Isabel was making rectangular strips 2 units wide using 2 x 1 tiles. She was interested in the number of different strips of each length she could make.
The attached image shows some of her examples arranged according to the units of length. All strips are different even though some are just reflections
Isabel noticed that the number of ways of making strips followed a pattern: The number of strips n units long is alwasy the sum of the numbers of strips of the two previous lengths. eg: Wn is the nuber of strips of length n, W4=W3+W2 Ingeneral her guess is that : W1=1, W2=2 and Wn=W(n-1) +W(n-2) when n is greater than or equal to 3
a)Explain why isabels guess is true
b) isabel experimented with 3x1 tiles, making strips 3 units wide. Finda formula, similar to that above for the number of strips of length n
c) Find a similar formula for the number of ways of making strips of width m and lenght n from mx1 tiles
please help. much help is very appreciated. Thanks in advance