Question 43436: This problem is really crazy. Here goes
In the alphabet of the primitive ABA tribe there are only two letters, A and B. Moreover many words have the same meaning. There are three rules which can be used to change words without altering their meaning:
a. three consecutive A letters (AAA) can be added or deleted
b. two consecutive B letters (BB) can be added or deleted
c. AAB can be replaced by BA and BA can be replaced by AAB
For example, BAAA and B have the same meaning. How many words with distinct meanings are there in the ABA language?
I would appreciate any help!
Answer by psbhowmick(878)   (Show Source):
You can put this solution on YOUR website! Distinct words with only letter A: A, AA, AAA,
Any more words with A only is not possible e.g. AAAA has same meaning as A, AAAAA has same meaning as AA and so on.
Distinct words with only letter B: B, BB
Any more words with B only is not possible e.g. BBB has same meaning as B, BBBB has same meaning as BB and so on.
Distinct words with A and B: AB, BA
There are 6 number of 3-letter words. Let us analyze each one.
ABA
= AAAB (BA replaced with AAB) = B (AAA deleted) = already existing word
ABB
= A (BB deleted) = already existing word
BAB
= AABB (BA replaced with AAB) = AA (BB deleted) = already existing word
AAB
= AABAAA (AAA added) = AAAABAA (BA replaced with AAB) = ABAA (AAA deleted) = AAABA (BA replaced with AAB) = BA (AAA deleted) = already existing word
BAA
= AABA (BA replaced with AAB) = AAAAB (BA replaced with AAB) = AB (AAA deleted) = already existing word
BBA
= A (BB deleted) = already existing word
Thus no 3 letter words exist which have meanings different than the previously mentioned words. So there is no question of any such distinct words of 4 or more letters.
Hence, all the words with different meanings are: A, AA, AAA, B, BB, AB, BA - 7 words altogether.
I think this is the answer. Let me know if it is or even if it is not. My email id is partha.s.bhowmick@gmail.com
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