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Omni-MATH / Let N be the number of ways in which the letters in "HMMTHMMTHMMTHMMTHMMTHMMT" ("HMMT" repeated six times) can be rearranged so that each letter is adjacent to another copy of the …

Problem

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problem

Let NN be the number of ways in which the letters in "HMMTHMMTHMMTHMMTHMMTHMMT" ("HMMT" repeated six times) can be rearranged so that each letter is adjacent to another copy of the same letter. For example, "MMMMMMTTTTTTHHHHHHHHHHHH" satisfies this property, but "HMMMMMTTTTTTHHHHHHHHHHHM" does not. Estimate NN. An estimate of EE will earn ⌊20min(NE,EN)4⌋\left\lfloor 20 \min \left(\frac{N}{E}, \frac{E}{N}\right)^{4}\right\rfloor points.
Plain-text mathematical notation (without MathML)
Let N be the number of ways in which the letters in "HMMTHMMTHMMTHMMTHMMTHMMT" ("HMMT" repeated six times) can be rearranged so that each letter is adjacent to another copy of the same letter. For example, "MMMMMMTTTTTTHHHHHHHHHHHH" satisfies this property, but "HMMMMMTTTTTTHHHHHHHHHHHM" does not. Estimate N. An estimate of E will earn ⌊20min((N)/(E),(E)/(N))⁴⌋ points.
Original LaTeX notation
Let $N$ be the number of ways in which the letters in "HMMTHMMTHMMTHMMTHMMTHMMT" ("HMMT" repeated six times) can be rearranged so that each letter is adjacent to another copy of the same letter. For example, "MMMMMMTTTTTTHHHHHHHHHHHH" satisfies this property, but "HMMMMMTTTTTTHHHHHHHHHHHM" does not. Estimate $N$. An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{N}{E}, \frac{E}{N}\right)^{4}\right\rfloor$ points.

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Source and history

task_id
7a1da9d7-d55c-55b6-8426-f0692ece2a9d
task_key
test--7a1da9d7-d55c-55b6-8426-f0692ece2a9d
task_revision_id
1
config / split
/ test

Official source

initial import