We are staying at the bottom of a cliff on Ibiza with relatively limited solving resources and had to drive across the island to the nearest ‘locutorio’ and cope in Ibizenco (the local version of Catalan) to get our weekly challenge – and the moment that I saw a quadruple carte blanche and the name Quinapalus, I knew that it was going to be that challenge. I read through the preamble and gave an awed gasp but did, of course, confirm that Quinapalus reserves his place at the Listener bar: after all, he is a previous winner of the Ascot Gold Cup. ‘Ale is recognised by these kings quaffing one (6)’ gave us SHAHS who were rather surprisingly drinking that beer but we put one (I) into them and got SHIAHS. So cheers, Quinapalus.

The preamble warned us that we were looking for someone with two preoccupations that would appear to us just before a riddle in a work of one or three words in yet another unclued light. Some cells were going to contain two letters entered diagonally – obviously leading to two different answers and there were going to be two gaps. There was one redeeming feature – top-bottom mirror symmetry.

We solved rather slowly as it was our turn to cook (for ten!) and these clues had the Sabre touch but with a few assumptions, I managed to begin a grid fill with that obvious KERB* giving us a Nellie or a BERK, and AITU, EMIGRE, RIZLA and KNEEPAD intersecting with it at the top right. Word lengths provided a putative grid but we were rather baffled by 38/41 and a string of clues from 30 to 42 that seemed to lead to those double solutions with letters entered diagonally: WITLESS/WITNESS, SCLIMS/SCRIMS, POOTER/POSTER, SCREE/SIREE, GLARY/GOARY, VEX/WEX (a new word for me and somewhat appropriate as the Ibiza temperature had just dropped to 8 degrees and it was pouring while we heard that in London the temperature was 29 degrees!) SUNG/LUNG and DORT/RORT.

We should have found LEWIS CARROLL and the REV C L DODGSON a lot earlier – an obvious choice of theme for Quinapalus with his mathematical riddle. ARGAND. DIAGRAM appeared using the diagonal GR of the two names but it took us several more hours and some Googling to find the remaining diagonal letters that helped us spell out PHANTASMAGORIA and RHYME AND REASON. I found the first riddle and groaned to see that I had to solve a quadratic equation and that somehow the solutions were to be marked in the ARGAND DIAGRAM obviously using the axes of the original carte blanche grid.

INDICES SURDS, MOVE BOTH Xs VERTICALLY, the corrected misprints told us. Fortunately there were five rather high-ranking CERN physicists in our party and I passed my problem over to them. X2 + 7X + 53 = 11/3. ” (Solving a quadratic equation is like falling off a log, they told me – it’s simple.) That’s minus 3.5 and plus or minus the square root of 37 i – that’s just a tad more than 6″. Then ensued a long discussion about exactly where in the grid we had to put those two Xs that we were moving vertically and marking (reasonably) accurately in the grid. I think that word ‘reasonably’ is an editorial addition to avoid another Poat hare. We have to have two solutions so those Xs must move just over the demarcation of their original cells (in TUXES and MIXEN) so that the also complete the words SEXT and SAXE and fill the empty cells and we have our two solutions. Too clever for me! It took us twenty-four hours to solve. I wonder how long it took to set. Many thanks to Quinapalus.