Puzzle Addiction

Every week, though not every day, I buy a few newspapers, mainly for the puzzles rather than the news. On Friday for instance the Guardian has a sudoku and kakuro that are usually a bit harder than during the week. The Guardian on Saturday always has a good prize crossword, often by Araucaria, but I don't always buy it because it has far too many sections, on subjects such as sport, travel, finance, fashion and so on, that I'm not really interested in.

I also tend to get the Times once or twice a week, mainly for the crossword and the killer sudoku. However this week the Times has started to include a four-page puzzle section every day! This will mean that I have to avoid buying the Times in future, because once I start on the puzzles I have the compulsion to solve them all, and waste most of the day when I should be doing something productive. Why they have changed to this new scheme I don't know, I thought their previous policy was just the right balance.

The Attraction of Puzzles

I enjoy doing the puzzles in the newspapers I buy, both the numerical ones like Sudoku or Kakuro or the letter ones like Crosswords or the Code type where numbers stand for letters, though the latter aren't usually very tricky. In fact the puzzles provide the main reason that I buy papers at all these days.

By far and away my favourite crosswords are those composed hy Araucaria in the Guardian. Unfortunately the other composers in the Guardian never seem to reach the same standard. Not only are his clues always fair, so that once you have found a solution you can tell with reasonable certainty that you have found the correct solution, but he also covers a wide range of knowledge (which is often exhibited in themed puzzles) and is also often humorous.

It is annoying however when puzzles are misprinted, or mistakenly set, so that they have no solution or more than one. I wrote to the Radio Times last week to complain that in two recent issues their Mandali puzzle, which is a sort of maze, had two numerical solutions. They were kind enough to reply and apologise. Unfortunately the Mandali puzzle in this week's issue has at least six solutions! This is just carelessness.

The attraction I find in puzzles I think has to do with the fact that they are soluble problems. There are too many problems in real life that are insoluble and simply frustrating. The only viable approach to them I have concluded is step by step and little by little, and maybe a little amelioration can be achieved.

Euler and Me

As noted before I'm in process of tidying up my notes on knight's tours. One of the sections I've not previously published, as far as I recall, concerns the enumeration of all the smallest knight-tourable boards, at least up to 12 cells. The illustration shows all the centrosymmetric tours on boards of 12 cells.

The first two of these diagrams are not merely centrosymmetric, in the sense of being unchanged by a 180 degree rotation, but are also axially symmetric about the two diagonal axes. The first of these was published by the famous mathematician Leonhard Euler in what waa probably the first scientific paper on knight's tours, presented in 1759. The second is one of my own favourite discoveries, it is the 12-cell tour whose containing rectangle is the largest possible, the 6 by 6 square.