Summing Triples problem is strongly $NP$-complete as shown by McDiarmid.
Summing Triples problem:
Input: list of 3N distinct positive integers
Question: Is there a partition of the list into N triples $(a_i, b_i, c_i)$ such that $a_i + b_i= c_i$ for each triple $i$?
The condition that all numbers must be distinct makes the problem interesting and McDiarmid calls it a surprisingly troublesome .
If the input is a multiset of positive integers, What is the complexity of Summing Triples? Does it remain NP-complete?
May be I overlooked an easy reduction from the original problem.