How much does a proton weigh
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You should have given us a table, but I think my table shouldn't be too different.
Let's put oxidation numbers first.
You would have to know that Mg(s) is a reducing agent and Br2(l) is an oxidizing agent. But it is pretty common knowledge that the halogens will tend to take the electrons and alkali and alkaline earth metals will tend to give up electrons.
Mg is oxidized because it gives up electrons; Br2(l) is reduced because it gains electrons. Since the reaction conforms to what we would expect to <em>naturally</em> (thermodynamically favored) occur, it can take place given that the activation energy is supplied.