Problem:
Terri produces a sequence of positive integers by following three rules. She starts with a positive integer, then applies the appropriate rule to the result, and continues in this fashion.
Rule 1: If the integer is less than , multiply it by .
Rule 2: If the integer is even and greater than , divide it by .
Rule 3: If the integer is odd and greater than , subtract from it.
A sample sequence:
Find the term of the sequence that begins .
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The sequence is After terms the cycle is repeated. The term is the fifth term of the cycle, and this is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions