MathDB

29

Part of 2013 Harvard-MIT Mathematics Tournament

Problems(1)

2013 HMMT Guts #29: (Almost) Always Intersecting Sets

Source:

3/26/2013
Let A1,A2,…,AmA_1,A_2,\ldots,A_m be finite sets of size 20122012 and let B1,B2,…,BmB_1,B_2,\ldots,B_m be finite sets of size 20132013 such that Ai∩Bj=∅A_i\cap B_j=\emptyset if and only if i=ji=j. Find the maximum value of mm.
HMMTinequalities