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There are several molecules with known oxidation numbers, for example O is known to have an oxidation number of -2. Using the known oxidation numbers you can solve for oxidation numbers of other molecules, for example if you have the molecule MnO4 with an overall charge of -1, then you know that Mn would have an oxidation number of +7 so that the overall molecule has a charge of -1.
Here is a website with some common rules that one should follow when assigning oxidation numbers: https://www.thoughtco.com/rules-for-assigning-oxidation-numbers-607567.
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