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Posts Tagged ‘Elementary Number Theory’

Elementary number by Oyler, a perfect square

Posted by shirleycurran on 11 March 2011

Gloom! A numerical. However, Numpty number one explains what the rubric says. These are elementary rules – simple mathematics! All you have to do is apply each of those rules to all  of the answers to make sure that only the stipulated ones apply. That’s the way you eliminate the others – like that rule R, ‘It has a double digit’. None of them obeys rule R, but a lot of the possibilities do – so they are ruled out! Simple! Best to start with the ones with the most rules and the two-digit numbers, as those are likely to be the easiest to solve.

Well, I leave him to it and soon he has the north-west corner almost complete and an intriguing feature emerging. There are no zeros at all (we knew there couldn’t be any as leading zeros) and we already have most of the digits from 1 to 9 and EACH ONCE ONLY!

When the south-east corner is almost complete and the centre top, our suspicion becomes near certainty and even Numpty 2 is capable of participating. Too much of life is already consumed by crosswords, and I have promised myself never even to look at a S—-U for fear of being hooked. However, Oyler’s construction obliges me to break my promise. Completing this was almost a pleasure and I made a little bit of mathematical progress, learning what a ‘composite number with a three-digit prime factor’ and a ‘sum of four consecutive integers’ are.

With a complete grid, we have to apply those 18 rules to the two long unclued entries: 139854276 and 627953481. My little plastic Donald Duck calculator has problems with such long numbers but between us, we tease out DINO and EI, learning, with surprise, that the vertical unclued light is I, a perfect square.

DINO and EI produce only one convincing word, IODINE, symbol I (see above – a perfect square) and isn’t that exactly what Oyler has produced? A perfect square! That’s clever! What is more, Wikipedia tells us that the element Iodine was discovered just 200 years ago. That must be why that number 5 appeared in the centre of our ‘perfect square’ with a 3 to complete iodine’s atomic number just below it in the grid.

Easy for the experts, I am sure, (still, nothing is stopping them from having a go at those fiendish Magpie numericals is it?) but just right for many of us. What an encouraging first numerical puzzle of the year. I almost enjoyed it (almost!) Thank you, Oyler.

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