On five Saturdays per year, the Times newspaper in London publishes a crossword which most people pass over without a second glance, but which is quite one of the most extraordinary things every created for human satisfaction. As you can imagine there is some stiff competition.

If they are regular readers they will be aware that where crosswords and other puzzles are concerned, there is a kind of hierarchy at work. Languishing at the bottom, but cheery and welcoming, is the ‘concise’, the simplest kind of crossword there is. The clues are all definitions of words, and all you have to do is work out the words themselves, and slot them into the grid so that they intersect pleasingly. If they don’t intersect, you know you’ve got it wrong. This is not very hard, and the only difference between the Times’ version and those once bought to amuse eight year olds on long journeys is the breadth of vocabulary required.

Alongside this, for the more numerically minded, since about 2005, there is the Su Doku, a grid divided into nine boxes of nine boxes, into which some of the numerals have been entered, the arrangement, abundance, and variety of the numerals mystically determining the difficulty of the puzzle, called variously ‘easy’, ‘hard’, ‘fiendish’ and ‘super-fiendish’. I’ve not yet seen one called ‘Satan, Lord of Darkness’ but I guess it’s out there. You have to complete the grid so that each of the digits 1 to 9 appears exactly once in each block, row and column.

Super-fiendish or not, the Su Doku requires essentially the same techniques, and those who have a prodigious memory for what number can’t go where, can complete them in, I would imagine, boringly quick time. The rest of us mortals either have to scribble possible answers very small in the corners of the squares, or more likely, go off and do something slightly less pointless. Completing a SuDoku of any difficulty always leaves me without the brief sense of satisfaction I get doing a crossword, and thinking instead that I really shouldn’t have bothered. I call this the inverse Mallory effect. Just because it was there doesn’t mean I had to do it.

Returning to word crosswords, the Times Cryptic Crossword is the prince of crosswords, infamous for its mischief. No other language or nation has anything quite like it. Solvers need a huge sense of the ambiguous as words like ‘flower’, for example, can be required to be interpreted as the name of a river, because a river flows and is hence a ‘flower’, a correspondingly vast vocabulary and awareness of usage, a knowledge of all kinds of abbreviations, including roman numerals, initials and the like, then tricks like reversing parts of the word, extracting the boundaries, centres, or, in extreme cases, alternate letters of clue words, and above all, they need a master at whose feet they can learn. Mercifully, the Times has recently begun to include a Quick Cryptic. These are the less subtle puzzles of the same sort that experienced solvers can do before the kettle boils, but which serve as the real deal for those still fledgling in the art.

This, however, is all still straightforward stuff in the crossword world. This is where the Listener crossword comes in, so called because it is a refugee of the erstwhile BBC magazine of the same name, and was rescued by the Times when that organ folded back in the 80s, along with the death of Mary Whitehouse. The most striking thing about it is usually its extraordinary grid. Unlike usual ones which have some boxes black, every square of the listener crossword is to be filled, leading to an extraordinary amount of intersection, or ‘checking’ as it is technically called. A checked square is one which belongs in the word of at least two clues. This ought to make it easier, but there is usually a particularly sharp sting in the construction of the puzzle, conveyed in a blurb. Something like ‘a letter is to be omitted from each of the correct solutions prior to entry onto the grid, and entered at the bottom to give a thematically relevant word’ or ‘each clue contains a misprint in the definition part only’. Given my limited capacity to do the normal cryptic, these are all well outside my ability.

On those five Saturdays, however, there is a difference. A similar looking grid (or two sometimes) will appear, but readers will search in vain for any proper words as clues. Instead, the clues will be strings of letters, or will look disturbingly (for many) like algebraic expressions. The degree of ingenuity in these is extraordinary. No two puzzles have ever seemed (to me at least) to be even of the same style, and certainly there is no single approach to tackling them, except in the most abstract sense. They are accompanied by a paragraph of explanation which describes, in the most remarkably succinct manner, what the hell the puzzle is about. It usually takes about three reads of the paragraph even to understand what the clues mean. Then there follows about ten minutes of saying ‘Oh, I really don’t think I can do this one. I mean, I just can’t get started. I mean, they could be anything, I mean….’

If you’re lucky, these ten minutes will pass, you will put the puzzle aside, and then you will forget about it. However, all too often, in my own experience, there comes a moment when you suddenly think you can see a way in. Just one of the clues, you suddenly realise, has only one possible answer. Sometimes this actually enables you to put an entry onto the grid, but more likely it just enables you to come to a conclusion about what one of the values if the letters is.

For me, that’s it. Once I’ve started, I tend to get dragged in. If it’s Christmas, or during one of my many holidays, that will be me locked in a room for as long as it takes – and to my shame it can take a very long time. The trouble is I just can’t put the damn thing down.

Turn the page. Turn the page.