FOR CHILDREN

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

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?

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SOLUTIONS TO PROBLEMS ON 02/09/06

FOR CHILDREN

PROBLEM # 1
Ram is 20% older than Shyam, and Shyam is 40% younger than Bhim. The sum of their ages is 23.2 years. How old will Ram be on his next birthday? 

SOLUTION
8 years.

FOR GROWNUPS

PROBLEM # 2
The expression
(x+y+z)^2006 + (x-y-z)^2006
is simplified by expanding it and combining like terms. How many terms are in the simplified expression? 

SOLUTION
1,008,016.

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