Assume that Personal Identification Numbers (PINs) are formed by nine-digit combinations of numbers 0 to 9. Assume that an adversary is able to attempt three PINs per second. a. Assuming no feedback to the adversary until each attempt has been completed, what is the expected time to discover the correct PIN? b. Assuming feedback to the adversary flagging an error as each incorrect digit is entered, what is the expected time to discover the correct PIN?

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