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# Climbing 10 Steps - Puzzle for CPT

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 CA CS Prakash Somani (A helpin CA CS B. Com. NCFM (Capital market) [ Scorecard : 21747] Here is one more question on Permutations. Find the number of ways in which you can climb 10 steps if you can go up 1 or 2 steps at a time. __________________ Cheers, CA CS Prakash Somani (A helpin CA CS B. Com. NCFM (Capital market) [ Scorecard : 21747] Here is the answer..(JUST select the below area) at end: The answer for this question is 89. Solution:   Following combination will show the number of 1-step and 2-step jumps needed for completing 10 steps.   (10,0) (8,1) (6,2) (4,3) (2,4) (0,5) Now the question is, "For each of these possibilities, how many ways can the different steps be arranged?". Lets take the first one (10,0). Here only one way to complete the 10 steps. Next (8,1). Here you can get 9 ways to complete the 10 steps. The nine ways are as follows... (2,1,1,1,1,1,1,1,1) (1,2,1,1,1,1,1,1,1) (1,1,2,1,1,1,1,1,1) (1,1,1,2,1,1,1,1,1) (1,1,1,1,2,1,1,1,1) (1,1,1,1,1,2,1,1,1) (1,1,1,1,1,1,2,1,1) (1,1,1,1,1,1,1,2,1) (1,1,1,1,1,1,1,1,2) Like these ways we get the number of way from the following combination. (6,2) - we can get 28 ways. (4,3) - we can get 35 ways. (2,4) - we can get 15 ways. (0,5) - we can get 1 way. So the total number of ways to climbing 10 steps is. 1+9+28+35+15+1 = 89. -----------------------------

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