I know that the editors are keen to publish ‘easy numericals’. For this Numpty, that is an oxymoron. However, if anyone is able to produce a numerical Listener puzzle to order, it has to be Oyler. We approached this ‘Square Time Sums’ with more than the usual trepidation (at least, the other Numpty did) as we were travelling between a son’s wedding and granddaughter’s christening with nothing but pencil and paper. However, I did manage to print out tables of the first 1000 prime numbers and square numbers of two, three and four digits and purchase a £1 calculator which later gave my three-year old grandson immense glee when he found out that you can change a whole row of nines to zeros by simply adding one. I suppose numbers can be fun.

Does Oyler qualify for the Listener Setters’ Toping Club? As I scan his clues and preamble, I realize that he is confirming his seat of honour as a founder member with not just doubles but triples – and even worse, four of them! How on earth did he stay sober enough to compile this! Cheers! Bottoms up.

The other Numpty grumbled and muttered for a few minutes and then announced “I know I can compute the possible triples in my old favourite GWBASIC if I can convert my French laptop keyboard to an English one to find the odd characters like <, $ and % and there are at most about 20,000 triplets. The 1-9 appearing once only requirement might cut this down a lot!” Soon afterwards he happily remarked “Well, there are only seven possible triples'”- and shortly after that he slotted in 1, 9 and 15 across and 2 down and fixed JKL and XYZ

ABC = 36, 729, 5184

JKL = 16, 784, 5329

PQR = 81, 576, 3249

XYZ = 25, 841, 7329

A steady solve followed, with the usual backtrack to find where the fat-fingering on the tiny £1 calculator had led to an error but a couple of hours later the grid was full and a careful check confirmed that it all worked.

What was left to do? Two complete rows and two complete columns “that are related to the theme” had to be highlighted. It didn’t take much nous to see that only four of the rows and columns contained all the digits from 1 to 9 but what was special about those? The answer astonished me – they are all perfect squares! How did Oyler manage that! Thanks to Oyler.