8th grade
posted by rob on .
a rabbit can climb one or two steps at a time on a ten step staircase, but he never goes back down. In how many different ways can the rabbit climb a flight of ten steps

5 2's  one way
4 2's 2 1's  number of ways = 6!/(4!2!) = 15
(e.g. 222211, 11222, 212122, etc )
3 2's 4 1's  number of ways = 7!/(4!3!) = 35
2 2's 6 1's  number of ways = 8!/(2!6!) = 28
1 2 8 1's  number of ways = 9!/(1!8!) = 9
all 1's  one way
total 1+15+35+28+9+1 = 89
Wow for grade 8!!! 
89