you attend the World Sudoku Championship this year?” and he says, “Sorry, but it’s two weeks before the International Clown Conference Conglomeration and I don’t have time for that silliness.”

Until 2005, Americans were not terribly interested in number puzzles. That was the year sudoku took the nation and the rest of the world by storm, much to everyone’s surprise. Sudoku puzzles quickly started appearing in newspapers, radio program guides, and on television. In 2005 the first live TV competitive Sudoku show came out, called Sudoku Live, and in 2006 the first World Sudoku Championship was held in Lucca, Italy.

This simple logic puzzle was just one of many that Japan was creating at the time. Its main producer was Nikoli, a publishing company that produced puzzle magazines and books, run by Maki Kaji. Nikoli has created more than 250 puzzles, among them sudoku, through “a kind of democratization of puzzle invention” according to Mr. Kaji. Nikoli uses its magazines as a way of testing new puzzles; its main magazine has about 50,000 readers, any of whom can send in ideas which then may be printed in the next issue. Nikoli encourages its readers to send in feedback on its puzzles so that it may improve them. The result has been puzzles such as sudoku, kakuro, hashi, and nurikabe, to name a few.

Interestingly enough, the foundations of some of the more popular puzzles, such as sudoku and kakuro, came from Europe or America, but just never caught on. Word puzzles, particularly crosswords, have always been much more popular than number puzzles in America, whereas the complexity of the Japanese language (not to mention there are three writing systems) never lent itself well to word puzzles, and so number puzzles have always dominated in Japan.

In fact, this interest in mathematical puzzles can be dated back to 1603, the beginning of the Edo period. For 250 years Japan closed its borders and attempted to seal itself off the rest of the world’s “corrupting” influence. During this time Japanese culture flourished and education became very important for people of all social classes, even peasants. People would create sangaku, which literally translates to “mathematical tablet,” which would depict some geometrical problem, and leave them in shrines for others to solve. It was considered a tribute to the gods to create or solve one of these puzzles. The first book of mathematical puzzles in Japan was also published during this time in 1634. Thus an interest in number puzzles is deeply rooted in Japanese culture and history.

The purpose of this blog will be to hopefully give the reader a new appreciation for (and techniques for solving!) some of the more popular logic puzzles coming out of Japan today. Some of these puzzles, such as sudoku and kakuro, have grown out of the refining of other, lesser-known puzzles, whereas others such as nonograms, hashi, and nurikabe are very new. Each has varying popularity in the rest of the world and many different names, depending on how that puzzle was released in a particular country.  Yet however different they may seem, they are all simple in concept and (potentially) devilishly complex in execution.  Happy puzzling, dear reader; many fiendish challenges await you!

 

Sources:

http: //www.nytimes.com/2007/03/21/business/worldbusiness/21sudoku.html?_r=0#addenda

http://kknop.com/math/sangaku.pdf

 

My roommate’s best friend Bryce is an employee for the Japanese puzzle company Nikoli.  People are always asking him, “Bryce, what made you apply to that company in the first place?” and he says, “Actually, I thought I was applying to work at Nikoli “Creme de la Clown” Clownrich the Third’s company, because I have always greatly admired him and wanted to work with him.  His grandfather, Nikoli “Clown” Clownrich the First established the first Clown Academy and his work has essentially defined the modern clown.  His father Nikoli “Cream of Clown” Clownrich the Second was an international sensation and received a Nobel Peace Prize for being the clown who finally settled the dispute between Israel and Palestine.  I have every book they’ve ever published and every night I go over Cream of Clown’s clown parables and try to live my life by them.  I can say without a doubt that they have guided me through my darkest times and I would be a completely different man without them.  It was my life’s dream to work at his company.

 

But this is okay too.”