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February's Problem

 

The average (arithmetic mean) of P and Q is 18, while the average of R, S, and T is 43. What is the average of P, Q, R, S, and T?

 

A solution to this problem will appear along with next month’s problem.

 

January's Problem

 

Bay Street has between 1 and 15 houses, numbered 1, 2, 3, and so on. Mr. Sullivan lives in one of the houses. The sum of all the house numbers less than his equals the sum of all the house numbers greater than his. How many houses are there on Bay Street?

 

Answer is: 8

STRATEGY: Make a table.
Consider the first few houses on a street, then the house Mr. Sullivan might live in, and then the first few houses that come after that.
Beginning of Street Mr. Sullivan End of Street.

Beginning of Street
Mr. Sullivan
End of Street
1 + 2 + 3 = 6
4
5 + 6 = 11…… Too big
1 + 2 + 3 + 4 = 10
5
6 + 7 = 13…… Too big
1 + 2 + 3 + 4 + 5 = 15
6
7 + 8 = 15…… Equal sums

Therefore, there are 8 houses on Bay Street.


FOLLOW-UP: Suppose the product of the house numbers before Mr. Sullivan's is the same as that of the house numbers after his. How many houses are on Bay Street? [10]

 
December's Problem

David has 4 cages of hamsters.
The second cage has ½ as many hamsters as the first.
The third cage has ½ as many hamsters as the second.
The fourth cage has ½ as many hamsters as the third.
What is the smallest number of hamsters David can have?

Answer is: 15

STRATEGY: Work backwards.
To have the smallest number of hamsters, David must have only one hamster
in the fourth cage (we assume all hamsters are whole). If there is one in the
fourth cage, there are two in the third, four in the second, and eight in the first.
The smallest number of hamsters David can have is 8 + 4 + 2 + 1, or 15.

 

For many additional problems we highly recommend the following books:

Math Olympiad Contest Problems for Elementary and Middle Schools by Dr. G. Lenchner
and
Math Olympiad Contest Problems Volume 2 edited by Richard Kalman

are sources of many such problems.

Creative Problem Solving in School Mathematics 2nd Edition by Dr. George Lenchner

can help you to teach solving these types of problems