Collatz conjecture? I, the Listenernumericalcrosswordiphobe had never heard of it but the other Numpty had. I find it difficult to conceive that a professional mathematician would devote his mental energy to developing and exploring such a conjecture. However, Elap’s puzzle clearly confirmed it for the case in point, so it can be added to all that tremendously useful intellectual baggage that the Listener crossword provides and that I can slip into the next lagging dinner conversation.

Through habit I scan the clues to confirm Elap’s continued membership of the Listener drinky club but no, he almost manages RUM in his clues and there is a very small gt, but that is the sum total of his alcohol, so, in view of the daunting preamble, we have to compensate and pour ourselves a couple of large ones and get going on the solve. Cheers, Elap, anyway.

The 1dn NNNN was an easy way in, followed by 8ac NP+PP. This allowed one to have a look at the possible ‘Collatz accomplices’ for N=2 (just 1 and 4) and P=7 (just 2 and 22), making things less intimidating. It was possible to nibble away at the clues without a lot of options to try and track, and (which seems rare nowadays, no need for a spreadsheet) but it was easy to go astray- with G as 160, I took a long time and much muttering to notice that 53 was an option for g, not just the hastily assumed 80!

There were a couple of hitches like this and muttered retreats before the more numerical Numpty finally had a grid-fill and we had to work out what to do next. Fortunately, my skills at decoding are fairly limited and the alphanumeric option is the one that springs to mind. There was even a useful hint there too, since we were told that this decoding had to be done in a ‘thematic direction’. I’ve rarely seen snow or hail fall in any dramatically different direction from down, so we worked downwards and speedily got PRODUCE. My only useful contribution was to spot that the 2-digit 38 appeared next and we were told that there were to be 38 entries, so we were able to complete the message: HAILSTORM NUMBERS FROM 988 AND FILL GRID.

We carefully listed the 38 relevant hailstorm numbers then enjoyed the jigsaw puzzle of fitting them in with just enough hints given by those circled numbers that were already there. (Yes, I have to admit, albeit a numerical Listener puzzle, this was fun!) The quarterly Listener number puzzle without spreadsheets, heaps of discarded worksheets, chewed pencils and frayed temper? And one with two grids to be completed with two different methods. This must be a numerical triumph. Many thanks, Elap.