The 8X8 team was just a little bit troubled by the part of the preamble that warned us about numbers after clues disagreeing with the lengths of words to be entered – this in addition to extra letters in the wordplay and clashes. At least, we have learned what careful attention we must pay to the preamble (those words ‘derived from’ – see below!)
Solving went fairly quickly with some lovely moments: ‘White’ as the definition for CUE BALL ‘cell lab regenerated around nucleus of corpuscle’; that ingenious clue for URETER where we had to remove the letters of ‘clamp’ from ‘permaculture’ and the similar ON HEAT where we took ‘tack’ from ‘on the attack’, producing our extra T into the bargain.
Soon we had a convincing set of letters about THE SMALLEST NUMBER … IN TWO WAYS, and the brains of the team shouted out “Ah, the taxi! 1729”, which was somewhat mystifying to me, even though I had just asked why 17d would be ‘HACKNEY’ and 29ac. CAB(INET). “Ramanujan”, he explained, “and G.H.Hardy” (how useful it sometimes is to have a partner who is a compendium of useless knowledge!) Naturally, the set of putative clashes now sorted themselves into the two names, though I still wonder whether just putting the M an J of RAMANUJAN into those little cubes in the middle was all that was required (or was I supposed to work out the cubes of the letters M and J and add them, or subtract one from the other? But no, that gives 3913 – just an 8X8 red herring).
Still some way to go! CUEBALL, CUTLERY, REBEL, BEARABLE, CUBEBS and BEGONE seemed to be the words with extra letters (though misreading Chambers gave me a potential ON from the end of PLEURON. It took my wise friend to explain to me that PLEURA also fits with the singular ‘side piece’ of the definition – alas the potential pitfalls of the Listener!) CU and BE squeezed into the little cubes with numbers in them at 1, 9, 10 and 12. What a beautiful penny drop moment! Here were the two ways of producing 1729 that Ramanujan, in his hospital bed, provided. (1^3 + 12^3) or (9^3 + 10^3).
A moment of doubt here. What was the subject of the disagreement? Do I enter ‘Cubes’? That was what was in the cells in question. The two men were actually disagreeing about the dullness of the number of a Hackney cab … Hmm. But there were those words ‘derived from’ (at least I had been able to use my highlighter there! I was longing to highlight AACKNEY CAB and RAMANUJAN).
The number 1729 was derived from what was in those cells. How very elegant! Thank you, Stan! From start to finish this was most satisfactory.