At the annual meeting of the knights, King Arthur notes that several of knights

have started to develop conflicts. Sending his undercover agents, he has managed

to find out a list of all possible duelling pairs. He now wishes to exile a small set of

knights away so that no duelling pair remains at the annual meeting. Merlin is now

set with this task of finding out which knights to send away. Being a perfectionist,

Merlin wishes to find the smallest set she could send into exile. However, after much

thought, she is unable to find the optimal solution using any efficient algorithm.

Explain why? $($i$.$e How did Merlin model the problem? What problem is Merlin

trying to solve and why is she unable to do it$.)$