Problem:
Many calculators have a reciprocal key that replaces the current number displayed with its reciprocal. For example, if the display is and the key is depressed, then the display becomes . If is currently displayed, what is the fewest number of times you must depress the key so the display again reads
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Depressing the key one time yields the reciprocal of or . Thus depressing the key a second time yields the reciprocal of or .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions