Problema Solution
A male bee is born from an unfertilized egg, a female bee from a fertilized one. in other words, a male bee only has a mother whereas a female bee has a mother and father.How many total ancestors does a male bee have going back 10 generations.(try drawing a diagram to help organize this problem's information.)
Answer provided by our tutors
Let's begin with the male bee or male bee.
Going back 1 generation, we see he has 1 ancestor, a female.
Going back to the 2nd generation there are 2 ancestors a male and female.
Going back to the 3rd, there are 3 ancestors, 2 females and 1 male.
Going back to the 4th generation there are 5 ancestors, 3 females and 2 males.
Going back to the 5th generation there are 8 ancestors, 5 female and 3 male.
We see a pattern emerge:
For each generation we go back, the total number of ancestors is the sum of the 2 subsequent generations, which is the famous Fibonacci sequence, given recursively by:
F(n + 1) = F(n) + F(n - 1)
where F(0)=0, F(1)=1
Interestingly, the number of females and males in any previous generation is itself a Fibonacci number. To find the total number of ancestors for the male bee going back 10 generations, we can make use of an identity for Fibonacci numbers:
(F(0) + F(1) + ...+ F(n)) = F(n + 2) - 1
The sum we need is:
F(2) + F(3) + ...+ F(11) = F(0) + F(1) + ....+ F(11) - 1 = F(13) - 1 - 1 = F(13) - 2 = 233 - 2 = 231
So we find the male bee has a total of 231 ancestors going back 10 generations.