[math-fun] what's the best way of finding n unknown integers from their sums taken k at a time

In WW Rouse Ball's A short account of the history of mathematics he gives the following "characteristic problem from Diophantus": Find four numbers, the sum of every arrangement 3 at a time being given; say 22, 24, 27, 20. What about Find four numbers, the sum of every arrangement two at a time being given, say 14, 12, 23, 16, 27, 25 ? I'm interested in what work might have been done on problems like this. I'm particularly interested in the good algorithms for such problems. Hard, easy, or what? -- Thane Plambeck tplambeck@gmail.com http://www.plambeck.org/ehome.htm