MathDB

2

Part of 2016 Serbia Additional Team Selection Test

Problems(1)

Combinatorial geometry

Source: Serbia Additional IMO TST 2016, P2

4/5/2016
Let ABCDABCD be a square with side 44. Find, with proof, the biggest kk such that no matter how we place kk points into ABCDABCD, such that they are on the interior but not on the sides, we always have a square with sidr length 11, which is inside the square ABCDABCD, such that it contains no points in its interior(they can be on the sides).
combinatoricsgeometryTST