Thank you everyone for the help provided, it has been incredibly worthwhile and will allow the group to complete the task at hand!

 

The TS is asking for the design of a complete game electronics package that will be competitively priced, and quite reliable, all for free. Yes it can be delivered, even with a prototype, in 2 weeks but it comes with a 5 digit price tag. Or you can get it in 4 to 6 weeks with no prototype for a 4 digit price.
BUT, to provide a reasonable way of making it work without a micro and software, use a pulse-gating circuit, then a trigger from a one point switch gives one pulse, a trigger from a 3 pint switch gives 3 pulses, and a trigger from a 5 point switch gives 5 pulses. And because the circuit gets triggered, contact bounce is not a problem, so no de-bounce to fight with. And no processor to program. And just a few CMOS IC devices, and a small 5 volt power supply, or perhaps 10 or 12 volts.It will need a clock oscillator , probably around i KHz.The pulse gating part uses D pps and a 4017 decade counter and a few and gates.any input sets one of 3 ffs ns as the counter counts up, at the right number of counts the output resets the decade counter. fairly simple logic, easy to add LEDs to indicate what is going on, and it should get a good grade.