Imagine you’re part of a team tasked with tackling a tricky computer virus that has infiltrated your mainframe. This virus has a peculiar way of interacting with your antivirus team. It corrupts one of the four disks that are crucial to your system, and each disk’s status is indicated by a light.
The virus selects one member of your team—let’s say it’s you—and tells you which disk has been corrupted. Your mission is to switch one disk on or off before the virus ejects you from the system. Your team then has one chance to destroy the corrupted disk. If you succeed, the virus is defeated. If you fail, the entire system is lost. The catch is that you can only see the status of the disks once you’re inside the mainframe.
To communicate which disk is corrupted, you can use binary code, a system that uses only 1s and 0s. Each of the four disks can be represented by a 2-bit binary number: 00, 01, 10, or 11. Your task is to find a mathematical operation that uses the lit disks as input and identifies the corrupted disk as output.
For instance, if the corrupted disk is 00 and no lights are on when you enter, you could turn on 11 to signal that disk. If 11 is already on, you might switch 00, as adding 00 to 11 still results in 11.
Consider another scenario: if 00 is the corrupted disk and 01 and 10 are lit, the sum of the lit disks is 11. You need to adjust this to a sum of 00 by flipping one switch. If the available options don’t work, you might treat the sum as 22 instead of strictly adhering to binary rules. This suggests a strategy: observe the sum of the lit disks, treating 2s as 0s. If the sum matches the desired result, flip 00; if not, find the switch that will achieve the correct sum.
This method works because of a concept called parity, which indicates whether a value is even or odd. In this context, you’re considering the number of 1s in each digit place of your binary sums. By manipulating the switches, you can adjust the parity and create the desired disk number.
This solution isn’t just limited to four disks. It can be applied to any mainframe with disks that are a power of two. Even for a system with 1,048,576 disks, the approach remains feasible. Fortunately, your mainframe is smaller. By making the necessary adjustments, your team successfully destroys the corrupted disk and restores the system.
Engage in a hands-on workshop where you will practice converting decimal numbers to binary and vice versa. This will help you understand how binary code is used to represent the status of the disks. Work in pairs to solve binary conversion puzzles and discuss strategies for efficient conversion.
Participate in a game that involves adjusting the parity of a set of numbers. You will be given a series of binary numbers and tasked with flipping bits to achieve a desired parity. This activity will reinforce your understanding of how parity can be used to solve the computer virus riddle.
Take part in a simulation where you and your team must identify the corrupted disk using the binary code method. Use a computer program to simulate the disk lights and practice making decisions based on the binary sums. Discuss the strategies you used and their effectiveness.
Engage in a group discussion to explore different mathematical operations that could be used to identify the corrupted disk. Share your ideas and analyze the pros and cons of each approach. This will help you think critically about the problem and explore alternative solutions.
Work on a challenge that involves scaling the solution to a larger number of disks. Use the principles discussed in the article to devise a strategy for a system with more disks. Present your solution to the class and explain how you adapted the method to handle increased complexity.
Your antivirus team is facing a particularly challenging piece of malicious code that has taken control of your mainframe. From previous infected systems, you’ve learned that this malware has a unique way of interacting with antivirus agents. It corrupts one of the four disks that operate your mainframe, which are indicated by lights that show their status.
The malware selects one member of the antivirus team—this will be you—and informs them which disk has been corrupted. You are then allowed to switch one disk on or off before the malware removes you from the system. Your team can launch an attack to break into the mainframe and destroy one disk before being eliminated. If you destroy the corrupted disk, the malware will be defeated. However, destroying any other disk will result in the loss of the entire system. The status of the disks is only visible within the mainframe, so you won’t know which disks are on or off until you arrive.
To communicate which of the four disks has been corrupted with your single action, consider using binary code—a numbering system that uses only 1s and 0s. Each of the four disks can be represented by a 2-bit binary number ranging from 00 to 11. The goal is to find a mathematical operation that takes the lit disks as input and identifies the corrupted disk as output.
For example, if the corrupted disk is represented by 00 and no lights are on when you enter, you could turn on 11 to indicate that disk. If 11 is already on, you need to switch one light. The most straightforward option might be to change 00, as adding 00 to 11 would still yield 11.
However, if 00 is the corrupted disk and 01 and 10 are lit, the sum of the lit disks would be 11. You need to adjust this to a sum of 00 by flipping one switch. The options available do not yield the desired result, so you might consider a different approach by treating the sum as 22 instead of adhering strictly to binary rules. This suggests a strategy: observe the sum of the lit disks, treating 2s as 0s. If the sum matches the desired result, flip 00; if not, find the switch that will achieve the correct sum.
This method works because of a concept called parity, which indicates whether a value is even or odd. In this case, you are considering the number of 1s in each digit place of your binary sums. By manipulating the switches, you can adjust the parity and create the desired disk number.
This solution is applicable to any mainframe with disks that are a power of two. For larger systems, such as one with 1,048,576 disks, the approach remains feasible. Fortunately, your mainframe is smaller. You make the necessary sacrifice, and your team successfully destroys the corruption, restoring the system.
Computer – An electronic device that processes data and performs tasks according to a set of instructions or programs. – The university’s computer lab is equipped with high-performance machines for coding and data analysis.
Virus – A malicious software program that can replicate itself and spread from one computer to another, often causing harm or stealing information. – The IT department regularly updates antivirus software to protect the network from new virus threats.
Disk – A storage device used to save and retrieve digital information, such as a hard drive or SSD. – The computer science students were taught how to partition a disk to optimize storage efficiency.
Binary – A base-2 numeral system that uses two distinct symbols, typically 0 and 1, to represent data in computing. – Understanding binary is crucial for students learning how computers process and store information.
Code – A set of instructions written in a programming language that a computer can execute. – The professor asked the students to debug the code to ensure it runs without errors.
Sum – The result of adding two or more numbers or values, often used in programming to calculate totals. – The algorithm efficiently calculates the sum of all elements in the array.
Parity – A method of error detection in data transmission where an extra bit is added to ensure the number of set bits is even or odd. – Parity checks are used in data communication to detect errors in transmitted messages.
Mainframe – A large, powerful computer that can handle and process very large amounts of data quickly, often used by large organizations for critical applications. – The university’s research department relies on a mainframe to process complex simulations and data analysis.
Team – A group of individuals working together to achieve a common goal, often used in the context of software development projects. – The software development team collaborated to build a new application for the university’s online portal.
System – A set of interconnected components that work together to perform a specific function, such as a computer system or an operating system. – The students learned how to design a robust system architecture for their final project.
