FOR CHILDREN

PROBLEM # 1
The Math Team in Addville traveled to Subtractville for a math competition.  The bus averaged 40 mph from Addville to Subtractville but averaged 60 mph during the return trip.  What was the average speed of the bus for the entire trip?

FOR GROWNUPS

PROBLEM # 2
Find the integral of the function sqrt(1 + 1/(x^2/3)) from 0 to 8.

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SOLUTIONS TO PROBLEMS ON 02/23/06

FOR CHILDREN

PROBLEM # 1
How many sets of two or more consecutive positive integers have a sum of 15?

SOLUTION
3.

FOR GROWNUPS

PROBLEM # 2
A bug starts at one vertex of a cube and moves along the edges of the cube according to the following rule. At each vertex the bug will choose to travel along one of the three edges emanating from that vertex. Each edge has equal probability of being chosen, and all choices are independent. What is the probability that after seven moves the bug will have visited every vertex exactly once?

SOLUTION
4/729.

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