Variants of the 3-Partition problem
One variant of 3-partition is the following distinct 3-partition problem, shown to be NP-complete in [1].

Distinct 3-partition
Input: A set $X = \{a_1,a_2,\ldots,a_{3n}\}$ of positive distinct integers, and a positive integer $B$ where $\Sigma_{i=1}^{3n} a_i = nB$, and $B/4 &lt; a_i &lt; B/2$, where $i \in [3n]$.
Question: Is there a partition of $X$ into $n$ triples such that the elements in each triple sum to $B$?

The problem is also NP-complete when $B$ is bounded above by a polynomial in $n$. For an &quot;application&quot;, a reduction from the problem is used in [2] to show a certain graph problem is hard.

[1] H. Hulett, T.G. Will, G.J. Woeginger, Multigraph realizations of degree sequences: Maximization is easy, minimization is hard, Operations Research Letters 36 (2008) 594–596.
[2] Bonato, Anthony, Jeannette Janssen, and Elham Roshanbin. &quot;Burning a graph is hard.&quot; arXiv preprint arXiv:1511.06774 (2015).