Question
Laura’s pet bunny, Ghost, hops up a flight of 12 stairs. Ghost can hop up one or two steps at a time, and never hops down. How many ways can Ghost reach the top
Answers
Reiny
number of cases, not worrying about order:
2hops 1 hop
6 0
5 2
4 4
3 6
2 8
1 10
0 12
number of ways each of the above can be arranged
e.g. the 5 double hops and 2 single hops could be
dddddss
sddddds
etc
6 0 --- 1
5 2 -- 7!/(5!2!) = 21
4 4 -- 8!/(4!4!) = 70
3 6 -- 9!/(3!6!) = 84
2 8 -- 10!/(2!8!) = 45
1 10 -- 11!/10!1! = 11
0 12 -- 1
different ways = sum of those = 233
2hops 1 hop
6 0
5 2
4 4
3 6
2 8
1 10
0 12
number of ways each of the above can be arranged
e.g. the 5 double hops and 2 single hops could be
dddddss
sddddds
etc
6 0 --- 1
5 2 -- 7!/(5!2!) = 21
4 4 -- 8!/(4!4!) = 70
3 6 -- 9!/(3!6!) = 84
2 8 -- 10!/(2!8!) = 45
1 10 -- 11!/10!1! = 11
0 12 -- 1
different ways = sum of those = 233