During the Second World War, the Royal Air Force $($RAF$)$ had many foreign pilots speaking

different languages and more or less trained on the different types of aircraft. The RAF had to form

pilot$/$co$-$pilot pairs $(\text{'}$crews$\text{'})$ for every plane with a compatible language and a sufficiently good

knowledge of the aircraft type.

Suppose there are $8$ pilots, and each pilot is characterized by a mark between $0($worst$)$ and $20$

$($best$)$ for his language skills

And his experience with two$-$seater aircraft

A valid flight crew consists of two pilots that both have at least $\frac{10}{20}$ for the same language and

$\frac{10}{20}$ on the same aircraft type.

Is it possible to have all pilots fly? Subsequently, calculate for every valid flight crew, the sum of

their scores for every aircraft type for which both pilots are rated at least $10/20.$ Which is the set

of crews with maximum total score?