Problem of the Week 1160

Many Pairs Dividing a Sum

Given four distinct positive integers a, b, c, d, let S be their sum.

Let x₁, x₂, x₃, x₄, x₅, x₆ 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.