Solution to 4:
It helps to have a list of Fibonacci numbers in front of you when you start:
| 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 |
If you always use the biggest ones you can, they will also be non-consecutive (no two together)
a. 48 = 34 + 13 + 1
| 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 |
The biggest Fibonacci less than 48 is 34, so we will use that: 48=34+???
48-34=14. The biggest Fibonacci less than 14 is 13, so we will use that: 48=34+13+???
14-13=1 which is a Fibonacci number, so we use it to end our sum: 48 = 34 + 13 + 1
b. 41 = 34 + 5 + 2
| 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 |
The biggest Fibonacci less than 41 is 34, so we will use that: 41=34+???
41-34=7. The biggest Fibonacci less than 7 is 5, so we will use that: 41=34+5+???
7-5=2 which is a Fibonacci number, so we use it to end our sum: 41 = 34 + 5 + 2
c. 29 = 21 + 8
| 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 |
d. 33 = 1 + 3 + 8 + 13 + 21
| 1 | 2 | 3 | 5 | 8 | 13 | 21 | 34 |