# Posts Tagged ‘Primes’

## Latin Primer by Nipper

Posted by shirleycurran on 11 Dec 2020

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.

## A Defter Premier by Arden

Posted by shirleycurran on 7 Sep 2018

There was my usual despondency as I downloaded A Defter Premier by Arden. The dreaded numerical! There was not much hope of Arden’s earning his Listener oenophile qualification with this. Then I saw the title. It had to be a premier cru! “It must be an anagram” said the other Numpty who had his pencil and paper ready to begin (yes, he solves the numerical ones that way!) TEA suggested to me that we were dealing with FREE TRADE PRIME. Well, there’s hope for us all with Brexit looming – maybe those prime wines will escape heavy duties. Numpty disillusioned me with a delighted snort. “Primes indeed, but it spells PIERRE DE FERMAT. it is going to be about his theory of prime numbers”. Cheers anyway, Arden!

Must be a hard problem, a numerical compilation! Absurd ideas, going off on a tangent, rooting around… Log in looking for topics? Prime the pump how? It’s an irrational field, sometimes, and there’s a limit to solvers’ tolerance in seeking a complex solution. How to differentiate between rational options, integrate odd ideas, converge to a real result? This was a splendid example of an approachable numerical, I think, with the corner clues being fairly easy , and strongly hinting at an ‘all prime numbers’ solution. The clues made it possible to decide on the ‘sum’ or ‘product’ variety with relative confidence, and without generating too many options to check, which can be a real ‘off putter’ for those who aren’t experts.

The other Numpty now laboriously worked his way through the clues, happily solving the ones where the clue was ‘the product’ of those two integers but muttering when the clue was the ‘sum of the integers’. Of course, knowing that only primes were being used helped enormously and, with a break for dinner, we had a full grid by mid-evening.

We suspected from the start that the two diagonals were the two symmetrically placed 9-digit numbers that share that feature (prime). I use a really valuable website (is this cheating? I really don’t know whether GCSE maths, which is the ‘supposed’ level of a solver of Listener mathematical puzzles, teaches one how to work out whether a 9-digit number is a prime  http://www.bigprimes.net/primalitytest but this does) and those two numbers were primes. I double checked and found that no other symmetrically placed pair fitted the requirement.

Clearly we needed the squares of two 5-digit numbers to produce those 9-digit primes and we both squared the available ones in the grid but as I despairingly discovered that all but two of the available solutions were way too large, the other Numpty gave his second happy shout. Of course, he had worked out that we were looking for those four diagonal 5-digit primes. What an achievement. I imagine Arden must have formed the skeleton of his grid with the two main diagonals and those four intersecting primes, then built his grid round them. I hope he will tell us how he did it!