Latest TCS Aptitude Question SOLUTION: A staircase contains 12 steps. We can climb it 1 or 2 steps. But 8th step contains a snake so we cant step on it. In how many ways can we the top? Please solve this question

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(#M40155031) TCS Numerical Ability question A stair case Keep an EYE

A staircase contains 12 steps. We can climb it 1 or 2 steps. But 8th step contains a snake so we cant step on it. In how many ways can we the top? Please solve this question

Asked In TCS venkatesh ksl (8 years ago)

Solved Manjunath Read Solution (7)

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Manjunath  (8 years ago) Best Solution

it is devided into 3 parts
1. 1-7 step
2. 7-9th step
3. 9-12th step
1-7th step can be reached in 21 ways i.e,,
all 1's step 1 way
(5) 1's and 1 with 2 step 6 ways in that way it is 1+6+10+4 =21 ways
7-9 th step 1 way
and 9-12 3 ways
so 21+1+3=25 ways totally

Is this solution Helpfull? Yes (24) | No (15)  

Manjunath  (8 years ago)

First 7 steps can be reached with
1. all 1's(all single steps)
2. 5 steps with single steps and one with 2 steps
3.3's single and 2 with 2 steps
4.1 single and 3's double
all 1's in only one way i.e.,7!/7!=1
5 with 1's and 1 two is 6!/5!=6
similerly for
3 with 1,s and 2 with 2 steps is 5!/(3!*2!)=10
similerly we have to solve

Is this solution Helpfull? Yes (15) | No (2)  

annu kumari  (8 years ago)

MANJUNATH , would you plz explain how it come 10 in (1+6+10+4)..plz explain

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

jeeva  (8 years ago)

105 ways.
If u want climb n steps with 1 or 2 jumps, then possible ways are = (n+1)th fibo. Number.

First 7 steps can be climbed in 21 ways.
[ since 8 th fibo. Number ].

9-12 th steps ( totally 4 steps ) can b climbed in 5 ways [ 5 th Fibo. No ].

So totally 21*5=105 ways.

Is this solution Helpfull? Yes (7) | No (2)  

Abhishek nkumar  (8 years ago)

@MANJUNATH you are genius man..!!hats off..

Is this solution Helpfull? Yes (4) | No   

S Kannan  (8 years ago)

It is divided into 3 parts 1. 1-7 step 2. 7-9th step 3. 9-12th step
1-7th step can be reached in 21 ways i.e,,
All 1's step + Five 1's and 1 with 2 steps + Three 1’s and two 2 steps + One 1’s and three 2’steps
1 way + 6 ways + 10 + 4
In that way it is 1+6+10+4 =21 ways
7 to 9th step 1 way
All 1's step + one 1’s and one 2 steps
1 way + 2 ways
So 21 x 1 x 3 = 63 ways totally

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

Ritendra Pratap Singh  (4 years ago)

t is devided into 3 parts
1. 1-7 step
2. 7-9th step
3. 9-12th step
1-7th step can be reached in 21 ways i.e,,
all 1's step 1 way
(5) 1's and 1 with 2 step 6 ways in that way it is 1+6+10+4 =21 ways
7-9 th step 1 way
and 9-12 3 ways
so 21+1+3=25 ways totally

Is this solution Helpfull? Yes | No   

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