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?
2007-03-03 10:58:26 · 10 answers · asked by Bob G 3 in Education & Reference ➔ Trivia
Everybody except me is wrong. Doesn't anybody see that this equation is a fibonacci sequence.
All you have to do is to find out the first two way Ghost can go up the steps. The first way he can only go up is one way. (1-1)
The second way he can go up two steps. (1-1,0-2)
Now that you have the first two steps just add the second step to the first step all the time and you get this.
1
2
3
5
8
13
21
34
55
89
144
The answer is 144.
2007-03-04 00:17:52 · answer #1 · answered by encikus 2 · 0⤊ 0⤋
Hmmm ... let's see. First figure out how many combinations of one-step and two-step hops are possible. To make things simpler, call a one-step hop a "single" and a two-step hop a "double".
12 singles OR
10 singles + 1 double OR
8 singles + 2 doubles OR
6 singles + 3 doubles OR
4 singles + 4 doubles OR
2 singles + 5 doubles OR
6 doubles.
Now, figure how how many permutations are possible for each combination of types.
For either 12 singles, or 6 doubles, only one permutation is possible.
For 10 singles plus one double, there are 11 possible permutations:
10 singles, then 1 double
9 singles, then 1 double, then 1 single
8 singles, then 1 double, then 2 singles
7 singles, then 1 double, then 3 singles
6 singles, then 1 double, then 4 singles
etc. etc. , ending with ...
1 double, followed by 10 singles
... equals eleven possible permutations.
The formula for figuring out the total permutations is
(S+D)! / ((S!) * (D!))
... where S is the number of single hops and D is the number of double hops.
12 singles = 1 way
10 singles + 1 double = 11 ways
8 singles + 2 doubles = 45 ways
6 singles + 3 doubles = 84 ways
4 singles + 4 doubles = 70 ways
2 singles + 5 doubles = 21 ways
6 doubles = 1 way
TOTAL: 233 different ways
2007-03-03 21:38:57 · answer #2 · answered by jackalanhyde 6 · 0⤊ 0⤋
Hm Hm Hm your confusing me.... Im blond and i get confused very easily maybe this isn't the greatest section for me to be in!!!!
When i was reading your question i was getting all cross eyed and sooo confused. If you watched this season of Beauty and the Geek you know when Jenny Lee first met Niels and he was telling her about the clock thing or whatever it was she was going cross eyed, and also when she was interviewing that author she was doing it again... well thats what i do when i hear something.
Tell your math teacher that he should use questions that even a blind could answer... im so glad im not in your math class (by the way im just passing mine how im passing im not puite sure but oh well)
2007-03-03 21:45:18 · answer #3 · answered by it's me 3 · 0⤊ 0⤋
well you got to consider that Ghost doesn't have to hop the same way all the way up so 12!/2 which would be 239,500,800
2007-03-03 20:56:08 · answer #4 · answered by sarahanne_2001 2 · 0⤊ 0⤋
TWO WAYS:
1ST WAY: JUST HOP ONE STEP AT A TIME
2ND WAY: IF U WANNA GO FAST JUST HOP OVER 2 STEPS
2007-03-03 20:14:59 · answer #5 · answered by faileider_lucky7 2 · 0⤊ 0⤋
8 ways
2007-03-03 19:38:05 · answer #6 · answered by gone 3 · 0⤊ 0⤋
100 ways because she could go 1 then 2
or 2 then 1 or 2211or 1122 or 1111222 or 222111 or 11112222 or 22221111 or 1111122222 or 1122211222 and so on
2007-03-03 22:07:10 · answer #7 · answered by carmen111 2 · 0⤊ 0⤋
only two b.cause one by one thats ONE and two by two thats another One so its 2 two
2007-03-03 20:10:48 · answer #8 · answered by Anonymous · 0⤊ 0⤋
im not really sure but i think i might be 479001600
i just did 1x2x3x4x5x6x7x8x9x10x11x12
2007-03-03 21:17:03 · answer #9 · answered by bekk 1 · 0⤊ 0⤋
hopping, duh!
2007-03-03 19:44:58 · answer #10 · answered by Anonymous · 0⤊ 1⤋