Latest TCS Aptitude Question SOLUTION: In a staircase, there are 10 steps. A child is attempting to climb the staircase. Each time, she can either make 1 step or 2 steps. In how many different ways can she climb the sta

• Placement Papers
• /
• TCS
• /
• Numerical Ability
• /
• Age Problem

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40012358) TCS Numerical Ability question Keep an EYE

In a staircase, there are 10 steps. A child is attempting to climb the staircase. Each time, she can either make 1 step or 2 steps. In how many different ways can she climb the stair case?
a. 10 b. 21 c. 36 d. None of these.

Asked In TCS sukrati pandey (11 years ago)

Unsolved Read Solution (17)

Is this Puzzle helpful?   (107)   (40) Submit Your Solution Age Problem

Read Solution (17) :

jaya prakash reddy  (11 years ago)

she can go by
1 steps-1 way

that is choosing 1 two-step in 9 moves:
9C1 : 9 ways//

2 two-steps:
choosing 2 two-steps in 8 moves:
8C2 = 28 ways//

3 two-steps
7C3 = 35 ways//

4 two-steps//
6C4 = 15 ways//

5 two-steps//
which covers all the 10 stairs.. that means only one way
2 2 2 2 2 = 1 way//

Adding all the ways:
1 + 9 + 28 + 35 + 15 + 1 = 89 ways//

Is this solution Helpfull? Yes (110) | No (8)  

John Mathew  (9 years ago)

He can go by 1 step or 2 step
So a recurrence relation can be formed as

T(n) = T(n-1) + T(n-2) ;

T(n) is the no of ways for climbing 'n' steps
T(n-1) is the no of ways for climbing 'n-1' steps
T(n-2) is the no of ways for climbing 'n-2' steps

T(1) = 1 and T(2) = 2

T(3) = T(2) + T(1) = 2 + 1 = 3

T(4) = T(3) + T(2) = 3 + 2 = 5

T(5) = T(4) + T(3) = 5 + 3 = 8

T(6) = T(5) + T(4) = 8 + 5 = 13

T(7) = T(6) + T(5) = 13 + 8 = 21

T(8) = T(7) + T(6) = 21 + 13 = 34

T(9) = T(8) + T(7) = 34 + 21 = 55

T(10) = T(9) + T(8) = 55 + 34 = 89 ways//

Is this solution Helpfull? Yes (33) | No (4)  

MUNISH YADAV  (9 years ago)

Using only 1-steps: 1 way
Using only 2-steps: 1 way
Using two 1-steps & four 2-steps: 6!/4!2!=15 ways
Using four 1-steps & three 2-steps: 7!/4!3!=35 ways
Using six 1-steps & two 2-steps: 8!/6!2!=28 ways
Using eight 1-steps & one 2-steps: 9!/8!1!=9 ways
TOTAL : 89 ways

Is this solution Helpfull? Yes (26) | No (1)  

Natarajan. R  (8 years ago)

fibonaaci series logic is very best to solve this problem.
answer is 89

Is this solution Helpfull? Yes (12) | No   

sai spandana  (11 years ago)

ans d none of these

Is this solution Helpfull? Yes (11) | No (11)  

amam  (11 years ago)

ans will be 10

Is this solution Helpfull? Yes (4) | No (31)  

jaya prakash reddy  (11 years ago)

there are 10 steps right so by 1 step climbin all she can go in 1 way.
if she goes by takin one two step and remainin 8 steps by 1 step each..den she can go in 9c1 ways..i.e only 1 two step next 8 one step climbin.
by takin 2 two steps remainin 6 steps can be climbed in 8c2 ways..and so on like tat..3 two steps. :SUKRATI PANDEY

Is this solution Helpfull? Yes (3) | No (4)  

manimehalai  (9 years ago)

ans is not clear enough to understand

Is this solution Helpfull? Yes (2) | No (4)  

Pallavi  (8 years ago)

answer is d
explanation:
For 1st step there is one way
1-1 way
2-2 ways
3-3 ways
4-5 ways
so we can se the ways are in Fibonacci series so the next sequence is,
5-8 ways
6-13 ways
7-21 ways
8-34 ways
9-55 ways
10-89 ways
so the total ways are 89 ways

3-4 ways

Is this solution Helpfull? Yes (2) | No (6)  

prachitrivedi  (11 years ago)

explain properly

Is this solution Helpfull? Yes (1) | No (5)  

sukrati pandey  (11 years ago)

jaya prakash : i got d answer bt plz explain clearly

Is this solution Helpfull? Yes (1) | No (9)  

varun singh  (11 years ago)

for climbing the stair he have 2 option(either one step or two step).
for each step he climbs he will be having 2 opions only to proceed further.
but when he comes on 9th step of the stair he will have only one choice that is only 1 step.and on 10th step of stair case no choice(0)
so total ways will be 2^8+1+0 ways.

Is this solution Helpfull? Yes (1) | No (6)  

gowthami k  (6 years ago)

use fibonacci series -> 1 2 (starting two terms) next terms as 3 5 8 13 21 34 55 89....10 th is 89 so 89 ways

Is this solution Helpfull? Yes (1) | No   

Sampurna Ghosh  (4 years ago)

10 one-step in 10 moves: 10C10 ways = 1 way
1 two-step and 8 one-steps in (1+8)=9 moves: 9C1 ways = 9 ways
2 two-steps and 6 one-steps in (2+6)=8 moves: 8C2 ways = 28 ways
3 two-steps and 4 one-steps in (3+4)=7 moves: 7C3 ways = 35 ways
4 two-steps and 2 one-steps in (4+2)=6 moves: 6C4 ways = 15 ways
5 two-steps 5 moves: 5C4 ways = 1 way

Total number of different ways = 1+9+28+35+15+1=89

Is this solution Helpfull? Yes (1) | No   

poonam yadav  (11 years ago)

10C2+10C1/10C10 =46 (d)

Is this solution Helpfull? Yes | No (17)  

  (3 years ago)

d. none of these because if she climbs 2 steps at a time she will only take 5 times to make it

Is this solution Helpfull? Yes | No   

apoorav  (3 years ago)

D. because the answer will be 89 ways of doing the thing

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.