It’s 11 am Saturday and I’ve all but finished yesterday’s Listener puzzle, which is called “Sine Qua Non”. It has one of the most bewildering preambles I remember seeing in a Listener puzzle:

Most clues contain a misprint of one letter in the definition. The correct letters, in clue order, reveal hints for deriving two versions of a question from the remaining clues. The penultimate element of the first version is one of four that share identical components, as described by a five-letter definition concealed in the grid. These four elements and another five-letter word must be highlighted to show key information relating to the question and an initial representation of the questioner.

One of the four elements, interpreted differently, indicates which letter of which word in each non-misprint clue contributes to another message. The action it describes must be applied to the letters of the five-letter definition (and their counterparts) to reveal a representation of that element which must be highlighted in full. Finally, the key information must be modified to provide a consistent rendition. All entries are words in both the initial and final grids.

However, as I solved the puzzle, the instructions became clear, little by little. I have filled in the grid, found the two versions of the question, found the five-letter definition (which is a new word to me, and a surprising one, both because of its odd meaning and because of the way it ties in with the rest of the puzzle), found the four elements, found the key information, found the second message in the clues, and applied the second message to the five-letter definition to reveal the representation of the element.

The only thing left is to figure out how to alter the key information to “provide a consistent rendition”. A difficulty here is that there seem to be quite a few plausible choices for what I should alter this information to, and fully 11 of them will lead to valid entries in the grid after the alteration.

One of those possibilities sort of leaps out as being an obvious choice, but that’s based on the, um, representation of the element rather than on the phrase “consistent rendition”. I haven’t figured out how to interpret that phrase yet, and until I do I can’t be sure that the obvious choice is the right choice.

Very ingenious puzzle.

I finished the new Listener puzzle, “The Fragmentation of Reality”, this morning. I found it very tough to break into; when I started on it yesterday I must have stared at the clues for 15 minutes or more before I finally figured one out. This morning, though, I figured out the name and one of the two titles that have to be found in the completed grid, and once I had that the rest fell very quickly. The way that the puzzle’s title and the first line of the instructions — “Having solved the clues, solvers must choose between 65,536 possible solution grids” — fit in with the theme is very funny! Nice puzzle.

I’ve had the latest Listener puzzle for about 24 hours now, and I have one empty square left. (The middle square of 32 down. It’s three letters long, and I have the first and last letters from the crossing words, but the middle letter is unchecked.)

The puzzle is called “Forced Entry”. It’s an unusually straightforward puzzle, for the Listener anyway. There’s a gimmick in the clues that makes them more difficult to solve, but no secret theme to be discovered or anything like that.

I like the straightforwardness, but the gimmick seems a bit fussy. The wordplay portion of the clue includes an extra letter that indicates how many spaces in the alphabet forward or backward you have to change one of the letters in the answer to the clue to get the word you enter into the grid. It’s a bit dull to do the figuring and it doesn’t seem to add anything to the puzzle. I think I would have liked the puzzle better if the gimmick were made even simpler and you just had to change one letter of the answer to form a different word before entering it into the grid.

Curiously, a gimmick of this sort means that a few crossing letters are actually more helpful in solving the long entries than they are in solving the short ones. I don’t want to give away anything in the puzzle, so I’ll make up an example. Let’s say you have two crossing letters in a nine-letter word, like P---C----. There’s a chance that one of these is the changed letter, of course, but there’s a better than even chance that neither of them is, and in that case you’re looking for a pair of words that fit that pattern and are different by only one letter. So if you do a search for nine-letter words with P and C in those positions, and you run your eye down the list looking for words that are one letter away from other words, then when you see PRESCRIBE or PROSCRIBE it’ll jump out at you. Then it’s not hard to see whether the clue contains anything that looks like a definition of either word, and if it does then you know the other one is what goes into the grid. Because there are going to be very few other possibilities, if any, for a word of this length, chances are good that the first word you come across that jumps out at you like this is going to be part of the right answer. All this without having to consider the clue, which in this puzzle is not a normal cryptic clue. The clues in this puzzle, in fact, can be tricky to figure out even after you know what the answer should be, so being able to narrow the possibilities way down with two or three crossing letters is a very big help.

Whereas, say you have the same two crossing letters in the three-letter entry C-P. The middle letter is unchecked, so this time either the C or the P definitely is the changed letter. (The rules of the puzzle state, very sensibly, that the changed letter will always be checked by a crossing word.) The word in the grid could be CAP, COP, or CUP. Because this is the Listener puzzle and anything in Chambers Dictionary is fair game, however uncommon, it could also be CEP, which Chambers gives as a type of edible mushroom. So the word that answers the clue could fit any of the patterns CA-, CE-, CO-, CU-, -AP, -EP, -OP, and -UP. There are several dozen possible words, and short words are typically the ones that have the most possible meanings, half of which are Scottish or dialect or Shakespearean or archaic or otherwise obscure, and you could be staring at the right word for a while not even see how the clue leads to it.

Which is why in this puzzle the longer entries fell into place for me fairly early, and the hardest work has been in nailing the last eight or nine short words.

Still, one by one they have fallen, and I’m sure 32 down will fall soon as well.

Finally finished this week’s Listener puzzle last night. It’s called “Square-bashing”. Four times a year, the Listener puzzle is a crossnumber instead of a crossword and this is one of those times. All the entries in the grid are perfect squares, but the clues lead not to the square numbers themselves but to their roots. 20 letters are assigned values from 1 to 20, and the clues are algebraic expressions like TA + INT and ETER + NAL.

To complicate things further, the grid is divided into two halves, left and right. The two halves have the same pattern of bars, and each half is numbered separately, so that there are two of each clue number — two 11 acrosses, two 6 downs, and so on. The two clues at each clue number are given together, and you have to work out for yourself which clue goes with which side of the puzzle. You have to solve the two halves as separate puzzles, and then at the end there’s a way to figure out which half goes on the left and which on the right. Finally, the number that goes along the bottom of each half is left unclued, and you must find two words that can serve as clues for them, using the discovered values of the 20 letters.

It didn’t take me long to see a likely way to break into the puzzle. It had to do with the lengths of the squares; if a clue leads to an answer with four spaces in the grid, for example, then the entry must be a perfect square between 1000 and 9999, which means that the expression in the clue (which is of the entry’s square root) must be between 32 and 99. Particularly helpful is the fact that if an answer has just two spaces in the grid, then it can only be 16, 25, 36, 49, 64, or 81, and its clue must be an expression equalling 4, 5, 6, 7, 8, or 9; not too many possibilities there.

Believe me, I’m not giving much away there. Even seeing this pretty quickly, it took me a long time to actually break in. I think it was an hour of fiddling around before I figured out which letter represented 1. Another half hour or so and I found the letter that represented 6. Only 18 more to go! At one point I hit an impossibility and couldn’t figure out why, and I had to go back and recheck what I’d done. I decided to print out a new clean copy of the puzzle and go over my reasoning right from the start, which of course made it inevitable that I would discover that my error was a silly one in the very last step I’d made, writing down one incorrect digit in a calculation.

I worked on the puzzle on and off through the weekend. Sometimes it went pretty quickly, a couple times it stalled while I searched for a way to break through to the next deduction. On Monday over lunch I finally filled in the last of the entries in the grid, figured out which half of the puzzle was which, and looked for words that could clue the bottom two entries.

Fail.

For one of the two entries, there was an obvious answer. For the other, there was only one possible way to factor the root into numbers of 20 or less, and there was no way to make a word out of these letters, even with the fact that I could add in the letter that represented 1 any number of times.

I didn’t take the puzzle to work with me on Tuesday, figuring I needed to give it a rest and come back to it with a clearer head. So of course in the middle of the workday it occurred to me what I might have done wrong, but having left the puzzle at home I couldn’t test it. When I got home that evening, I headed straight for the puzzle and redid a calculation. Things worked out as I had suspected they would, and a few moments later I had what was very obviously the intended answer. Very neat.