We have just failed to manage a ferocious numerical in the Magpie by Zag and were meaning to give ourselves the long-awaited easy life by ceasing to enter the numerical crosswords or even to attempt them, and here was a Listener numerical by Zag’s mate (they are the co-editors of the Crossnumbers Quarterly). “Let’s go ski-ing and have a break from crosswords!” However, yesterday’s rain has turned our little low-lying resort into a sort of ducks’ paradise and the other Numpty said “It doesn’t look too bad – I’ll have a go”.

Entries went in thick and fast but elation turned to despair as every entry seemed to have several alternatives (I’m told there were 2760 possibilities). This just wasn’t working. I was watching the paper and frustration pile up and just skimmed the clues to see whether Oyler has any hope of retaining his entry to the Listener Oenophile Elite – and of course he has, with all those multiples, I am surprised he is still standing! Cheers Oyler!

However, it seemed it was time to abandon, wax the skis, hunt up some gannex or ventile gear and head for the slush, but it was pretty clear that the message we were to extract from the last digits of down entries was the way in. We fed possible letters into TEA and got gobbledygook from the first seven acrosses RE????E with an odd Q or G thrown in. I persevered and light dawned. The possibilities from the last seven down clues gave ENTRIES. We had to rethink and check our arithmetic to make REVERSE work, but which entries could we reverse? Of course, we had, for example 169 and 961 as possibilities for 3 across, a couple of palindromes and both 1229 and 9221 answering 20 ac. It had to be ACROSS entries.

We did it and checked our new grid, clue by clue, uttering gasps of amazement and delight. Now we understood why 3d was ‘plus or minus 3 – in one grid it was plus, in the other it was minus! What an achievement! And oh, how sneaky – there was a sting in the tail. 174 or 134 would work at 20d. Which to choose? This would snare a careless solver but 31 now appears at 18d so we opt for 71 at 25ac. Fiendish, Oyler but magical!