document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=43436>Question 43436</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This problem is really crazy. Here goes\r<BR>\n" );
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document.write( "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: <BR>\n" );
document.write( "a. three consecutive A letters (AAA) can be added or deleted<BR>\n" );
document.write( "b. two consecutive B letters (BB) can be added or deleted<BR>\n" );
document.write( "c. AAB can be replaced by BA and BA can be replaced by AAB\r<BR>\n" );
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document.write( "For example, BAAA and B have the same meaning. How many words with distinct meanings are there in the ABA language? \r<BR>\n" );
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document.write( "I would appreciate any help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #28459 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=28459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Distinct words with only letter A: A, AA, AAA, \r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Distinct words with only letter B: B, BB \r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Distinct words with A and B: AB, BA \r<BR>\n" );
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document.write( "There are 6 number of 3-letter words. Let us analyze each one.<BR>\n" );
document.write( "ABA <BR>\n" );
document.write( "= AAAB (BA replaced with AAB) = B (AAA deleted) = already existing word\r<BR>\n" );
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document.write( "ABB <BR>\n" );
document.write( "= A (BB deleted) = already existing word\r<BR>\n" );
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document.write( "BAB <BR>\n" );
document.write( "= AABB (BA replaced with AAB) = AA (BB deleted) = already existing word\r<BR>\n" );
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document.write( "AAB <BR>\n" );
document.write( "= AABAAA (AAA added) = AAAABAA (BA replaced with AAB) = ABAA (AAA deleted) = AAABA (BA replaced with AAB) = BA (AAA deleted) = already existing word\r<BR>\n" );
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document.write( "BAA <BR>\n" );
document.write( "= AABA (BA replaced with AAB) = AAAAB (BA replaced with AAB) = AB (AAA deleted) = already existing word\r<BR>\n" );
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document.write( "BBA <BR>\n" );
document.write( "= A (BB deleted) = already existing word\r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "Hence, all the words with different meanings are: A, AA, AAA, B, BB, AB, BA - 7 words altogether.<BR>\n" );
document.write( "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 </SPAN>\n" );
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