Problem:
Consider the operation * defined by the following table:
∗123411234224133314244321
For example, 3∗2=1. Then (2∗4)∗(1∗3)=
Answer Choices:
A. 1
B. 2
C. 3
D. 4
E. 5
Solution:
Substituting the values from the table yields
(2∗4)∗(1∗3)=3∗3=4.
Query. Would evaluating the products
((2∗4)∗1)∗3,(2∗(4∗1))∗3,2∗((4∗1))∗3) and 2∗(4∗(1∗3))
yield the same result?
Answer: D.
The problems on this page are the property of the MAA's American Mathematics Competitions