Problem:
An equilateral triangle is originally painted black. Each time the triangle is changed, the middle fourth of each black triangle turns white. After five changes, what fractional part of the original area of the black triangle remains black?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Since turns white, it follows that remains black after the first change. After the second change, of the remaining stays black, or remains black. Thus, after the fifth change, the amount remaining black is
of the original area.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions