Counting Your Ancestors Is Easy, If This Doesn't Happen

In the fifth generation we have $2 ^ 5$ ancestors

In the fourth generation as each previous ancestor had only one child we have to the number of people from that generation is $\dfrac{2 ^ 5}{2} = 2 ^ 4$

In the third generation, similarly we have $2 ^ 3$ ancestors

In the second generation we have $2 ^ 2$ ancestors

And finally, in the first generation we have $2$ ancestors

Note: we considered the previous generations and Zilly is not an ancestor.

Soon we have

$2+2^2+2^3+2^4+2^5=(1+2+2^2+2^3+2^4+2^5)-1=(2^6-1)-1=63-1=62$ ancestors.

I doubled the amount all the way up to the 5th generation and then I added all the numbers that I found. So it was 2+4+8+16+32 which gave me a total of 62. I dont think it was the "smartacular" way but I just wanted to share how I got my answer.

Its a geometric sequence with first term(x)=2, number of terms(n)=5 and common rate(r)=2 * since for every parent we have 2 grandparents(given the condition of no inbreeding)*. The formula for this is x{(1-r^n)/(1-r)}, if you followed PEMDAS you'll get 62 by substituting the givens. :)

by counting the nos in pic

This problem seems overrated... Just saying..

You have a family tree with two parents. Each parent gave birth to two children. It repeats with these children, over, and over, and over, again. (observe the picture)

So you have: $2$ , which is from the two great parents (let's just leave it at that) and two + two babies, from the above description, which is $2^2$ . Hmmm.... If we continue, and these four 'parents' go on to create two babies each, it becomes $8$ , or $2^3$ . It continues on until we reach five generations.

So our answer is, by adding up the ancestors, or "parents", we get $2+4+8+16+32$ , which is $2+20+40$ , which is finally $\boxed{62} \textbf{ Ans.}$

It's a really simple geometric progression that goes multiplying by 2

SIMPLY , a progression of 32, 16, 8... so on till 2 ... find the sigma. is 62

for father 2.....for grandfather 2 2.....for great grandfather 4 2......then 8 2+16 2.sum=62