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You can probably determinate the number of supernovas/hypernova/etc that happened before the sun by analyzing the proportions of different elements in the solar system and then use the various equations to compute how many explosions you would need to create the heavy elements (heavier than iron) that are observable since they are mostly created in these situations.

You probably can get these equations by analyzing nebula composition and the type of star which was there.

Also, the type of star gives an indication of it's history.