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: https://cms.math.ca/10.4153/CMB-1969-059-3

PDF: https://cms.math.ca/openaccess/cmb/v12/cmb1969v12.0471-0474.pdf

Entry: http://read.somethingorotherwhatever.com/entry/Onsubsetswithintersectionsofevencardinality

jsiehler@jsiehler@mathstodon.xyz@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 \(j\in\{1,2,\ldots,n\}\).