jerbil

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About jerbil

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  1. jerbil added a post in a topic   

    I disagree slightly with Semper Video.

    There is a record (Reader's Digest, I think) of an aircraft sergeant who fell out of a crashing bomber in World War II without a parachute from 10,000 feet.

    He collided with a pine tree after reaching terminal velocity (200 mph?) whose gentle branches delivered him to the equally gentle embrace of a conveniently placed thick snowdrift. He then escaped thanks to the efforts of a local resistance group-
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  2. jerbil added a post in a topic   

    I was interested in Magicians note in #2, with which I fully concur.

    The Gamma function, defined for positive x as the integral from 0 to infinity of yxe-y with respect to y, means that, when x is integral, then Gamma(x+1) = x!, though the definition, as noted by Magician, holds valid for non-integral x.

    For any positive x, a useful approximation to x!, considered to be valid for large values for x, is Stirlings approximation, which is the product of two terms:-

    (1) The square root of 2 pi x,
    (2) (x/e)x.

    This approximation can be improved immensely by multiplying these two terms by the following:-

    (3) The exponent, to base e, of the term 1/12x 1/360x3 + 1/1260x5 1/1680x7 + 1/1188x9.

    Even for x = 1 this yields an over-estimate of a mere 0.05%, whilst for x = 3, the error is lessened to less than a millionth of a percent.

    If one wishes to evaluate x!, or for that matter Gamma(x), for small positive values for x, a convenient method is to evaluate say Gamma(x+20) and then divide down using the relation Gamma(x) = Gamma(x+1) / x.

    Of course, another approach is to subscribe to Mathematica and get Wolfram to do the work for you.
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  3. jerbil added a post in a topic   

    Who needs eliminations? The problem is solved very simply from elementary analysis.

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  4. jerbil added a post in a topic   

    On another thread, a newly joined member suggested that whenever someone supplies a blunt answer to a problem, then if he or she is able so to do an explanation should be provided. Here is a justification for the answer supplied for this particular riddle:-

    Einstein Riddle.doc
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  5. jerbil added a post in a topic   

    It would help a non-American (there are a few of us, you know) exactly what a "school number" is. I have a passport number, a number on my driving licence, a number on my PPL and a number whenever I took an official examination, but cannot recollect being given a "school number" in Britland.
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  6. jerbil added a post in a topic   

    Sorry, ljb, you seem to have beaten me to it. The point to these puzzles is in providing oneself with a simple "Ariadne's thread" which allows one quickly to discard impossible configurations. The technique is also useful in solving otherwise difficult Sudoku puzzles, especially when one cannot visualize, for example, a valid XY argument to make the solution obvous.
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  7. jerbil added a post in a topic   

  8. jerbil added a post in a topic   

    They have to be integers, M.

    Try the following triplets :-

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  9. jerbil added a post in a topic   

    Acuerdo, K4D (I live in Spain.)
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  10. jerbil added a post in a topic   

    I question your statement, Kewal.

    In my view, a "number" might be a positive integer or not, and certainly not necessarily integral. The term "complex number" refers to a pair of what we might otherwise refer to as numbers, and some writers refer to whole n * m matrices as "numbers."
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  11. jerbil added a post in a topic   

  12. jerbil added a topic in New Logic/Math Puzzles   

    A ribbon comprises a line of squares numbered sequentially from 0 to n. A marker can initially be placed on any square. After positioning such a marker, it may be repositioned by moving it p squares to the right or q squares to the left, provided that one does not fall off the ribbon. The numbers p and q are mutually co-prime.

    Show that n = p + q – 2 is the smallest value for n which permits all squares to be visited after a successive number of moves.
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  13. jerbil added a post in a topic   

    I think that this question is beautifically succinct, and just now I am at a loss as to how to approach an answer.
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  14. jerbil added a post in a topic   

    Nicely done, solvers. I append my own ideas, which also explains why I entitled the problem the way I did.

    Explanation of Problem.doc
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  15. jerbil added a topic in New Logic/Math Puzzles   

    For what integral numbers a, b and c, where 0 < a < b < c < 90, is the following equation satisfied, and why?

    cos2aº + cos2bº + cos2cº = 1.
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