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4546: Proposed by Heinz-Jürgen Seiffert, Berlin, Germany.
Editors' Note: This problem appeared originally in the December,
1995 issue. Since no solutions were received, the problem remains-"open"
until March 31, 1997.
4590S: Student Problem - only undergraduate and pre-college
students are eligible to submit a solution.
Proposed by J. Sriskandarajah, Richland Center, WI.
4591: Proposed by F.J. Flanigan, San Jose, CA.
4592: Proposed by Richard L. Francis, Cape Girardeau, MO.
Suppose the coordinates of the vertices of a triangle in the plane
are even perfect numbers of two or more digits.
(a) Show that the triangle's centrold has integral coordinates. (b)
Are these coordinates necessarily even?
4593: Proposed by Richard L. Francis, Cape Girardeau, MO.
A thorough number is one which contains each of the ten digits at least
once. Show that the set of thorough primes is infinite.
4594: Proposed by Murray S. Klamkin, Edmonton, AB, Canada.
A circle is inscribed in a quadrilateral. Determine its radius
r
if the lengths of successive tangents from the vertices of the quadrilateral
to the circle are a, a, b, b, c, c, d, d, respectively.
4595: Proposed by William R. Klinger, Upland, IN, generalized
by the editors.
