You have to go with say 6V and remember to put protection diode over the relay (or the photo resistor might die over time) and you need eg. a zener diode to get the motor voltage down to the 3V it expects.
Unfortunately it says "Electric components shall be limited to batteries, wires, motors, switches, resistors, capacitors, commercial photocells (i.e., cadmium sulfide (CdS) cell, photoresistors or light dependent resistors), mechanical relays, lightbulbs, and LEDs. No computers or transistors will be permitted in the device."
Diodes are not allowed, but then again it really only needs to work a few times, and could I just use a resistor to get the motor voltage down? Or instead just use the 6 volts to power the coil in the relay and have the part that switches run at 3 volts?