E-commerce companies like Amazon have gained efficiency by delivering parcels to centrally-located hubs of lockers, rather...

  

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E-commerce companies like Amazon have gained efficiency by delivering parcels to centrally-located hubs of lockers, rather than delivering to individual homes. Customers pick up their parcels by entering a unique code, which causes the appropriate locker to open. Hubs come in many sizes. Cathy the criminal thinks she has a slick idea; she plans to enter random codes into the hub until a locker opens, and then she'll take the parcel inside it. Amazon wants to protect their customers from criminals like Cathy. They want the passcode system to be strong enough that there will be <0.1% chance of Cathy succeeding on any given try. 1. How many lockers are in the hub pictured? 35 lockers 2. Assuming the passcodes may only use digits 0-9, and passcodes allow repeated characters, what is the shortest passcode that gives Cathy less than 0.1% or 0.001 chance of success? 3. What passcode policy would give Cathy as close to a 0.1% chance as possible? Feel free to modify the number of characters and the number of digits to achieve this. E-commerce companies like Amazon have gained efficiency by delivering parcels to centrally-located hubs of lockers, rather than delivering to individual homes. Customers pick up their parcels by entering a unique code, which causes the appropriate locker to open. Hubs come in many sizes. Cathy the criminal thinks she has a slick idea; she plans to enter random codes into the hub until a locker opens, and then she'll take the parcel inside it. Amazon wants to protect their customers from criminals like Cathy. They want the passcode system to be strong enough that there will be <0.1% chance of Cathy succeeding on any given try. 1. How many lockers are in the hub pictured? 35 lockers 2. Assuming the passcodes may only use digits 0-9, and passcodes allow repeated characters, what is the shortest passcode that gives Cathy less than 0.1% or 0.001 chance of success? 3. What passcode policy would give Cathy as close to a 0.1% chance as possible? Feel free to modify the number of characters and the number of digits to achieve this.