FOR CHILDREN

PROBLEM # 1
For how many positive integer values of x is sqrt(120 - x) an integer?

FOR GROWNUPS

PROBLEM # 2
What is the smallest number such that the product of the digits is 10!
(Ten Factorial)

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SOLUTIONS TO PROBLEMS ON 02/08/07

FOR CHILDREN

PROBLEM # 1
The product of 3 brothers' ages is 175. Two are twins. How old is the other one?

SOLUTION
7 years old.

FOR GROWNUPS

PROBLEM # 2
A snug-fitting belt is placed around the Earth's equator.  Suppose you added an extra 1 meter of length to the belt, held it at a point, and lifted until all the slack was gone.  How high above the Earth's surface would you then be?  That is, find h in figure below.

(Assume that the Earth is a perfect sphere of radius 6400 km, and that the belt material does not stretch.)

SOLUTION 
121.6 m. 

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