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Omni-MATH / The Antarctican language has an alphabet of just 16 letters. Interestingly,…

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problem

The Antarctican language has an alphabet of just 16 letters. Interestingly, every word in the language has exactly 3 letters, and it is known that no word's first letter equals any word's last letter (for instance, if the alphabet were {a,b}\{a, b\} then aaba a b and aaa could not both be words in the language because aa is the first letter of a word and the last letter of a word; in fact, just aaa alone couldn't be in the language). Given this, determine the maximum possible number of words in the language.
Plain-text mathematical notation (without MathML)
The Antarctican language has an alphabet of just 16 letters. Interestingly, every word in the language has exactly 3 letters, and it is known that no word's first letter equals any word's last letter (for instance, if the alphabet were {a,b} then aab and aaa could not both be words in the language because a is the first letter of a word and the last letter of a word; in fact, just aaa alone couldn't be in the language). Given this, determine the maximum possible number of words in the language.
Original LaTeX notation
The Antarctican language has an alphabet of just 16 letters. Interestingly, every word in the language has exactly 3 letters, and it is known that no word's first letter equals any word's last letter (for instance, if the alphabet were $\{a, b\}$ then $a a b$ and aaa could not both be words in the language because $a$ is the first letter of a word and the last letter of a word; in fact, just aaa alone couldn't be in the language). Given this, determine the maximum possible number of words in the language.

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task_id
5fc7a1d5-87ab-5f72-94aa-5f2fc0205bf9
task_key
test--5fc7a1d5-87ab-5f72-94aa-5f2fc0205bf9
task_revision_id
1
config / split
/ test

Official source

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