On subsets with intersections of even cardinality
Article by E.R. Berlekamp
In collection: Fun maths facts
This paper solves a question by Paul Erdős
URL: cms.math.ca/10.4153/CMB-1969-0
PDF: cms.math.ca/openaccess/cmb/v12
@esoterica The title reminds me of a problem I composed but never submitted to any journal: Suppose $A_1, A_2, \ldots, A_n$ are finite sets, and each $A_i$ has odd cardinality. Prove there must be a set $S\subseteq \{1,2,\ldots,n\}$ such that $\sum_{i\in S} |A_i\cap A_j|$ is odd for every $j\in\{1,2,\ldots,n\}$.
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