PROBLEMS           Vol. 99(8),December 1999

4681-OBG: Oldie But Goodie - Proposed by Daniel Kreth, Wellman, IA. If x be any prime number except 2, the intergral part of  , diminished by 2 is divided by 4x.
As no solutions were received, the problem remains open.
 

4727: Propsed by C. W. Yang, Clarion, PA. (edited)
Joe Dimagio hit 0.357 in the 1941 season when he hit in 56 consecutive games. Assume eaach at-bat was independent of other at-bats and tthe probability of a hit waas 0.357. Find the probability of a 56-game hitting strak assuming

i)    there were four at-bats per game.
ii)   Find the same probability assuming the number of at-bats each game is a Poisson random variable with mean 

4728: Student Problem - Only undergraduate and pre-college students are eligible to submit a solution.
Proposed by the editor.
The integer 235 is an "additive" three digit number because 2 + 3 = 5. The integer 624 is a "subtractive" three digit number because 6 - 2 = 4. Given a three digit integer n where  with a, b, and c are digits (a is not equal to zero).

a)  how many additive three digit numbers are there?
b)  how many three digit numbers are additive or subtractive?
c)  how many base b three digit numbers are additive or subtractive?

4729: Given the quadratic equation  where all coefficients are real. Let p and n be the solutions to the quadratic equation where

Are there values of a, b, and c such that p and n are real numbers and the four points (a,b), (b,c), (c,a), and (p,n) are the vertices of a square? If there are such values, find them.
Proposed by the editor.