  In 1957 Leo Moser published a problem in American Mathematical Monthly asking
whether knowing the set of all pairwise sums of five numbers one could
determine the original numbers. Problem was quickly generalized as "Is it
always possible to restore a collection of $n$ numbers from the collection of
its $s$-sums?"; it turned out to be a very interesting and nontrivial question
in additive number theory and combinatorics. On its sixtieth anniversary we
present here a survey of all the known research, results and techniques used in
various attempts to solve this problem. Some new findings and open questions
are presented as well.
