[EE]: four buttons on one A/D pin by "Rob Robson" .

Here's a head-scratcher for the brain trust. I want to connect four momentary pushbuttons to a single A/D input such that each and every combination of pressed buttons will present a unique voltage to the A/D. To minimize errors, it seems there should be a wide and fairly even distribution between the fifteen possible voltage levels (not including the "no-buttons-pressed" option). The proposed circuit consists of four different resistor values, each one tied between the A/D input and a pushbutton. The other side of each pushbutton is tied to ground. A fifth resistor ties the A/D input to +5V to complete the voltage divider. My limited math abilities are hampering my attempts to optimize the five resistor values for a nice safe spread between all the resulting single- and multiple-button voltages. Has anyone seen or done something like this? Googling hasn't turned up anything so far. I'm completely open to changing the circuit if there's a more clever arrangement. Many thanks in advance for your skulduggery, RR