## The Properties of Numbers II by Piccadilly

Posted by shirleycurran on 8 Sep 2017

I downloaded a rather large symmetrical grid with the usual anxiety I feel when the three-monthly numerical crossword appears. My trepidation only increased when I read that more than half the clues consisted of digit sums or simple additions of other solutions and not of mathematical information that could give us a tiny claw hold as a way in. “20 = 10 + 10”. Well, I know that and all the other simple addition and multiplication facts like 6 = 3 x 2 but it wasn’t so simple was it? Though it was indeed admirable how Piccadilly made all those mathematical basics correspond with the reality of his far more complex mathematics. He didn’t convince me, though, of his right to retain his admission ticket to the Listener setters’ winos outfit as I couldn’t find any alcohol in his grid – unless I count the doubles (20 =10 + 10) Hmm – into doubles? Cheers, Piccadilly! More about that solitary hare later.

We got out the tables and one clue yielded almost instantly and with 15625 at 1, we had either 53 or 59 at 2 since the digit sum of 2 had to be even. Simples! Using logic, we were able to fill a few more cells with the digit 1 and managed to suss that 27 had to be 125 but then seemed to be faced with a task that involved vast strings of possibilities for each solution. For example, 22 had to be a palindrome and we had sussed that 2 (59) was a factor of it so we had to do a Numpty troll though a long list of multiples of 59 that would give ?9?9?

12 and 9 had to intersect and it was that 7 that was the start of a long trail to the finish until the joyful moment when 23, a small digit sum that had to be a prime, and had to be greater than itself when reversed, produced the wonderful 11213 that confirmed all and roused a Eureka!

A mere ten pages of notes or so and just a few hours of mutters – “This isn’t maths, this is string-searching!” – and groans about numerical crosswords. Well, many thanks, Piccadilly, and now I know that 5 is a factor of 15 etc. No, joking apart, how very clever to make all those statements in the clues correspond to the reality of simple arithmetic.

That elusive hare? I expected him to be gallivanting across the grid in alphanumeric style (8 1 18 5) but, in fact, it was a rather timid alphanumeric DOE crouching at the foot of the grid this time (4 15 5).

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