Part III. Move It
DOI link for Part III. Move It
Part III. Move It book
In homage to Martin Gardner for his 90th birthday, I wish to describe a very simple idea that has been familiar to me for many, many years, but, strangely, I have never seen it discussed in any detail. This is the notion of a railway maze.1 As far as my own experience is concerned, the basic idea came from my father (Lionel S. Penrose, FRS, 1898-1972, who had been Professor of Human Genetics at University College, London, from 1945 until his retirement from the university), although this idea is such a simple one that I cannot imagine that it had not been originated long, long ago, in the shadows of antiquity. I was certainly a child when he first acquainted me with the idea, but I have no recollection of how old I was. The maze consists of a connected network of smooth curves drawn in the plane (though planarity plays no critical role here), branching and rejoining at various places. The object is to find a smooth path along the curves, from the starting point S to the final point F. We may think of a railway engine, with no reverse gear, travelling along the track from S to F. I recall, from a quite early age, my father showing a fairly simple example, perhaps like the one illustrated in Figure 1, which I found to be surprisingly tricky to do, considering its simplicity. Most routes return the en-
gine back to S, and it is a matter of “puzzle psychology,” in the design of such a maze, to try to guide the solver to take the wrong routes in attempting to progress from S to F.