The Prouhet-Tarry-Escott Problem and Generalized Thue-Morse Sequences

We present new methods of generating Prouhet-Tarry-Escott partitions of arbitrarily large regularity. One of these methods generalizes the construction of the Thue-Morse sequence to finite alphabets with more than two letters. We show how one can use such partitions to (theoretically) pour the same volume coffee from an urn into a finite number of cups so that each cup gets almost the same amount of caffeine.