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    Ancient Richard
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    English Midlands
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    SF, Maths, Science, Computing, Philosophy, Gardening, Cooking, History, Board Games

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  1. Thank you for the links to the videos.
  2. ancientrichard

    Chapter 11

    Many thanks for the link to Google Earth. The lads were very brave to stand on that rock !!
  3. ancientrichard

    Chapter 3

    I was expecting PHP and scripts, but not quite to soon. Those lads are having fun
  4. ancientrichard

    Chapter 2

    I can identify with those characters. I had great fun teaching myself HTML a few years ago. It's wonderful when the layout works just as you hoped. Cascading Style sheets are fun too of course, and the lads have PHP to look forward to 🙂
  5. ancientrichard

    The Dark

    I apologise for the multiple postings of my previous comment. It showed up on my screen as a blank comment and I couldn't find any way to delete it.
  6. ancientrichard

    The Dark

    I think I shall enjoy this story. There's a mystery and a young man who appears powerless but seems likely to astonish by turning out to be very powerful in an unusual way. I look forward to learning more with each installment.
  7. ancientrichard

    The Dark

    I think I shall enjoy this story. There's a mystery and a young man who appears powerless but seems likely to astonish by turning out to be very powerful in an unusual way. I look forward to learning more with each installment.
  8. Thank you very much for that story. I can remember when diapers were called 'nappies' . They were made of some sort of cloth - flannel I suspect -and were washed after use so they could be used again. One could see who had a small baby by looking at the long rows of nappies hanging out to dry. In those days Jacob wouldn't have needed to make that chilly journey.
  9. ancientrichard

    Chapter 44

    Thank you for that story. I enjoyed it very much. As a matter of interest, when did Regis and Royal change their names to Andy and Matt ?
  10. ancientrichard

    Chapter 37

    This has become very exciting. I love exciting stories I'm looking forward to finding how how the odious Fergus perishes - I'm sure he will !
  11. ancientrichard

    Chapter 3

    I'm finding this very hard to follow, and hope the hypnosis will end very soon.
  12. ancientrichard


    I love the humour in this story. In the context of the calendar with naked footballers "my friend can touch you up on her computer" was a delightful double entrendre.
  13. Indeed; I wonder about all those questions, and especially what prevented Trevor from attending the award ceremony.
  14. I read the last chapter and the epilogue today. I've enjoyed it very much. It includes one of my favourite characters, Miss Jenkins, and as a bonus mentions a number of towns I know. The story is supposed to be the first of a trilogy, so there should be a lot more to come. Johnny is supposed to receive a medal so royalty may be involved eventually.
  15. I've been thinking about this for several days, butt still can't prove it though I do believe it. This is as far as I've got: Notation: In expressions of the form: abcd... a, b, etc are integers in the range 0 to 9 and abcd represents the number with digits a, b, c, d All numbers are assumed to be in base ten unless otherwise stated. The transformation T is defined to that T(abcd) = abcd + dcba The Sum S of any number N is defined as S(N) = sum of the digits of N, so S(abcd) = a+b+c+d The 'Hypothesis' is that any positive integer can be converted into a palindrome by a sufficient number of applications of transformation T I have so far been unable to proved the hypothesis but have several observations that may help in constructing a proof. (1) The hypothesis has some plausibility, since, if all the digits of some number N are sufficiently small T(N) will be a palindrome. Suppose N = abcd, then T(N) = abcd + dcba We evaluate that by performing the additions (d+a), (c+b), (b+c), and (a+d) If all those sums are less than or equal to 9 they all produce single digits, so T(abcd) = (a+d)(b+c)(b+c)(a+d) which is a palindrome For example T(2417) = 2417 + 7142 = 9559 On the other hand, we do not get a palindrome when the addition of two digits gives an answer greater than or equal to 10, because the resulting carrying figure destroys the pattern and more applications of T are then needed to get a palindrome. (2) It may help to consider the sum of the digits of a number. If none of the additions involved in calculating T(N) is greater than or equal to 10, then T(N) is a palindrome and S[T(N)] = 2*S(N) If v of the additions of digits give an answer greater than or equal to 10, then T(N) is not a palindrome and S[T(N)] = 2*S(N) - 9v so there may be a tendency for the digits to get smaller when T(N) is not a palindrome. (3) The property of palindrome is not an intrinsic property of a number considered in isolation, but only of a number expressed in a particular base. Every number is a palindrome when expressed in base 1. In base N, N = 10 and is not a palindrome.
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