# Listen With Others

## The Properties of Numbers II by Piccadilly

Posted by shirleycurran on 8 Sep 2017

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).