www.logiccircuit.org

At university, the teacher had given us a project about logical circuits. But we have to come up with our own ideas. The important thing is we can't use certain things like flip-flops, counters, multivibrators, etc. We can use logic gates, encoders, decoders, code converters, MUXs, DEMUXs, and comparators. We didn't even see these topics but we have to decide on the project according to these. I don't know anything except logic gates. I think this is bullsh.. but we have to

I come up with an idea. This is only a concretization of the idea. If we can say that there are five different servers in a data center, there will be a status checker for the servers. If two random servers get down, the first LED will turn on the check unit. If two more random servers get down, the second LED will turn on too. But all five get down the third will turn on too.

My question is, can I complete this project idea with the tools that I said up there?

Your restriction is not clear. What does it mean you can't use curtain things: can you build them from logical gates and then use them or even this is not allowed?
If it's possible to build your own flip-flops, then it's possible, in relatively easy way to build a project you described. Without them it may be possible too, but I did not figure out it yet.

Sorry for this confusion. I didn't know that we can build flip flops with gates. We have to use the tools within first 8 topics. And they're not including these flipflops, counters etc. So we can't use own built ones neither. So only the ones that I said.

Can you please provide more detailed descriptions for code converters and comparators?

Converters are converting decimal to BCD like. Comparators are comparing the numbers. Magnitude comparison. a>b, a=b, a<b. And really I don't know these. I just read the teacher's documentation.

Well, I guess you can do it using gates only by brute force. You will need to check conditions of all pairs of fail status to check if any two are down this will take 10 AND gates assuming fail signal is one and working signal is zero. Then do the same to all pairs this will take 6 AND taking results from previous ten and finally for the third LED you just check if all five are ones.
But if you must use all other components then it is too simple project for this. I suggest you talk to your teacher about it before going into implementation.

If you're saying it can be done with only gates, it's ok. As I said it will be random two and I assume that you understand it like that. Teacher said you can not use forbidden ones . But you can tell me what are they which if I use them to make it more simpler. And thanks for your help. Have a good day!