Find the smallest integer n for which the following is possible:

Consider a set of positive integers {1,2...n}. Each number is painted with either red or blue paint, but no matter which numbers have which color, you can always find four (not necessarily different) numbers x, y, z and w that are coloured with the same paint and satisfy x+y+z=w.

The required minimum value of n is 11.

Posted by K Sengupta on 2024-01-18 06:58:13