Challenging Puzzles - There is A staircase having n steps (odd or even). A person standing at the base Can take one or two

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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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Last Update: August 08, 2008

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July 15, 2005 06:51:13

Rajesh

RE: There is A staircase having n steps (odd or even). A person standing at the base Can take one or two...

With Two Legs

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August 08, 2005 10:44:17

Pooja

RE: There is A staircase having n steps (odd or even). A person standing at the base Can take one or two...

Two Ways

Take 1 step
Take 2 step

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August 10, 2005 17:48:50

Vasanth

RE: There is A staircase having n steps (odd or even). A person standing at the base Can take one or two...

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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August 22, 2005 01:43:49

murali

RE: There is A staircase having n steps (odd or even). A person standing at the base Can take one or two...

nC1+nC2

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September 09, 2005 07:39:15

G.R.Venkatesh

RE: There is A staircase having n steps (odd or even). A person standing at the base Can take one or two...

only one way by steping in stairs

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September 12, 2005 11:43:50

pramod

RE: There is A staircase having n steps (odd or even). A person standing at the base Can take one or two

the person can go in two steps

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September 16, 2005 03:56:53

PALLAV PARIKH

RE: n steps, at a time one or two steps climb

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

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January 05, 2006 10:51:03

pradeep narra

RE: There is A staircase having n steps (odd or even)....

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

f(1)=1;

f(2)=2;

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

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July 06, 2006 13:48:09

Ravindra

RE: There is A staircase having n steps (odd or even)....

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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September 24, 2006 08:47:48

#10

shalini

RE: There is A staircase having n steps (odd or even)....

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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