Listen With Others

The dreaded numerical! We download it with a groan of shock – it’s a carte blanche! (Numbers jumbled and added in knights’ moves? That one still has to come!) Roman numerals! That really is an original touch and the preamble tells us that we are converting 28 distinct prime numbers to those, and gives us lower-case letters representing 16 of the 28 primes we must enter and telling us the lengths of those.

Then there are those six equations that will give us the relationships of those primes to each other. With surprise, the other Numpty comments that there are, in fact, very few candidates for a and b, the 2-digit primes (II, XI and CI) and, in fact only ten candidates for the 3-digit primes of which we are going to use eight – so it isn’t perhaps going to be the numerical nightmare we have come to expect every three months.

The last equation is the most powerful with a potential valid difference of 90 between s and t. This suggests that 283 + 101 = 383 + 11, and we can putatively place those 9 and 2-digit solutions, so we are underway, and so it goes, until a hiccup at the end.

But I digress. Of course I have to establish whether this apparently new Listener setter can be admitted to the Listener Setters’ Oenophile outfit, and, as usual, I hold out little hope for these numerical fellows. Hoh. sneaky! He’s opted for the pseudonym Nipper and Chambers tells me that that is a double definition headword and that a nipper is a small drink in the USA. Then, as our grid fills, I find triple X all over the place – so he undoubtedly qualifies – Cheers and welcome (to the Zoom bar?) Nipper!

We are slightly worried by that preamble statement that there are exactly two Ds and one M in the completed grid, appearing in three entries, all of which are longer than three letters. The first equation works out as 5 X 283 + 59 + 37 = 1511 which gives MDXI and it seems to us that the M and D are in the same entry: however, we realize that the D is also part of the k entry as DXLI, so all is well.

All is well – until our final check shows us that we have only fourteen of those listed entries in our grid and our 211 and 53 in that second equation have to be wrong. There’s some grumbling and head-scratching and I do a careful re-fill of the grid, finding that we can use 13 and 251, producing exactly the same result as our 53 and 211.

Then we have to do a careful check that the 12 other entries are indeed all primes and distinct ones too, and we breathe an immense sigh of relief – only Magpie numericals and the Crossnumbers Quarterly to darken our days between now and the penultimate Friday of February 2021.

Here’s a Crossnumbers Quarterly plug (though I find it difficult to imagine that anyone can extract moments of joy from the odious things, but we are told that the numericals produce more entries than the Listener verbal puzzles (Really?) so someone, somewhere must like them – and I grudgingly admit that this one had its moments). I understand that Oyler and Zag, in their New Year edition, are including only prime problems, so if you are a numerophile, this might be the moment to indulge yourself with a subscription as a Christmas treat.

Many thanks, Nipper. There must be a lot of relieved solvers after that imaginative numerical puzzle.