This question is related to an answer I posted in response to another question.
The 3-partition problem is the following problem:
Instance: Positive integers a1, …, an, where n=3m and the sum of the n integers is equal to mB, such that each ai satisfies B/4 < ai < B/2.
Question: Can the integers a1, …, an be partitioned into m multisets so that the sum of each multiset is equal to B?
It is well-known that the 3-partition problem is NP-complete in the strong sense that it remains NP-complete even if the numbers in the input are given in unary. See Garey and Johnson for a proof.
Questions: Does the 3-partition problem remain NP-complete if the numbers a1, …, an are all distinct? Does it remain NP-complete in the strong sense?
(My feeling is that the answers to both questions are probably yes because I do not see any reason why the problem should become easier if all numbers are distinct.)
It does not seem that the proof in Garey and Johnson establishes the NP-completeness of this restricted version.
In the answer to the other question linked above, I gave a proof that the 6-partition problem (defined analogously) with distinct numbers is NP-complete in the strong sense.