Unlocking Lockers: A Fun Riddle to Solve
What is the solution to the locker problem where 100 students change the state of 100 lockers according to specific rules? Write a program to determine which lockers are open after all students have passed through.
Analysis:
Design:
The major steps to solve the problem:
1. Initialize an array of 100 boolean elements to represent the state of each locker (true for open, false for closed).
2. Iterate through students from 1 to 100 and, for each student, iterate through lockers from 1 to 100.
3. If the student's number evenly divides the locker's number, toggle the locker's state.
4. After all students have passed through, determine which lockers are open.
5. Display the numbers of the open lockers.
Coding:
*You can write your code here.*
Testing:
To test the program, you can run it with the given parameters of 100 lockers and 100 students. Check if the output matches the expected open locker numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Final answer:
The lockers that are open after all the students have passed through the building and changed them are: Locker 1, Locker 4, Locker 9, Locker 16, Locker 25, Locker 36, Locker 49, Locker 64, Locker 81, and Locker 100.
Explanation:
To solve this problem, we can use an array of 100 boolean elements, where each element represents the state of a locker. Initially, all lockers are closed. We can iterate through the students from 1 to 100, and for each student, iterate through the lockers from 1 to 100. For each student, we can check if the student's number evenly divides the locker's number. If it does, we can change the state of the locker by toggling its value (from closed to open or from open to closed). We can use the modulo operator (%) to check if the locker's number is divisible by the student's number. After iterating through all the students and lockers, we can output the lockers that are open. We can keep track of the open lockers by adding their numbers to a list or printing them directly.