6. (10 points) The sequence $1,1,2,3,5,8, \cdots$ is such that each term from the second onward is equal to the sum of the two preceding terms, forming the Fibonacci sequence. Each term in this sequence is called a Fibonacci number. It can be proven that "any positive integer $n$ can be expressed as the sum of several different Fibonacci numbers." How many ways are there to express 100 as the sum of several different Fibonacci numbers? (Different orders of the addends are considered the same method)
【Solution】Solution: First, list out the Fibonacci numbers less than 100. $1,1,2,3,5,8,13,21,34,55$, 89.
(1) $100=89+3+8$
(2) $=89+1+2+8$
(3) $=89+1+2+3+5$
(4) $=55+34+1+2+3+5$
(5) $=55+34+1+2+8$
(6) $=55+34+3+8$
(7) $=55+13+21+1+2+3+5$
(8) $=55+13+21+3+8$
(9) $=55+13+21+1+2+8$

Therefore, the answer is: 9