A pennant is a sequence of numbers, each number being 1 or 2. An n-pennant is a sequence of numbers with sum equal to n. For example, (1,1,2) is a 4-pennant. The set of all possible 1-pennants is {(1)}, the set of all possible 2-pennants is {(2), (1,1)} and the set of all 3-pennants is {(2,1), (1,1,1), (1,2)}. Note that the pennant (1,2) is not the same as the pennant (2,1). The number of 10-
pennants is ______________.
(A) 88.9 to 89.1
Answer: (A)
Explanation:
1-pennant {(1)} - #1
2-pennant {(1,1),(2)} - #2
3-pennant {(1,1,1),(1,2),(2,1)} - #3
4-pennant {(1,1,1,1),(2,2),(1,1,2),(1,2,1),(2,1,1)} - #5
5-pennant {(1,1,1,1,1),(2,1,1,1),(1,2,1,1),(1,1,2,1),
(1,1,1,2),(2,2,1),(2,1,2),(1,2,2)} - #8
If one observe carefully they are the terms(part of) a Fibonacci series. (0,1,1,2,3,5,8,13 ….). Hence the # of 10-pennant is the 12th term of the series ie. 89
Quiz of this Question