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Omni-MATH / Let A₁,A₂,…,A_(m) be finite sets of size 2012 and let B₁,B₂,…,B_(m) be finite sets of size 2013 such that A_(i)∩B_(j)=∅ if and only if i=j. Find the maximum value of m.

Problem

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problem

Let A1,A2,…,AmA_{1}, A_{2}, \ldots, A_{m} be finite sets of size 2012 and let B1,B2,…,BmB_{1}, B_{2}, \ldots, B_{m} be finite sets of size 2013 such that Ai∩Bj=∅A_{i} \cap B_{j}=\emptyset if and only if i=ji=j. Find the maximum value of mm.
Plain-text mathematical notation (without MathML)
Let A₁,A₂,…,A_(m) be finite sets of size 2012 and let B₁,B₂,…,B_(m) be finite sets of size 2013 such that A_(i)∩B_(j)=∅ if and only if i=j. Find the maximum value of m.
Original LaTeX notation
Let $A_{1}, A_{2}, \ldots, A_{m}$ be finite sets of size 2012 and let $B_{1}, B_{2}, \ldots, B_{m}$ be finite sets of size 2013 such that $A_{i} \cap B_{j}=\emptyset$ if and only if $i=j$. Find the maximum value of $m$.

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Source and history

task_id
d227a065-2c76-544d-97ed-f06150894a5a
task_key
test--d227a065-2c76-544d-97ed-f06150894a5a
task_revision_id
1
config / split
/ test

Official source

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