The Path to Fill-a-PixTuesday, February 4, 2003
In the late 1970s I began contributing games and then puzzles to Games & Puzzles Magazine and then became puzzles editor. Among my quota of ten new puzzles a month were a few based on the idea of a cell and its neighbors.
These were not picture puzzles but brainteasers. Usually, from some information in a grid, the solver had to fill in the next line. Often the puzzle depended on looking at the two or three neighbours of a square that were directly above it or of looking at the neighbours all around a square.
This probably arose from my interest in one of John Horton Conway's mathematical recreation, known as the Game of Life, which used the concept of considering a cell and its neighbours to determine which cells 'lived' and 'died' over several generations. The most popular articles on the subject were by Martin Gardner in books based on his Scientific American articles (for additional information about the Game of Life see radicaleye.com/lifepage).
Later I came across a European puzzle where a group of touching circles had a number in each, from which you could deduce if a circle had to be filled or left empty. The result was not a picture and you could only tell if you were right by examining your answer, circle by circle, with the one given. The puzzles worked but they weren't fun.
I then came up with the idea of a grid of squares completely filled with numbers - from 0 to 9 - while each number tells you how many of its cell and its neighbours had something in them - but, having filled in the squares there had to be some result other than a random group of splodges. I called these puzzles "internal-referencing" to distinguish them from the cross-referencing puzzles (where the information is outside the grid) that I was also developing at that time, following an early creation - Whittleword.
Bang To Rights
Having virtually no ability to form mental pictures, only logical constructs, it's not surprising that I did not then consider brightening the idea up with picture puzzles. I stuck to squares and, to give a "purpose" to the puzzle - created maze-related concepts. The two main puzzles were Bog Hopping and Bang To Rights.
In Bog Hopping, each square either had a stepping-stone or was pure swamp. Every square was given a number, which told you how many stones there were in it and its neighbours. By logically finding the stones, you could see your way through the swamp. In Bang to Rights the grid became a minefield and the numbers let you work out where they were, and so find the unique safe path through the area. This was in the early 80's before we all had PC's with a free Minesweeper game and was a totally independent creation.
Picture puzzles, of a sort, eventually arose when I experimented with grids containing triangles and hexagons - Something that doesn't seem to work too well with Tsunami. Using triangles allowed the creation of perspective drawings and some oddball cartoon picture puzzles were made - including Snake Sliding Over a Razorblade! Eventually the penny dropped that Tsunami puzzles would work if the numbers were inside the grid and the neighbours' principle applied.
The problem for a hand-compiled puzzle as opposed to a computer-generated one is that it is extremely slow and tedious to make the solution unique and almost impossible to determine precisely how many squares need to have numbers in them. In early attempts such as Admirable Portrait, either every cell was given a number, or every second cell. After several attempts and changes a unique answer could be proved to exist, but the puzzle was weak in that it contained redundant information. In addition, it was simply uneconomic to spend so much time manually creating a relatively small product.
Thanks to Conceptis who have invested considerable expertise, both artistic and computing, time and, no doubt, a lot of dollars - the concept of Fill-a-Pix reached its full potential - a satisfying, picture-forming logic puzzle, with minimal information and maximum puzzling. Though the logic concepts required are not complicated and the puzzles can be created to have varying degrees of difficulty, Fill-a-Pix gives plenty of mental exercise within the framework of a small grid and a simple concept.
About the author
Trevor Truran is the editor of puzzle magazines published by Puzzler Media Ltd. UK (formally known as BEAP), and inventor of the Fill-a-Pix puzzle concept.