This 2005 four-star problem from Colin Hughes at *Maths Challenge* is also a bit challenging.

“**Problem**

For any set of real numbers, R = {x, y, z}, let sum of pairwise products,

________________S = xy + xz + yz.

Given that x + y + z = 1, prove that S ≤ 1/3.”

Again, I took a different approach from Maths Challenge, whose solution began with an unexplained premise.

See the Pairwise Products