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The positive integer 4 can be represented as a sum of 1's or 2's in
five ways, such as 1 + 2 + 1 and 1 + 1 + 2. Show all the ways that
the positive integer 5 can be represented as a sum of 1's or 2's.

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I can express 5 the following way

a)all 1's no 2's --- that's 1 way

b)three 1's one 2 --- thats' 4 ways
(the 2 can be in 4 different places, eg
1+1+2+1 or 1+2+1+1)

c) two 2' and one 1 --- that's 3 ways

which is a total of 8

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