There is A staircase having n steps (odd or even). A person standing at the base Can take one or two-steps at a time. My query is in how many ways can The stairs can be climbed?

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  • Jul 15th, 2005

With Two Legs

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  • Aug 8th, 2005

Two Ways 
Take 1 step 
Take 2 step 

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  • Aug 10th, 2005

SIGMA (n-x){B}C{/B}(x) 
where x ranges from  
0 to n/2 when n is even 
0 to (n-1)/2 when n is odd 
nCr is nothing but the number of combinations of n different things taken r at a time, which = n!/(n-r)! r! 
Ex 1: n=5 
since n is odd x ranges from 0 to (5-1)/2 i.e., from 0 to 2 
applying the above formula, answer is 5C0 + 4C1 + 3C2 = 1 + 4 + 3 = 8 ways 
Ex 2: n=8 
x ranges from 0 to 4 
answer is 8C0 + 7C1 + 6C2 + 5C3 + 4C4 = 1 + 7 + 15 + 10 + 1 = 34 ways

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  • Aug 22nd, 2005


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  • Sep 9th, 2005

only one way by steping in stairs

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  • Sep 12th, 2005

the person can go in two steps

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  • Sep 16th, 2005

ans: 1* N + 2*N = 3N ways

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pradeep narra

  • Jan 5th, 2006

If f(n) is the number of ways to climb n steps;



then f(n)=f(n-1)+f(n-2);

this is nothing but a fibonacci series 1,2,3,5,8,13,21,34,  and so on


  • Jul 6th, 2006

by n ways.

Suppose n=2 then one can go by 2 ways taking 1 step at a time or taking 2 at a time when n=3 then by 3 ways ....... so for n stairs one can go by n ways.

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  • Sep 24th, 2006

nC1+nC2 ways

i.e.. in [n(n+1)] /2 ways. As the action here is not simultaneous we add both the possibilities.


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  • Dec 6th, 2009

This can be solved easily by considering an analogy.
Cansider two steps as one step......
Then there are totally n/2 steps.
Now He has to land on every step(new step-doubled) because he cannot take more than two steps at a time.
Now either one or two steps can be selected in a (newer) step in 2C1 +2C2 ways...
Total No. of ways to climb is n/2*(2C1+2C2) ways...

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  • Feb 7th, 2010

A person can take 1 or 2 steps at a time and steps..

   Odd = 1 step
   Even = 2 steps
   so the ways are
  1.         1s     1s
  2.         1s     2s
  3.         2s     1s
  4.         2s     2s
     so Four (4) ways.

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It depends on odd number or even number if its 4 then
so 1+1+3+3
answer is 8 which is 2n of given number

odd 3
so 1+2+1=4
which is n+1
so answer is canot predict

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  • Mar 27th, 2012

Ans is Fibonacci series.... if its n steps., then its n+1th fibo no.

Its not the n+1th fibonacci no., the ans is nth fibanacci no.
for eg:-
if no of steps is 3 then n=3
if no of steps is 4 then n=5
if no of steps is 5 then n=8
for 6 n=13
for 7 n=21
for 8 n=34 and so on...

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