Copyright © University of Cambridge. All rights reserved.
'Sheep Talk' printed from http://nrich.maths.org/
In sheep talk the only letters used are B and A. Sequences of words
are formed as follows:
The first word only contains the single letter A.
To get the next word in the sequence change each A in the previous
word into B and each B in the previous word into AB.
Write down the first ten words in this sequence.
Count the number of A's in each word in the sequence. Then count
the number of B's in each word in the sequence. Finally count the
number of letters in each word in the sequence. You now have three
sequences of numbers. What do you notice? Will the same patterns
continue if you generate longer sequences of words?