Five Hundred Mathematical Challenges

Five Hundred Mathematical Challenges

Edward J. Barbeau
Murray S. Klamkin
William O. J. Moser
Series: Spectrum
Copyright Date: 1995
Edition: 1
Pages: 238
https://www.jstor.org/stable/10.4169/j.ctt13x0n6v
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  • Book Info
    Five Hundred Mathematical Challenges
    Book Description:

    This book contains 500 problems that range over a wide spectrum of areas of high school mathematics and levels of difficulty. Some are simple mathematical puzzlers while others are serious problems at the Olympiad level. Students of all levels of interest and ability will be entertained and taught by the book. For many problems, more than one solution is supplied so that students can see how different approaches can be taken to a problem and compare the elegance and efficiency of different tools that might be applied.

    eISBN: 978-1-61444-507-4
    Subjects: Mathematics

Table of Contents

  1. Front Matter
    (pp. i-vi)
  2. PREFACE
    (pp. vii-viii)
    E. Barbeau, M. Klamkin and W. Moser
  3. Table of Contents
    (pp. ix-x)
  4. PROBLEMS
    (pp. 1-46)

    Problem 1. The length of the sides of a right triangle are three consecutive terms of an arithmetic progression. Prove that the lengths are in the ratio 3 : 4 : 5.

    Problem 2. Consider all line segments of length 4 with one endpoint on the liney=xand the other endpoint on the liney= 2x. Find the equation of the locus of the midpoints of these line segments.

    Problem 3. A rectangle is dissected as shown in Figure 1, with some of the lengths indicated. If the pieces are rearranged to form a square, what...

  5. SOLUTIONS
    (pp. 47-210)

    Problem 1. The three lengths are of the formad,a,a+dwith (ad)2+a2= (a+d)2. This reduces toa(a− 4d) = 0, ora= 4d. Thus the sides are 3d, 4d, 5d.

    Problem 2. LetA(a, 2a) be an arbitrary point on the liney= 2x, and letB(b,b) be an arbitrary point on the liney=x. The midpoint of segmentABis the point (x,y) with$x=\frac{a+b}{2}$and$y=\frac{2a+b}{2}$, and the length of the segmentABis 4. Hence (a...

  6. THE TOOL CHEST
    (pp. 211-226)

    While the ingenuity of the solver alone will unravel many of the problems in this collection, many others require elementary knowledge in some mathematical area. Herewith is a brief list of “tools” that may be needed; your textbook should provide fuller details of those facts you do not wish to (or cannot) verify yourself.

    A 1. “rfactorial”

    r! =r(r− 1) · … · 2 · 1

    is the number of ways of listing (in order)rdistinct objects.

    A 2. “nchooser\[\left( \begin{matrix} n \\ r \\ \end{matrix} \right)=\frac{n(n-1)\ldots (n-r-1)}{1\cdot 2\cdot \ldots \cdot r}\]is the number of ways of choosing r objects from amongndistinct...

  7. Index of Problems
    (pp. 227-227)