In the puzzle comments someone said that he’d “like to hear about how Self-Explanatory was constructed”. Be careful what you wish for…

What follows is my attempt to lay bare the construction process. It might read as an advert for the Futility Closet website (https://www.futilitycloset.com/) and Quinapalus’s qxw setting software (https://www.quinapalus.com/qxw.html), but that’s mainly because without those things I wouldn’t have stood a chance.

Futility Closet is a gold mine of crossword ideas, but the magic square autogram (https://www.futilitycloset.com/2019/11/15/sums-and-sums/) stood out. All I had to do was think of a way to lead solvers to the solution, and they would surely agree with me that it’s a great work of geek art. Or, if not, they would at least agree that it’s the result of time well wasted.

An autogram is perfect anagram fodder, because simply counting letters allows the original to be built from any jumble of its letters. So if I could make a puzzle that contained the right letters, solvers had a clear but not simple logical route to the finished magic square. Sadly, with such a limited alphabet and such a large number of Vs, Fs, and Xs, I needed to break some rules to fill my initial grid. I realised that having answers that just dropped all the non-required letters would do, if I made sure that no answer dropped more than about a quarter of its letters. So I made a word list using that rule. Fortunately making a custom word list like this is very easy for anyone with a bit of programming experience.

So it was not a problem to restrict the letters in the grid to a certain subset of the alphabet, but it was still difficult to keep to a strict set of 79 letters. Qxw doesn’t have an option for this. However, it has a thing called a ‘free light’, allows lights to be filled from different dictionaries, and it also has an ‘allow anagrams’ option. As I was about to write to Mark Owen to ask about writing plugins, I realised that I could make the entire grid a single free light, then tell qxw to use a dictionary that contained one 79-letter word for that free light, allowing anagrams. Job done. I left it running overnight and, not very surprisingly, it failed to get close to a filled grid, so I gave it a start by putting the Xs, Vs and Fs in places that I thought might work… and with a bit of fiddling around I got a fill. It was reassuring when checking the words to discover that I could clue ‘vulviform’ using Chambers without getting too biological.

I didn’t want to use the non-Chambers word ‘autogram’ as part of the solution, but it ended up being the easiest way to explain everything tersely, and Wikipedia defines it fully. Autograms were invented by Lee Sallows, who is “known for his contributions to recreational mathematics” (I’m quoting from Wikipedia here). There is no way I could come up with an autogram myself, and I suspect that computers have exhausted the interesting ones now anyway. I am therefore indebted to Lee Sallows, and I hope he doesn’t mind me nicking his work.

Clearly I needed to avoid ambiguities when filling the magic square with duplicate numbers, so I devised the colour scheme. I apologise to colour-blind people for forgetting to also label the squares with letters. I had even thought about this before publication, but failed to alert AJ. I was pleased to find that I could make the colour pattern symmetrical in both grids. I’m a fan of symmetry.

A few months ago, Mark made a number puzzle based on a magic square of cubes, and I solved it by filling two cells, guessing that it would be available on the web, and searching for the complete answer. In other words, I cheated, but it was gratifying. It was fun to be able to tell people that they could complete my puzzle by cheating, which was really part of a disguised clue to the word ‘fox’, but doubled as an invitation to discover the answer online.

The gimmick of the puzzle involved reorganising letters into a new combination, so the clue gimmick was chosen to reflect that. I’m not very experienced at clue-writing, so it took me ages to write the small number required. The extra condition imposed by the treasure hunt made it harder still. One of the easiest clues to write was 1 across, which contains a surface reading referencing 1980s snooker, and a definition referencing 2012 pop. This turned out to be the one people liked the most, showing that serendipity outperforms sweat, but can’t be relied on. Further serendipity gave me a Quality Street with exactly the right number of letters – the only one feasible with the limited alphabet available.

Full credits: Futility Closet for the idea, qxw for the grid-fill, Lee Sallows for the autogram, AJ for the layout, and Mark, Shane and Jason for fixing about two thirds of the clues.

Posted on Tuesday, January 5th, 2021 at 4:56 pm under Setting the scene.
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