Listen With Others

I will begin by admitting that though I can get the Times cryptic out at marathon pace, I can’t do a word of your puzzle 92% of the time; but I have loved, and been in awe of, the mathematicals since The Listener moved to the Saturday Times. I’ve set Teasers in the Sunday Times since I was at school in the late 70s, and am well into three figures, but this is my first Listener.

In 2018 I set a Teaser based on Roman cubes, squares and primes, and I hoped Roman numbers might give me a Listener. Aristotelian unity said, ‘Just primes!’ and I immediately sketched a 9×9 grid because 7×7 felt cramped, 11×11 too baggy for a beginner, and even-sided grids give me flashbacks to Glasgow League chess matches in Knightswood and Bishopbriggs, desperate rear-guards under cover of my opponent’s pipe-smoke to reach the Dunkirk of move 40 and adjudication.

I only began to discover ‘Roman number theory’ as I filled the grid, and I hope solvers had the same pleasure in these discoveries that I did: all primes end I or IX; …XXC… isn’t properly formed; only II, CI and XI for 2-letter primes because MI is 7×11×13. I like the way prime numbers are a bit of a surprise beyond C: the cloudburst CI, CIII, CVII, CIX, CXIII, then the drought CXV, CXVII, CXIX, CXXI, CXXIII, CXXV, then the isolated Mersenne prime CXXVII.

One solver remarked on how few clues there are and how useless they seemed. The minimalism is a Teaser habit, a legacy of the postage-stamp space we had in the Magazine, much of it taken up by Harold Evans’s TYPOGRAPHY. In a Teaser, a toy universe unfolds from four axioms and some noise, like Euclid, or a lyric poem (the axioms of a lyric poem are sex and death). I suspect a Listener should look more epic than Latin Primer. The uselessness of the clues I found alarming when I started to do the puzzle from scratch during proofing. I was amazed that Shirley Curran arrived momentarily at a second solution if equation 2 is ignored; eek! I didn’t imagine the clueing was that skinny. And she targeted equation 6 like a beagle; I put it at the end with its hands in its pockets, hoping nobody would notice that it was a bit less useless than the rest. Now I know Shirley likes an alcohol reference, I’ll put (Vat) 69 next time; it will look less rude in Babylonian sexagesimal.

A number of solvers have told me that they liked Latin Primer because their solution path wasn’t a hypothetical house of cards: they could ink in some entries quite soon. This is a consequence of the Luddite method of composition: no spreadsheets were harmed during the making of this puzzle. Even so, I’m astonished by how quickly some readers solved it; this suggests that the logic and concentration honed on 92% of your puzzles is the same logic and concentration deployed on the 8%, though vice versa doesn’t work for me. Mind you, I’m not very good at the mathematicals either: my wife says the puzzle took me August to lay, and when I had to solve it for proofing it took nearly four hours, even though I remembered roughly where I’d buried the bodies two years back. I genuinely believe that Listener solvers should be conscripted for work of national importance in asbestos huts at a secret location in the Oxford-Cambridge arc.

I won’t be the first setter to appreciate the work of editors Roger and Shane; they bring an extraordinary combination of insight and care; they will be sentenced to Hut 6. You might think it was obvious to use Roman numbers in the clues; it wasn’t obvious to me, but Shane put that right. The elegance and rigour of the published solution path, which opens like an academic paper in number theory, is Roger’s.

Poems don’t exist without readers, nor puzzles without solvers. Thank you for letting me stand for a moment on the very pinnacle of puzzledom, your Listener crossword.