# Listen With Others

## 4164 by Kea

Posted by shirleycurran on 9 Dec 2011

Astonishment as the numpties downloaded this week’s crossword. Kea! We have been wondering when his next delight was due and there aren’t many weeks left this year. But a numerical!

A straight-forward preamble for once.  ‘Two numbers overlapping by at least one digit (but neither number entirely overlapping the other), where the second number is a multiple of the first’…

Where to start? Nine three-digit entries, fifteen fours, and four fives – no special hint there, but a three-digit can only overlap in one digit according to the rules. That’s fairly restrictive. The first digit can only be 11 to 99 and probably a lot less than 99 given the multipliers.

Immediately we know that the bottom right hand corner is a zero. 21d is a ‘multiply by 2’ so the answer has to be 250. (The numpties, as usual are beginning in the south-east corner.)Then 25ac, essentially a four-digit where the multiplier is 15, produces 46900 to intersect with that. And so are underway.

Just pencil and paper!

The curious multipliers 47, 34, 33, 31, 16, 14, 12 and 7 yielded quite quickly. The 2s and  3s sometimes had two possibilities. But, with a heap of paper, a pencil and a calculator, the solution took shape. The challenge was not fearsome. However, this was an excellent introductory numerical puzzle for people who have not attempted them before or who have been outfaced by them. Lots of us dread the numerical tri-monthly diversion and complain vociferously about it, so what a pleasure it was to have one that needed no skill with Excel, spread-sheets or computer programmes; one that could be solved by hard grind with a pencil and a heap of paper.

Kea should be commended for braving the critics and daring to produce a simple little numerical number that will undoubtedly encourage more people, like the numpties, to have a go at them. He is a clever setter, as we all know, and certainly didn’t produce this fine little thing because he is incapable of something more difficult (or ghastly). Thank you, Kea.

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