Problem:
By inserting parentheses, it is possible to give the expression
several values. How many different values can be obtained?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The three operations can be performed in any of orders. However, if the addition is performed either first or last, then multiplying in either order produces the same result. Thus at most distinct values can be obtained. It is easily checked that the values of the four expressions
are in fact all distinct.
The problems on this page are the property of the MAA's American Mathematics Competitions