<\/p>\n
After the recent discussions about Sudoku, Richard A. described to me another Japanese puzzle with a similar style. It goes under various names: Tsunami (perhaps an unfortunate name in 2005), Paint-by-Numbers (another unfortunate name), Nonograms and Griddlers, and more!<\/em> I am calling them nonograms, because it is the name I find least embarrassing.<\/p>\n The concept is kind of odd. There are various descriptions on the web<\/a>. Let me add my own description to the mix, using all of the computer jargon at my disposal.<\/p>\n Start with a small bitmap of a mystery icon – say 15×15. Using only a 1-bit bitmap is traditional, but not required. Use of limited colours is recommended. Use of white as one of those colours is mandatory.<\/p>\n For each row, summarise it with run-length encoding. That is, summarise sequences of pixels of the same colour with a description of the colour, and the number of pixels in a row of that colour. Do the same for each column.<\/p>\n Hide the pixels, but leave the encodings. So now you have an empty grid, and two sequences of encodings, each with a list of (colour, run-length) pairs, acting as clues. The puzzle will be to reconstruct the bitmap from the clues.<\/p>\n So far it is easy. You have enough information to reconstruct the bitmap perfectly. In fact, you have redundancy; there is twice as much data as you need. You could encode it with the row clues alone or with the column clues alone.<\/p>\n So, here is the sneaky part that makes it a challenging puzzle: Remove from your two lists all of the encodings describing runs of white squares. <\/p>\n The result is two partial descriptions<\/em> of the picture, from which (hopefully) you can still reconstruct the bitmap with a little bit of logic.<\/p>\n Like Sudoku, there is a lot of elimination. There is very little arithmetic involved (although there is some<\/em>, unlike Sudoku.)<\/p>\n This description may not be satisfying, so here are some reference sites with online versions of it to get a feel for it. <\/p>\n\n