# PublicationsManuscripts

## Riddle concerning $\pm1$ vectors

Yuval Filmus

A big sheet of paper contains $2^n$ rows consisting of all possible vectors of length $n$ whose entries are $+1$ or $-1$. Someone changes some of the entries to zero. Show that there must be a non-empty subset of the rows summing to zero.

Probably much harder than you think it is!