PROBLEMS           Vol. 99(3),March 1999

Solutions should be mailed before June 30, 1999. (Solutions sent after that date will be considered as deadlines permit.)
 

4704-S: Student Problem - only undergraduate and pre-college students are eligible to submit a solution.
Proposed by Roger Izard, Dallas, TX.
Given that  derive an algebraic expression in terms of a and b which is
equal to 

4705-OBG: Oldie But Goodie - Proposed by J. F. Howard, San Antonio, TX.
Circumscribe a square about a given convex quadrilateral.

4706: Proposed by V. C. Bailey, Naples, FL.
The verticles  of a regular pentagon ABCDE with side length s lie on one arch of the curve
y = asinx. Find a and s.

4707:Proposed by Richard L. Francis, Cape Girardeau, MO.
The nucleus N of  is the number formed by all the digits preceding the terminal zeros of . For example, is not perfect.

4708: Proposed by Richard L. Francis, Cape Girardeau, MO.
Euclid's inscribed polygon is a constructible polygon inscribed in a circle whose central angle degree measures form a positive integral arithmetic sequence with a non-zero difference.
(a) Show that Euclid's inscribed pentadecagon (15-sided polygon) exists.
(b) Is there a prime number n > 5 such the Euclid's inscribed n-gon exists?
(c) Is there a composite number such that Euclid's inscribed n-gon does not exist?

4709: Proposed by William D. Markel, Hanover, IN.
There are n different numbers availabel for a lottery. Tickets are sold with each number equally likely to be on each ticket. Suppose that n tickets are sold.
(a) determine the probability that exactly k different numbers will appear among the n tickets sold.
(b) On the average, how many different numbers will appear among the n tickets sold?