Year 1988- Volume 24

There are three items I wish to bring to the reader's attention.

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Readers of Parabola are especially invited to consider entering this years School Mathematics Competition.

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Paul Erdős

For reasons which are not entirely clear to me the ancient Egyptians considered fractions  1 b  much simpler than fractions of the form  a b  and they were interested in representing

a b = 1 x 1 + + 1 x n

 

where  a  and  b  are positive integers and \(x_1 < x_2 <\cdots< x_n\) .

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Charles McGilchrist

Survival of a cockroach is unfortunate, survival of an endangered species is important, survival of a human (probably the least endangered species) is essential.

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David Tacon

If one wishes to appear wise in the eyes of one's friends it is generally sufficient to inform them that space is not Euclidean, that in fact it is "curved".

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Q.732 Let  L  be the set of  n  line segments with the property that three of them can be assembled to form a triangle.

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Q.720 When the initial digit of a whole number  x  is deleted, the number decreases by a factor of 13. Find all possible values of  x .

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Bill McKee

Suppose we have two quantities,  x  and  y , and we are given that  y  may be expressed as an infinite power series in  x :
\[y = a_1x + a_2x^2 + a_3x^3 + \cdots \,.\]

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You are given 6 balls, which appear to be identical except that 1 is white and 5 are black.

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Q.744 Define \(f(x) = \displaystyle\sum_{k=114}^{184}\frac{k}{x-k}\) .

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Q.732 Let  L  be the set of  n  line segments with the property that three of them can be assembled to form a triangle.

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Peter Cooke

In probability theory and in everyday language we use the word `random' and, for many of us, our first encounter with the word would have been in drawing a name at random from a hat.

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Bob Hart

In probability theory and in everyday language we use the word `random' and, for many of us, our first encounter with the word would have been in drawing a name at random from a hat.

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Jason Middleton

Tsunami in the (Japanese) name given to a very long wave caused by an underwater earthquake or landslide.

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Q.744 Define \(f(x) = \displaystyle\sum_{k=114}^{184}\frac{k}{x-k}\) .

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Q.732 Let  L  be the set of  n  line segments with the property that three of them can be assembled to form a triangle.

Read the article in PDF