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    Olympiad Education
    Apr 03, 2021

    One question for the teacher

    in Euclid Math Contest

    why did we have to multiple 2 by the count of the string containig three ABBA in last exaxmple of last class?

    1 answer0 replies
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    1
    Olympiad Education
    Apr 03, 2021

    because ABBABBABBA contans three substrings ABBAs

    so it was included three times in the orginal count 448:

    ABBAxxxxxx

    xxxABBAxxx

    xxxxxxABBA

    we only can keep one in our counting so we have to subract two times the number of ABBABBABBA. Similiarly, strings containing two ABBAs with overlap and strings contaiinng two ABBAs without overlap were included in the orginal 448 for two times, so we only subscract once. 448-23-20-2*1 = 393


    This question is a very good question to practice how to remove overcounts.



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