Nonotext

Nonotext, also known as Nonograms, Picross, Griddlers, Pic-a-Pix, and 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 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. 4 8 3 ⊙...⊙▣▣▣▣⊙...⊙▣▣▣▣▣▣▣▣⊙...⊙▣▣▣⊙...⊙ 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; 8 ▧▧▧▧▧▧▧▧⊙⊙ the left border, leaving two spaces to the right; 8 ⊙⊙▧▧▧▧▧▧▧▧ or somewhere in between. As a result, the block must spread through the six centermost cells in the row. 8 ⊙⊙▣▣▣▣▣▣⊙⊙ 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. 3 1 ⊙⊙⊙▣⊙⊙⊙⊙▣⊙ First, the clue 1 is complete and there will be a space at each side of the bound block. 3 1 ⊙▧▧▣⊙⊙⊙⊙▣⊙ 3 1 ⊙⊙⊙▣▧▧⊙⊙▣⊙ 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. 3 1 ☒⊙⊙▣⊙⊙☒☒▣☒ 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. 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: 5 2 2 ⊙⊙▣▣⊙▣▣⊙⊙⊙▣⊙▣⊙⊙ 5 2 2 ⊙⊙▣▣⊙▣▣⊙⊙⊙▣☒▣⊙⊙ 5 2 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.