FOR CHILDREN

PROBLEM # 1
You have a large number of iron balls, all exactly two inches in diameter, that you need to move. You need to pack them into a large wooden rectangular crate that is 24.9 inches long, 22.8 inches wide, and 14 inches deep. What is the greatest number of the balls that can be packed into the crate?

FOR GROWNUPS

PROBLEM # 2
For 0 < x <2 pi, what is the sum of all values of x that satify the equation:
sin(2x) = cos(x).

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SOLUTIONS TO PROBLEMS ON 12/29/05

FOR CHILDREN

PROBLEM # 1
If the difference of two numbers is 9 and their product is 14, what is the
sum of the squares?

SOLUTION
109.

FOR GROWNUPS

PROBLEM # 2
Given f(x) = (x-a) (x-b)^2 ln(x^c) and 1<a<b<c
For what values of x is f(x) positive?

SOLUTION
0<x<1 or x>a.

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