Computational complexity of the 3-partition problem with distinct numbers 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 &lt; ai &lt; 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.
It is proved in [1, Corollary 7], that 3-partition is strongly NP-hard when the integers $a_1, \ldots, a_n$ are all distinct. The bounds $B/4 &lt; a_i &lt; B/2$ are not imposed in [1], but this should not make a difference.

[1]: Heather Hulett, Todd G. Will, Gerhard J. Woeginger: Multigraph realizations of degree sequences: Maximization is easy, minimization is hard. Oper. Res. Lett. 36(5): 594-596 (2008). DOI