Problem of the Week 1160Many Pairs Dividing a SumGiven four distinct positive integers a, b, c, d, let S be their sum. Let x_{1}, x_{2}, x_{3}, x_{4}, x_{5}, x_{6} be the six possible sums of the given four, two at a time. Find an example where the number of the six x's that divide S is as large as possible. Source: Bart de Smit, IMO 2011. © Copyright 2012 Stan Wagon. Reproduced with permission.
