Here, we show the successful implementation of advanced sequential logic in droplet microfluidics, whose principles rely on capillary wells establishing stationary states, where droplets can communicate remotely via pressure impulses, influencing each other and switching the device states. All logic operations perform spontaneously due to the utilization of nothing more than capillary-hydrodynamic interactions, inherent for the confined biphasic flow. Our approach offers integration feasibility allowing to encode unprecedentedly long algorithms, e.g., 1000-droplet counting. This work has the potential for the advancement of liquid computers and thereby could participate in the development of the next generation of portable microfluidic systems with embedded control, enabling applications from single-cell analysis and biochemical assays to materials science.