15 replies to this topic

[ujjagrawal]

There is a staircase with 10 steps. A child runs up the steps, either 1 step or 2 steps with each stride. How many different ways can the stairs be climbed by him?

[hhh3]

Spoiler for

one way.... he can either run up the stairs or walk .. lol

[hhh3]

Spoiler for

one way.... he can either run up the stairs or walk .. lol ... no sorry that makes it two...

easy answer... if u want to rest ur brain

[MouseMan]

I'm guessing around 75?

[MouseMan]

Either way, hh3 got it wrong with his answer. There was not one way as explained by him, but 2 ways.

[Peekay]

Spoiler for

Unless I missed something...
All 1 steps - 1 way
One 2 step - 8 ways
Two 2 steps - 6 ways
Three 2 steps - 4 ways
Four 2 steps - 2 ways
Five 2 steps - 1 way

Total = 22 ways

[hhh3]

Either way, hh3 got it wrong with his answer. There was not one way as explained by him, but 2 ways.

dude... look at the spoiler in my second post... hi hi.. but the answer still could me wrong..bt anyways..

[MikeD]

Spoiler for

I would say 89 because

1 1 1 1 1 1 1 1 1 1 (only 1 combination)
1 1 1 1 1 1 1 1 2 (9 combinations)
1 1 1 1 1 1 2 2 (28 combinations)
1 1 1 1 2 2 2 (35 combinations)
1 1 2 2 2 2 (15 combinations)
2 2 2 2 2 (only 1 combination)

[witzar]

Spoiler for

Let F(n) be the number of different ways staircase of n steps can be climbed.
You can start either with 2 steps (and n-2 remaining) or with 1 step (and n-1 remaining),
which leads to a recurrence relation:
F(n) = F(n-1) + F(n-2)
Obviously
F(0) = 1, F(1),
and
F(n+2) = F(n) + F(n+1)
so you are looking for 10th Fibonacci number, which is 89.

[Peekay]

Spoiler for

Unless I missed something...
All 1 steps - 1 way
One 2 step - 8 ways
Two 2 steps - 6 ways
Three 2 steps - 4 ways
Four 2 steps - 2 ways
Five 2 steps - 1 way

Total = 22 ways

Not only did I miss something, I missed a lot - combinations of the 2 step options! The actual ways would be much more.