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I don't believe there is a particular formula for determining the number of resonance structures, so you would count the number of possible resonance structures by drawing every valid lewis structure until there aren't any possible alternative configurations.
This isn't true for all cases but usually resonance structures can be drawn whenever the diagram of a molecule has different types of bonds to a center atom whose locations are interchangeable. All the possible combinations of how these bonds can be arranged would be the number of resonance structures.
If there are multiple places where the center atom can bond with the outer atoms and these bonds are interchangeable, I believe that you just have to count/take account of all of these different forms to get the number of resonance structures.
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