Paint by numbers
From Wikipedia, the free encyclopedia
- For the artistic activity, see Paint by number. For the album, see Paint by Number.
Paint by numbers are the first subset of picture logic puzzles, in which cells in a grid have to be colored or left blank according to numbers given at the side of the grid to reveal a hidden picture. In this puzzle type, the numbers measure 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 groups.
These puzzles are often black and white but can also have some colors. If they are colored, the number clues will also be colored in order 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 spaces, some empty spaces, and two red spaces, or it could simply mean four black spaces followed immediately by two red ones.
Another variant (the "triddler") uses a grid of equilateral triangles, with three banks of clues.
Contents |
[edit] Names
Paint by numbers are also known with many other names, including Crucipixel, Edel, FigurePic, Grafilogika, Griddlers, Hanjie, Illust-Logic, Japanese Crosswords, Japanese Puzzels, Kare Karala!, Logic Art, Logic Square, Logicolor, Logik-Puzzles, Logimage, Nonograms, Zakókodované obrázky, Maľované krížovky, Oekaki Logic, Oekaki-Mate, Paint Logic, Pic-a-Pix, Picross, Pixel Puzzles, Shchor Uftor and Tsunami. It has also been called Paint by Sudoku, although this name is technically inaccurate.
[edit] History
In 1987, Non Ishida, a Japanese graphics editor, won a competition in Tokyo by designing grid pictures using skyscraper lights which are turned on or off. At the same time and with no connection, a professional Japanese puzzler named Tetsuya Nishio invents the same puzzles. From this, the concept of Paint by numbers and picture-forming logic puzzles was born.
Paint by numbers puzzles started appearing in Japanese puzzle magazines. Nintendo picked up on this puzzle fad a while back 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 Picross" series) in Japan. Only one of these, Mario's Picross for the Game Boy, was released in the United States.
In 1988, Non Ishida published three picture grid puzzles 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.
In 1993, 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 are also published in Sweden, United States, South Africa and other countries.
In 1995, paint by numbers started appearing on hand held electronic toys such as Game Boy and on other plastic puzzle toys. Increased popularity in Japan launched new publishers and by now there were several monthly magazines some of which contain up to 100 puzzles.
In 1996, the Japanese arcade game Logic Pro was released by Deniam Corp, with a sequel released the following year. Both titles are emulated by MAME.
In 1998, The Sunday Telegraph ran a competition to choose a new name for their puzzles. Griddlers was the winning name that readers chose. Pic-a-Pix puzzles in Germany with PM Magazine, a wholly owned subsidiary of Gruner + Jahr AG the publishers of the famous Stern magazine.
In 1999, Paint by numbers were published by Sanoma Uitgevers in Holland, Puzzler Media (formerly British European Associated Publishers) in the UK and Nikui Rosh Puzzles in Israel.
Today, magazines with Paint by numbers puzzles are published in the USA, UK, Germany, Netherlands, Italy, Hungary, Finland and many other countries.
[edit] Solution techniques
In order to solve a puzzle, one needs to determine, which cells are going to be boxes and which are going to be empty. Determining, which cells are to be empty (called spaces), is as important as determining which are to be filled (called boxes). Later in the solving process, the spaces help to determine where a clue (continuing block of boxes and a number in the legend) may spread. Solvers usually use a dot or a cross to mark cells that are spaces for sure.
It is also important never to guess. Only cells that can be determined by logic should be filled. If guessing, a single error can spread over the entire field soon and completely ruin the solution. It usually comes to the surface only after a while, when it is very difficult to correct the puzzle. Only advanced and experienced solvers are usually able to fix it completely and finish such ruined puzzle.
The hidden picture plays no part in the solving process. Even if it is obvious from the picture that a cell will be a box, it is usually treacherous to rely on it. The picture, however, may help find and eliminate an error.
Simpler puzzles can usually be solved by a reasoning on a single row only (or a single column) at each given time, to determine as much boxes and spaces on that row as possible. Then trying another row (or column), until there are rows that contain undetermined cells.
Some 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: When a cell cannot be a box, because some other cell would produce an error, it will definitelly be a space. And vice versa. Advanced solvers are sometimes able to search even deeper than into the first "what if?" reasoning. It takes, however, a lot of time to get some progress.
[edit] 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;
- or it could spread from the left border, leaving two spaces to the right;
- or it could be somewhere between.
In result, the block will spread for sure through the conjunction in the middle.
The same of course 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 right, one just next to the other, leaving two spaces to the left;
- or be crowded to the left, one just next to the other, leaving two spaces to the right;
- or each block could be somewhere between.
In result, the first block of 4 boxes will spread for sure from the third to the fourth cell. The second block of 3 boxes will spread for sure through the eighth cell. Important note: While determining boxes from the conjuctions, you may not put a box to a cell, where one block overlaps another block. Only when the block overlaps itself from the other side.
[edit] Simple spaces
This method consist 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 till the sixth cell, because it always has to include the fourth cell. This, however, also leaves some cells, that may not be boxes in any case: the first cell and the seventh cell.
Note: In this example, all blocks are accounted for, which is not always the case. You have to be more careful, when there are clues or blocks that are not bound to each other yet.
[edit] Forcing
In this method, the significancy of the spaces will be shown. A space placed somewhere in the middle of an uncompleted row may force a large block to the one side or another. 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 cell 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 spaces.
- finally, the clue of 2 will spread through the ninth cell according to method Simple Boxes above.
[edit] Glue
Sometimes, there is a box near the border that is not further 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 to the right by the border.
For example, considering a row of ten cells with a box in 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.
Note: This method may also work in the middle of a row, further 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.
[edit] Joining and splitting
Boxes closer to each other may be sometimes joined together into one block or splitted 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;
- and will be a box, if splitting the two blocks by a space would result produce a too small block that does not have enough free cells around to spread through.
For example, considering a row of ten 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 4 boxes that is not allowed there;
- and the clues of 2 will split the last two blocks by a space, because a box would produce a block of 5 boxes, that is not allowed there.
[edit] Punctuating
To solve the puzzle, it is usually also very important to enclose each bound and/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.
[edit] Mercury
A method that is actually a special case of Simple spaces method is called Mercury. The name of the rule comes from the way mercury pulls back from the sides of a container.
If there is a box in a row that is in the same distance from the border as the length of the first clue, the first cell will be a space. This is because the first clue would not fit to the left of the box. It will have to spread through that box, leaving the first cell behind. Furthermore, when the box is actually a block of more boxes to the right, there will be more spaces at the beginning of the row, determined by using this method several times.
[edit] Contradictions
Some more difficult puzzles may also require advanced reasoning. When all simple methods above are not sufficient any more, searching for contradictions may help. It is wise to use a pencil (or other color) for that in order to be able to undo the last changes. The procedure includes:
- Trying an empty cell to be a box (or then a space).
- Using all available methods to solve as much as possible.
- When an error is found, the tried cell will not be the box for sure. It will be a space (or a box, if space was tried).
In this example a box is tried in the first row, which leads to a space at the beginning of that row. The space then forces a box in the first column, which glues to a block of three boxes in the fourth row. That is, however, wrong because the third column does not allow any boxes there, which leads to a conclusion that the tried cell may not be a box and it will be a space.
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. All other cells lead to dead ends, when a rubber takes place to clean all the just tried cells. Most worthy cells to start with may be cells that
- have many non-empty neighbours;
- cells that are close to the borders or close to the blocks of spaces;
- cells that are within rows that consist of more non-empty cells.
[edit] Deeper recursion
Some puzzles (one such is known as Old tree) 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 need to be searched.
[edit] Multiple solutions
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 give a reasonable picture.
[edit] Other picture logic puzzles
Paint by pairs or Link-a-Pix consists of a grid, with numbers filling some squares; pairs of numbers must be located correctly and connected with a line filling a total of squares equal to that number. When completed, the squares that have lines are filled; the contrast with the blank squares reveals the picture. (As above, colored versions exist with matching numbers of the same color.) Fill-a-Pix also uses a grid with numbers within; in this format, each number indicates how many of the squares immediately surrounding it, and itself, will be filled. A square marked '9', for example, will have all 8 surrounding squares, and itself, filled; if it is marked '0', those squares are all blank.
[edit] Mario's Picross
As noted above, the Game Boy saw its own version, entitled Mario's Picross (Mario no Picross in Japan). The game was initially released in Japan on March 14, 1995 to decent success. However, the game failed to become a hit in the U.S. market, despite a heavy ad campaign by Nintendo. The game is of an escalating difficulty, with successive puzzle levels containing larger puzzles. Hints (line clears) may be requested at a time penalty, and mistakes made earn time penalties as well (the amount increasing for each mistake). Each puzzle has a limited amount of time to be cleared. Mario's Picross 2 was released later for Game Boy and Mario's Super Picross for the Super Famicom, neither of which were translated for the U.S. market. Both games introduced Wario's Picross as well, featuring Mario's evil twin in the role. These rounds vary by removing the hint function, and mistakes are not penalized - at the price that mistakes are not even revealed. These rounds can only be cleared when all correct boxes are marked, with no mistakes. The time limit was also removed. Nintendo also released 8 Nintendo Power Picross volumes over the Japanese Satallaview system in Japan, each a new set of puzzles without the Mario characters.
[edit] External links
- Nonograms at the Open Directory Project
- NP-Completeness Results for Nonogram (PostScript) - Paint by numbers is NP-complete problem
- Nonogram Deluxe - Online nonogram game with 500+ puzzles
- Griddlers.net - 35000 online griddlers
- Griddlers Solver - Editor and advanced auto-solver that offers playing the solving process as an animation
- Nonogram introduction with examples
- Nonograms online
- conceptis - pic-a-pix, link-a-pix and fill-a-pix
- Online Paint By Numbers Solver
- Open-source Paint By Numbers Solver (windows application)
