Nonograms, also known as Hanjie, Paint by Numbers, Picross, Griddlers, and Pic-a-Pix, and by various other names, are picture logic puzzles in which cells in a grid must be colored or left blank according to numbers at the side of the grid to reveal a hidden pixel art-like picture. In this puzzle type, 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.
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 completely independently, and published them in another magazine.[1]
Joining the Cells and the Puzzles
Paint by numbers puzzles started appearing in Japanese puzzle magazines. Non Ishida published three picture grid puzzles in 1988 in Japan under the name of "Window Art Puzzles". In 1990, James Dalgety in the UK invented the name Nonograms after Non Ishida, and The Sunday Telegraph started publishing them on a weekly basis. 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[2]), 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.
Paint by numbers 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 and released two "Picross" (picture crossword) 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. Since then, one of the most prolific Picross game developers has been Jupiter Corporation, who released Picross DS on the Nintendo DS in 2007, 8 titles in the Picross e series for the Nintendo 3DS eShop (along with 5 character-specific titles, including ones featuring Pokémon, Zelda and Sanrio characters), and 7 titles in the Picross S series for the Nintendo Switch (along with two character-specific ones featuring Kemono Friends and Overlord respectively, and another featuring intellectual properties from SEGA's Master System and Genesis).
Increased popularity in Japan launched new publishers and by now 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.[3] In particular, the game enables players to share their creations.
Paint by numbers 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.
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 plays little or no part in the solving process, as it may mislead. The picture may help find and eliminate an error.
Many puzzles can be solved by reasoning on a single row or column at a time only, then trying another row or column, and repeating until the puzzle is complete. More difficult puzzles may also require several types of "what if?" reasoning that include more than one row (or column). This works on searching for contradictions, e.g., when a cell cannot be a box because some other cell would produce an error, it must be a space.
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
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.
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.
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.
For example, considering a row of ten cells with a box in the third cell and with a clue of 5, the clue of 5 will spread through the third cell and will continue to the fifth cell because of the border.
Some more difficult puzzles may also require advanced reasoning. When all simple methods above are exhausted, searching for contradictions may help. It is wise to use a pencil (or other color) for that to facilitate corrections. The procedure includes:
The problem of this method is that there is no quick way to tell which empty cell to try first. Usually only a few cells lead to any progress, and the other cells lead to dead ends. Most worthy cells to start with may be:
In the illustration, row 1 shows the cells that are filled under this procedure, rows 2 and 4 show how the blocks are pushed to one side in step 5, and rows 3 and 5 show the cells backfilled in step 5.
Using this technique for all rows and columns at the start of the puzzle produces a good head start into completing it. Note: Some rows/columns won't yield any results initially. For example, a row of 20 cells with a clue of 1 4 2 5 will yield 1 + 1 + 4 + 1 + 2 + 1 + 5 = 15. 20 - 15 = 5. None of the clues are greater than 5. Also, this technique can be used on a smaller scale. If there are available spaces in the center or either side, even if certain clues are already discovered, this method can be used with the remaining clues and available spaces.
Some puzzles may require to go deeper with searching for the contradictions. This is, however, not possible simply by a pen and pencil, because of the many possibilities that must be searched. This method is practical for a computer to use.
There are puzzles that have several feasible solutions (one such is a picture of a simple chessboard). In these puzzles, all solutions are correct by the definition, but not all must give a reasonable picture.
However, certain classes of puzzles, such as those in which each row or column has only one block of cells and all cells are connected, may be solved in polynomial time by transforming the problem into an instance of 2-satisfiability.[7]
Nintendo has released Picross DS for the Nintendo DS portable system in 2007. It contains several stages of varying difficulty, from 5x5 grids to 25x20 grids. Normal mode tells players if they made an error (with a time penalty) and free mode does not. A hint is available before starting the puzzle in all modes; the game reveals a complete row and column at random. Additional puzzles were available through Nintendo Wi-Fi Connection; some of the original Mario Picross puzzles were available. However, the service was shut down on 20 May 2014. Nintendo made new releases available bi-weekly. Picross DS was released in Europe and Australia on 11 May 2007 and in the United States on July 30, 2007 and has been received well by critics, including Craig Harris,[23] Jessica Wadleigh[24] and Dave McCarthy [25] labelling the game "Addictive".[26][27] A 3D version of the game, titled Picross 3D, was also released for the DS in Japan in 2009 and internationally in 2010. A sequel, Picross 3D: Round 2, was released for the Nintendo 3DS in 2015.[28] Another downloadable version of the game was released for Nintendo 3DS's Nintendo eShop, called Picross e, Picross e2, and Picross e3 released in 2013, with Picross e4 released in 2014. Nintendo has also released a Pokémon spinoff on December 7, 2015 in the form of the freemium game of Pokémon Picross for Nintendo 3DS. My Nintendo Picross The Legend of Zelda: Twilight Princess was released for Nintendo 3DS on March 31, 2016, exclusively as a premium reward for My Nintendo. 2ff7e9595c
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