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Omni-MATH / Suppose two distinct competitors of the HMMT 2021 November contest are chosen…

Problem

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problem

Suppose two distinct competitors of the HMMT 2021 November contest are chosen uniformly at random. Let pp be the probability that they can be labelled AA and BB so that AA 's score on the General round is strictly greater than BB 's, and BB 's score on the theme round is strictly greater than AA 's. Estimate P=⌊10000p⌋P=\lfloor 10000 p\rfloor. An estimate of EE will earn ⌊20min(AE,EA)6⌋\left\lfloor 20 \min \left(\frac{A}{E}, \frac{E}{A}\right)^{6}\right\rfloor points.
Plain-text mathematical notation (without MathML)
Suppose two distinct competitors of the HMMT 2021 November contest are chosen uniformly at random. Let p be the probability that they can be labelled A and B so that A 's score on the General round is strictly greater than B 's, and B 's score on the theme round is strictly greater than A 's. Estimate P=⌊10000p⌋. An estimate of E will earn ⌊20min((A)/(E),(E)/(A))⁶⌋ points.
Original LaTeX notation
Suppose two distinct competitors of the HMMT 2021 November contest are chosen uniformly at random. Let $p$ be the probability that they can be labelled $A$ and $B$ so that $A$ 's score on the General round is strictly greater than $B$ 's, and $B$ 's score on the theme round is strictly greater than $A$ 's. Estimate $P=\lfloor 10000 p\rfloor$. An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{A}{E}, \frac{E}{A}\right)^{6}\right\rfloor$ points.

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Source and history

task_id
0b9440fc-8921-5d81-83af-81cd1ad15dcc
task_key
test--0b9440fc-8921-5d81-83af-81cd1ad15dcc
task_revision_id
1
config / split
/ test

Official source

initial import