Nonograms, also known as Hanjie, Paint by Numbers, Griddlers, Pic-a-Pix, and Picross, are picture logic puzzles in which cells in a grid must be colored or left blank according to numbers at the edges of the grid to reveal a hidden picture. In this puzzle, the numbers are a form of discrete tomography that measures how many unbroken lines of filled-in squares there are in any given row or column. For example, a clue of "4 8 3" would mean there are sets of four, eight, and three filled squares, in that order, with at least one blank square between successive sets.
These puzzles are often black and white — describing a binary image — but they can also be colored. If colored, the number clues are also colored to indicate the color of the squares. Two differently colored numbers may or may not have a space in between them. For example, a black four followed by a red two could mean four black boxes, some empty spaces, and two red boxes, or it could simply mean four black boxes followed immediately by two red ones. Nonograms have no theoretical limits on size, and are not restricted to square layouts.
Nonograms were named after Non Ishida, one of the two inventors of the puzzle.
History In 1987, Non Ishida, a Japanese graphics editor, won a competition in Tokyo by designing grid pictures using skyscraper lights that were turned on or off. This led her to the idea of a puzzle based around filling in certain squares in a grid. Coincidentally, a professional Japanese puzzler named Tetsuya Nishio invented the same puzzles independently, and published them in another magazine. At this time, nonograms were also called picture-forming logic puzzles.
In 1988, Non Ishida published three picture grid puzzles in Japan under the name of "Window Art Puzzles". Ishida showed her puzzles to James Dalgety, a puzzle collector in the United Kingdom, who liked the puzzles and offered to help publish her work worldwide. Dalgety coined the name "nonogram" as a mashup of "Non" from their creator's name, and "gram" from the word "diagram".
Print publishing Dalgety made a deal with The Sunday Telegraph to publish Ishida's nonograms on a weekly basis starting in 1990. By 1993, the first book of nonograms was published by Non Ishida in Japan. The Sunday Telegraph published a dedicated puzzle book titled the "Book of Nonograms". Nonograms were also published in Sweden, the United States (originally by Games magazine), South Africa and other countries. The Sunday Telegraph ran a competition in 1998 to choose a new name for their puzzles. "Griddlers" was the winning name that readers chose. In 1993, Ishida published the "Book of Nonograms".
Electronic puzzles Nonogram puzzles were implemented by 1995 on hand-held electronic toys such as Game Boy and on other plastic puzzle toys. Nintendo picked up on this puzzle fad, claiming the trademark for the name Picross (short for "picture crossword") for their own use, and released two nonogram titles for the Game Boy and nine for the Super Famicom (eight of which were released in two-month intervals for the Nintendo Power Super Famicom Cartridge Writer as the NP series) in Japan. Only one of these, Mario's Picross for the Game Boy, was released outside Japan. Nintendo's Picross titles are primarily developed by Jupiter Corporation, who also released Picross DS on the Nintendo DS, nine titles in the Picross e series for the Nintendo 3DS, and nine titles in the Picross S series for the Nintendo Switch. They have also produced several Picross titles featuring licensed properties, including Pokémon, Sanrio characters, and Doraemon.
Increased popularity in Japan launched new publishers, and by then, there were several monthly magazines, some of which contained up to 100 puzzles. The Japanese arcade game Logic Pro was released by Deniam Corp in 1996, with a sequel released the following year. UK games developer Jagex released a nonogram puzzle in 2011 as part of their annual Halloween event for their role-playing game, Runescape. In 2013, Casual Labs released a mobile version of these puzzles called Paint it Back with the theme of restoring an art gallery. Released early in 2017, Pictopix has been presented as a worthy heir to Picross on PC by Rock, Paper, Shotgun. In particular, the game enables players to share their creations.
Today Nonograms have been published by Sanoma Uitgevers in the Netherlands, Puzzler Media (formerly British European Associated Publishers) in the UK and Nikui Rosh Puzzles in Israel. Magazines with nonogram puzzles are published in the US, UK, Germany, Netherlands, Italy, Hungary, Finland, the Czech Republic, Slovakia, Russia, Ukraine, and many other countries.
Numerous names have been developed for these puzzles, typically from names given by various publications or from computer programs that offer these puzzles. Including Griddlers, such names include CrossPix, Descarte's Enigma, FigurePic, IllustLogic, Oekaki-Logic, Paint by Numbers, PictureLogic, and StarPic. Although the name is trademarked by Nintendo, Picross has also been used to refer to nonogram puzzles.
Example + Empty nonogram 2 2 0 9 9 2 2 4 4 0 0 4 6 2 2 2 2 6 4 2 2 2 0 + Solved nonogram 2 2 0 9 9 2 2 4 4 0 0 4 6 2 2 2 2 6 4 2 2 2 0
Solution techniques
To solve a puzzle, one needs to determine which cells will be boxes and which will be empty. Solvers often use a dot or a cross to mark cells they are certain are spaces. Cells that can be determined by logic should be filled. If guessing is used, a single error can spread over the entire field and completely ruin the solution. An error sometimes comes to the surface only after a while, when it is very difficult to correct the puzzle. The hidden picture may help locate and eliminate an error, but otherwise it plays little part in the solving process, as it may mislead.
Many nonograms can be solved through line-by-line reasoning, analyzing one row or column at a time before moving to the next and repeating until the grid is complete. More difficult puzzles often require additional inference techniques, such as probing: tentatively assuming a value for an uncertain cell and checking whether it leads to a contradiction across more than one row or column. If a contradiction results, the opposite value can be deduced with certainty.
Simple boxes At the beginning of the solution, a simple method can be used to determine as many boxes as possible. This method uses conjunctions of possible places for each block of boxes. For example, in a row of ten cells with only one clue of 8, the bound block consisting of 8 boxes could spread from
the right border, leaving two spaces to the left; the left border, leaving two spaces to the right; or somewhere in between. As a result, the block must spread through the six centermost cells in the row.
The same applies when there are more clues in the row. For example, in a row of ten cells with clues of 4 and 3, the bound blocks of boxes could be
crowded to the left, one next to the other, leaving two spaces to the right; crowded to the right, one just next to the other, leaving two spaces to the left; or somewhere between. Consequently, the first block of four boxes definitely includes the third and fourth cells, while the second block of three boxes definitely includes the eighth cell. Boxes can therefore be placed in the third, fourth and eighth cells. When determining boxes in this way, boxes can be placed in cells only when the same block overlaps; in this example, there is overlap in the sixth cell, but it is from different blocks, and so it cannot yet be said whether or not the sixth cell will contain a box.
Simple spaces This method consists of determining spaces by searching for cells that are out of range of any possible blocks of boxes. For example, considering a row of ten cells with boxes in the fourth and ninth cell and with clues of 3 and 1, the block bound to the clue 3 will spread through the fourth cell and clue 1 will be at the ninth cell.
First, the clue 1 is complete and there will be a space at each side of the bound block.
Second, the clue 3 can only spread somewhere between the second cell and the sixth cell, because it always has to include the fourth cell; however, this may leave cells that may not be boxes in any case, i.e. the first and the seventh.
Note: In this example, all blocks are accounted for; this is not always the case. The player must be careful for there may be clues or blocks that are not bound to each other yet.
Forcing In this method, the significance of the spaces will be shown. A space placed somewhere in the middle of an uncompleted row may force a large block to one side or the other. Also, a gap that is too small for any possible block may be filled with spaces.
For example, considering a row of ten cells with spaces in the fifth and seventh cells and with clues of 3 and 2: the clue of 3 would be forced to the left, because it could not fit anywhere else. the empty gap on the sixth cell is too small to accommodate clues like 2 or 3 and may be filled with a space. finally, the clue of 2 will spread through the ninth cell according to method Simple Boxes above.
Glue Sometimes, there is a box near the border that is not farther from the border than the length of the first clue. In this case, the first clue will spread through that box and will be forced outward from the border. In the simplest case, whenever a box is present in the first or last cells of a row or column, the first or last clue must be aligned to the edge of that row or column.
Considering a row of ten cells with a box in the third cell and with a clue of 5, the clue of 5 will always span from the third to the fifth cell (but not necessarily to the second or the sixth). It is therefore possible to mark the third, fourth and fifth cell as belonging to the 5.
Note: This method may also work in the middle of a row, farther away from the borders.
A space may act as a border, if the first clue is forced to the right of that space. The first clue may also be preceded by some other clues, if all the clues are already bound to the left of the forcing space.
Joining and splitting Boxes closer to each other may be sometimes joined together into one block or split by a space into several blocks. When there are two blocks with an empty cell between, this cell will be: A space if joining the two blocks by a box would produce a too large block A box if splitting the two blocks by a space would produce a too small block that does not have enough free cells remaining
For example, considering a row of fifteen cells with boxes in the third, fourth, sixth, seventh, eleventh and thirteenth cell and with clues of 5, 2 and 2:
The clue of 5 will join the first two blocks by a box into one large block, because a space would produce a block of only 4 boxes that is not enough there. The clues of 2 will split the last two blocks by a space, because a box would produce a block of 3 continuous boxes, which is not allowed there. Note: The illustration picture also shows how the clues of 2 are further completed. This is, however, not part of the Joining and splitting technique, but the Glue technique described above.
Punctuating To solve the puzzle, it is usually also very important to enclose each bound or completed block of boxes immediately by separating spaces as described in Simple spaces method. Precise punctuating usually leads to more Forcing and may be vital for finishing the puzzle. Note: The examples above did not do that only to remain simple.
Mercury Mercury is a special case of Simple spaces technique. Its name comes from the way mercury pulls back from the sides of a container.