I can think of many ways to do this. Here is a simple design that can expand to any number.
In the unlikely event (but possible) of more than 1 button pressed within some nS from each other, the circuit could be modified as in the 2nd diagram. Here the extra transistor monitors the current to the LED's and any current higher than that for 1 LED will reset all the flip-flops. Because all switches have some contact bounce lasting (~10mS), after a reset pulse by the transistor one of the switches should be able get a valid set in this time. R10 will be calculated based on the LED current and Vb-e (worst case) of the transistor.
You can also do it with SCR's and lamps quite easy.
Can u tell me how to exactly calculate the value of the R10 resistor