5 boxes having distinct weights; boxes weighed in pairs

[marty.frmn]

There are 5 boxes having distinct weights. A person needs to find out the sum of their weights taking 2 boxes at a time. If his results are 17,21,16,15,18,12,12,13,7,9. Then find out the weight of the 2nd heaviest and 4th heaviest....????

[stapel_eliz]

This is an old puzzler, slightly re-packaged. It is customarily presented in terms of hay bales (dunno why), and the weights will vary from one presentation to another. Fortunately, being old, solutions to this puzzler are archived online!

. . . . .Math Forum: Weighing Bales of Hay (1996)

. . . . .Math Forum: Weighing Bales of Hay (1997)

. . . . .One Puzzle a Day: Five Bales

. . . . .Math Central: Bales of hay

Have fun!