Some problems have variants that appear to be harder. For instance, Graph Automorphism (GA) problem has quasi-polynomial time algorithm ( by Babai's GI result). However, the fixed-point free GA problem is NP-complete.
Also, Factoring decision problem has sub-exponential time algorithm and it is not believed to be NP-complete. Meanwhile, a variant of factoring problem is NP-complete.
Subset-sum and partition problems are weakly NP-complete problems since they have pseudo-polynomial time algorithms. I am interested in their variants that are strongly NP-complete.
Are there known variants of subset-sum or partition problem that are strongly NP-complete?
P.S. I am not interested in 3-partition problem.