Problem:
For any three real numbers a, b, and c, with bξ =c, the operation Ξ¨ is defined by:
Ξ¨(a,b,c)=bβcaβ.
What is Ξ¨(Ξ¨(1,2,3),Ξ¨(2,3,1),Ξ¨(3,1,2))?
Answer Choices:
A. β21β
B. β41β
C. 0
D. 41β
E. 21β
Solution:
Because
Ξ¨(1,2,3)Ξ¨(3,1,2)β=2β31β=β1,Ξ¨(2,3,1)=3β12β=1, and =1β23β=β3β
we have
Ξ¨(Ξ¨(1,2,3),Ξ¨(2,3,1),Ξ¨(3,1,2))β=Ξ¨(β1,1,β3)=1β(β3)1β=β41β.β
Answer: Bβ.
The problems on this page are the property of the MAA's American Mathematics Competitions