In layman terms, If they connect a test device at the input point on the wafer, would it travel thru every Die on the wafer and finish at the output point, resulting in a positive continuity test and verifying each and every Die on the wafer in one test?

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Let me ask further: if the method is to test all dies in sequence, how would this method determine which dies are flawed, if any? do they just discard the entire wafer? 

If they CAN figure out which are the problem dies, does the testing machine mark them somehow, so that they don't make it into the packaging process?