Just a little history to this:

I was at a good friends party celebrating his Ph.D. defence (after nearly six years of working on it) when a mutual friend of ours started talking about the '24 Game'. He's a math teacher and using it in his classroom.

Naturally, with the help of a couple of 'Mike's Hard Lemonade', some of us started solving the numbers he threw at us. We stumbled for about 20 minutes through possible solutions for '3 3 7 7' before he told us. I guess, the increasing amount of empty bottles made him believe we'd never find a solution to that one, even though there are multiple.
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There are two types of vessels, submarines and targets.