It is heading for Sunday lunchtime and we have only just finished slogging through Nod’s Analogy. We were working with lots of chewed pencils and erasers, a couple of fairly useless old school calculators that stop short when it comes to finding the square of numbers like 44215, computer produced lists of Pythagorean triples (6 sides) and a great deal of frustration. (A friend said to me “I’d be surprised if just one person solved this using only pencil and paper.” Hmmm! That was more or less our method!) The other Numpty has just stomped off with his parting shot “The editors obviously included this to make triple Play Fair codes seem like fun!” He had already laboriously ploughed his way through the clues to find the primary number values of A to Z, having to backtrack three times when obvious errors emerged when he attempted to work out the ratios they were to produce.

That is my main reason for loathing (yes LOATHING) numerical crosswords. Even if you keep a careful record of your calculations (and believe me, we do) you have to retrace your solve when things go wrong – not just rethink your last ‘Stripey horse (5)’ realizing that it isn’t OKAPI but …. ZORSE?

Ah well. There was no need to worry about Nod’s continued membership of the Listener tipplers’ club, as even I was able to see at once that with those clues reminiscent of that ‘Squaw on the hippopotamus (the one who is equal to the sum of the squaws on the two adjacent hides) we were in the world of Pythagorean triples. We needed a few triples to get to the end of this! Cheers, Nod, see you at the bar next March.

However, with those 26 values established this was going to be a romp wasn’t it? I should have known better than to join the fray – and fray it was as the other Numpty calculates numbers mentally at about twice my speed and short-cuts his work on the calculator, whilst I laboriously work out and record each multiplication and addition; then if our solutions don’t agree, we bicker over my fat-fingering or his careless haste. We slowly worked through our triples (the numerical ones I mean) with growing consternation as 3:4:5 or 5:12:13 kept appearing where we had to have multiples of the third part of the ratio to fill, for example at 10 across, a five-cell light, which had to be a multiple of 13.

What had Euclid to do with it? We are still not sure. Numpty No 1 attempted to use the theorem in his establishing of the values but produced the ratio 3:4.5, which was clearly not of much use. Perhaps one of the superior mathematicians will explain to us how we could have used it or where the short cuts are hiding, that allowed friends to complete this in 4 hours and not our 24.

Our only moments of joy (no, delete that word, say ‘less pronounced frustration’) came when the third part of the triple actually went into the grid, as in 1 down (949), 33 across (673), 14 across (94357), or 17 down (541). Of course, I realize how very clever it was of Nod to create this astonishing numerical feat with a unique solution that still obliged solvers to slowly eliminate possibilities in each cell and each quarter of the grid until only one set worked. So, while the other Numpty had a rather different comment (apocryphal – see ODQ) “A furore Nodmannorum libera nos, Domine”, I have to grudgingly say “Thank you, Nod”.

Just a postscript: A cleverer solver than us who didn’t take anywhere near so long sent me his entertaining comments on this puzzle and I think it might be amusing and instructive to add them (with his permission).

“I’d always meant to patent an electronic pen I invented for the iPad many years ago, where the colour of the ink starts at red then automatically heads through the colours of the rainbow – red, orange, yellow etc as time marches on. Great for crosswords as one can readily see the order in which you solved things. For Numericals, and to prepare for the (in my case, almost inevitable) slip up, I usually do the equivalent of this with coloured pencils, colouring in the clues as I go, to try and ease any backtracking should it be required – and with Nod’s puzzle I am very glad that I did! At the start, 12a and 11a in combination quickly showed where the only even prime must be (X=2) and I was away! The colouring proved very useful when an “Aaargh!” moment appeared briefly, when it seemed that LW needed to be 11×41 but A=41 was already taken – I only had to check back a couple of ‘orange’-marked clues to find that I should have put LW = 13×61. A PICNIC* moment – phew!! And I didn’t get to use my violet (or UV!) crayons this time, but I got as far as indigo with the ‘indigo’ clues being those containing F, O, U & Z, with O the last one found – so this was a pretty tough (might one call it an Indigo-grade?) one!