## BdMO National Junior 2009/10

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
Posts: 1004
Joined: Sat Dec 09, 2017 1:32 pm

### BdMO National Junior 2009/10

In a strange language there are only two letters,a and b,and it is postulated that the letter a is a word.Furthermore all additional words are formed according to the following rules:
\$(i)\$ Given any word ,a new word can be formed from it by adding one b at the right hand end.
\$(ii)\$ If in any word a sequence aaa appears ,a new word can be formed by replacing aaa by the letter b.
\$(iii)\$ If in any word a sequence bbb appears ,a new word can be formed by omitting bbb.
\$(iv)\$ Given any word,a new word can be formed by writing down the sequence that constitutes the given word twice.
For example \$(iv)\$, aa is a word and by \$(iv)\$ again aaaa is a word,Hence by \$(ii)\$ ba is a word,and by \$(i)\$, bab is also a word.Again by \$(i)\$ babb is a word,and so by \$(iv)\$ babbbabb is also a word.Finally ,by \$(iii)\$ we fond that baabb is a word.
Prove that in this language baabaabaa is not a word.