GATE | GATE-CS-2014-(Set-1) | Question 65

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


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