Sheep Talk

Thank you to all who sent in solutions to this problem. Many of you sent in very careful answers to the first 10 words of the sheep talk sequence. Well done Richard and Kevin and all of  you who also spotted the famous sequence of numbers involved.

Here is the solution sent in by Alistair of Histon and Impington School:

A

B

AB

BAB

ABBAB

BABABBAB

ABBABBABABBAB

BABABBABABBABBABABBAB

ABBABBABABBABBABABBABABBABBABABBAB

BABABBABABBABBABABBABABBABBABABBABBABABBABABBABBABABBAB

I noticed all the totals are Fibonacci numbers and the A column is what the B column was last row, and the B column is what the total used to be in the last row. I predict the next numbers will be:

This is because the A's come from the B's in the previous row and the B's come from the A's and B's (the total) in the previous row.