A pennant is a sequence of numbers, each number being 1 or 2. An -pennant is a sequence of numbers with sum equal to nFor 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 thepennant (2,1).The number of 10-pennants is________Correct answer is '89'. Can you explain this answer? - EduRev Computer Science Engineering (CSE) Question

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A pennant is a sequence of numbers, each number being 1 or 2. An -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 thepennant (2,1). The number of 10-pennants is________

Correct answer is '89'. Can you explain this answer?

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A pennant is a sequence of numbers, each number being 1 or 2. An -penn...

Let we denote number of n-pennants by f(n), so f(10) is number of 10-pennants.

So all 10-pennants can be formed by 8-pennants and 9-pennants, and no other pennant (since we can add only 1 or 2 into a sequence)
So f(10) = f(9) + f(8)
This is in fact a fibonacci sequence, in which F(1) = 1, f(2) = 2, so this sequence becomes
1, 2, 3, 5, 8, 13, 21, 34, 55, 89,..
So f(10) = 89.

Numbers could be any one of
(1,1,1,1,1,1,1,1,1,1),(1,1,1,1,1,1,1,1,2),(1,1,1,1,1,1,2,2),(1,1,1,1,2,2,2),(1,1,2,2,2,2),(2,2,2,2,2)
So, the number of 10 penants =1+ 9!/8! + 8!/6!2! + 7!/4!3! + 6!/2!4! +1 =89

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A pennant is a sequence of numbers, each number being 1 or 2. An -pennant is a sequence of numbers with sum equal to nFor 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 thepennant (2,1).The number of 10-pennants is________Correct answer is '89'. Can you explain this answer?

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