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10

Part of 2014 NZMOC Camp Selection Problems

Problems(1)

100 letter words in 2letter languages

Source: New Zealand NZMOC Camp Selection Problems 2014 p10

9/19/2021
In the land of Microbablia the alphabet has only two letters, ‘A’ and ‘B’. Not surprisingly, the inhabitants are obsessed with the band ABBA. Words in the local dialect with a high ABBA-factor are considered particularly lucky. To compute the ABBA-factor of a word you just count the number of occurrences of ABBA within the word (not necessarily consecutively). So for instance AABA has ABBA-factor 00, ABBA has ABBA-factor 11, AABBBA has ABBA-factor 66, and ABBABBA has ABBA factor 88. What is the greatest possible ABBA-factor for a 100100 letter word?
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