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Omni-MATH / Michel starts with the string HMMT. An operation consists of either replacing an occurrence of H with HM, replacing an occurrence of MM with MOM, or replacing an occurrence of T wi…

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problem

Michel starts with the string HMMTH M M T. An operation consists of either replacing an occurrence of HH with HMH M, replacing an occurrence of MMM M with MOMM O M, or replacing an occurrence of TT with MTM T. For example, the two strings that can be reached after one operation are HMMMTH M M M T and HMOMTH M O M T. Compute the number of distinct strings Michel can obtain after exactly 10 operations.
Plain-text mathematical notation (without MathML)
Michel starts with the string HMMT. An operation consists of either replacing an occurrence of H with HM, replacing an occurrence of MM with MOM, or replacing an occurrence of T with MT. For example, the two strings that can be reached after one operation are HMMMT and HMOMT. Compute the number of distinct strings Michel can obtain after exactly 10 operations.
Original LaTeX notation
Michel starts with the string $H M M T$. An operation consists of either replacing an occurrence of $H$ with $H M$, replacing an occurrence of $M M$ with $M O M$, or replacing an occurrence of $T$ with $M T$. For example, the two strings that can be reached after one operation are $H M M M T$ and $H M O M T$. Compute the number of distinct strings Michel can obtain after exactly 10 operations.

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Source and history

task_id
0e24f124-67dc-55b5-bfc5-19b12014f996
task_key
test--0e24f124-67dc-55b5-bfc5-19b12014f996
task_revision_id
1
config / split
/ test

Official source

initial import