# 3-partition problem: why $b/4 < x_i < b/2$?

Why does the definition of the 3-partition problem contain the condition $$\frac{B}{4}<x_i<\frac{B}{2}?$$

I don't understand why leaving out this condition changes the 3-partition problem.

• What can you deduce about the size of sets that sum to B when each element satisfies that condition? ​ ​ – user12859 Mar 2 '16 at 22:08

The fact that 3-PARTITION is NP-complete even when all integers are bounded in $(B/4,B/2)$ can be helpful when using 3-PARTITION to prove that other problems are NP-hard.