Tray Balance

A balance-the-tray logic puzzle. The serving tray is a beam on a centre pivot, with slots at distances 1..N to the left and right. Plates are pre-loaded on one side, tipping it over. Tap a plate from your hand, then tap an empty slot to set it down so the net torque — the sum of weight × distance — is exactly zero and the tray sits level. Tap a placed plate to lift it again.