Quiz Evaluator System using Logic Gates only

[Tahseen92]

I need to build to a "4 person, 8 questions" quiz evaluator using Logic gates/ICs only. No programmable device is allowed. After asking every question, a window of 5 seconds will be given. In that time, the contestants will press the buzzer. Whoever buzzed first, will be given a time of 10 seconds to answer the question. If he answers it correctly, then we will move on to the next question. In case he fails, the contestant who buzzed after him will answer the question and so on. I have to save the right answers(true/false) to check if the contestants are right or wrong. Then I have to show the score on a LCD display.

What types of ICs are necessary for this project? Any kind of help is appreciated. Thanks in advance!