Bin Packing with uniform size constraints
As Peter pointed out, the 3-partition problem is NP-hard even when the sizes are between $1/3-\delta$ and $1/3+\delta$ for any constant $\delta&gt;0$. Therefore, by a simple reduction from the 3-partition problem, for any constant $\delta&gt;0$, the Bin Packing problem is NP-hard when $1/3-\delta &lt; a_i$ for all $i$.