Given a set of nonnegative integers, the number partitioning problem requires the division of into two subsets such that the sums of number in each subset are as close as possible. This problem is known to be NP-complete, but is perhaps "the easiest hard problem" (Hayes 2002; Borwein and Bailey 2003, pp. 38-39).

# Number Partitioning Problem

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## References

Borwein, J. and Bailey, D.*Mathematics by Experiment: Plausible Reasoning in the 21st Century.*Wellesley, MA: A K Peters, 2003.Hayes, B. "The Easiest Hard Problem."

*Amer. Sci.*

**90**, 113-117, 2002.Mertens, S. "A Physicist's Approach to Number Partitioning."

*Theoret. Comput. Sci.*

**265**, 79-108, 2001.

## Referenced on Wolfram|Alpha

Number Partitioning Problem## Cite this as:

Weisstein, Eric W. "Number Partitioning Problem."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/NumberPartitioningProblem.html