ternary tree

Question

a full 3-ary tre with 100 vertices have 

a)57 leaves b) 67 leaves c)77 leaves  d) 87  leaves

Comments

tell me answer plz wheather i am correct or not

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correct as per the given ans key

Answer 1

Let $n$ is the height of tree.

No of vertices $=100$
$3^0+3^1+3^2+...+3^{n-1}+3^n=100$

$\frac{1-3^{n+1}}{1-3} =100$

$3^{n+1} =201$

leaves, (at height $n$)$= 3^n =67$

Answer 2

answer will be 67

to find that their is no hard rule .i derive this by using my intuition  by taking condition

like as n/2= x

then find   ceiling function of x/3 and said to be y

then do x+y and got your answer

where n is no of vertices  lets take our question for n=100 then u find x=n/2 so which is 50

then find y which is ceiling of  x/3 so 50/3 =17=y so 

then x+y= 50+17=67 answer