Problem Solving Essay

695 Words3 Pages
PROBLEM SOLVING – Problem 2 – Lockers The problem: At Copperfield College, Kings Park Campus, there are 1000 lockers – one per student. On the first day of the new school year the first student Ali Ahmed, runs through the school and opens every locker. The second student, Ben Bonder, closes every second locker (opens it if its closed and closes it if its open): the fourth student changes every fourth locker – and so on until 1000th student closes the 1000th locker door. 1. Which doors are left open 2. Find the rule for the problem 3. Using your rule how many lockers will be left open if there were 2000 lockers. Aim: The aim is to find out how many doors will be remain open until the 1000th student has closed the 1000th locker. Strategy: The strategy I’m going to use is try to make the problem simpler by reducing the numbers of lockers and the number of students so it’s easier to work with. I’m going to reduce it to 25 lockers and 25 students. I’m going to construct a table using the number of lockers as my row and the number of students as my column. I’m going to work my way through and symatically chart what happens as the student open and closes the lockers. By doing this I’m going to try and look for a pattern. Working out/ Solution Progress 1. Created a table with the 25 students as the columns and 25 lockers as the rows. 2. I charted the progress of each student opening and closing the lockers by using C and O. I then colour coded the closed lockers in green and open lockers in blue so it’s easier to identify. 3. I highlighted the lockers that will be opened after the 25th student closes the 25th locker in pink. 4. I listed down all the lockers that were open and listed down the number of students who opened and closed each certain locker. RESULTS: * The lockers that remain open are square numbers
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