Hi Jan,
How many different words can be formed using 1 character?
The answer is 2, they are 0 and 1.
How many different words can be formed using 2 characters?
Each of the two, one character words can be made into two, two character words by appending either a 0 or a 1 to the end. Thus there are 2 × 2 = 2^{2} = 4 two character words.
How many different words can be formed using 3 characters?
Each of the four two character words can be made into two, three character word by appending either a 0 or a 1 to the end. Thus there are 4 × 2= 2^{3} = 8 three character words.
How many different words can be formed using 4 characters?
Each of the eight three character words can be made into two, four character word by appending either a 0 or a 1 to the end. Thus there are 8 × 2= 2^{4} = 16 three character words.
Can you complete the problem now?
Penny
