Number Bars and Fibonacci

Below are Numbers Bars used to create different lengths. By using only 1s and 2s, how many different ways can you make a line of 10 units long?

How many different ways you can make a line of "15" units long if there is no 1s available?

Solutions

Part 1

You may have heard of the Fibonacci numbers will notice that the totals are the Fibonacci sequence, starting at the 2nd "1" in the sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Part 2

When there is not a "1" Number Bar available, the number sequence actually became the Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, ...

Further Reading