**The Stairs Riddle - 17 July**

You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

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You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

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For 1 step we have one option. 1 step

ReplyDeleteFor 2 Steps we have 2 options 1,1 or 2

For 3 steps we have 3 options

1,1,1

2,1

1,2.

The important thing to note is that we must always go up in 2 or 1 steps. So the final step is always 1 step or 2.

So if Fn is the number of ways to climb ten stairs the final steps will alays be Fn=Fn-1 + Fn+2. This is the fibonachi sequence. It must have seed values that F1=1 and F2=1

So F3=F3-1 +F3-2 so F3=F2+F1 f3=1+1 =2

sO

f1=1

F2=1 The answer for 1 stairs

F3=2 the answer for 2 stairs

f4=3 the answer for 3 stairs

similarly then the answer for 10 stairs will be equal to F11 which is equal to the tenth plus the 9th fibonachi numbers.

F11=F10+F9

f11=34+55

F11=89 the number of possible combinations.