## Thursday, January 13, 2011

### Problem Solving: the Locker Problem

An impending headache to the administrator in planning the locker operation in SST. He seeks your advise on how to resolve this issue:

Here is the problem:
In SST, there is a row of 100 closed lockers numbered 1 to 100. A student goes through the row and opens every locker. A second student goes through the row and for every second locker if it is closed, she opens it and if it is opened, she closes it. A third student does the same thing for every third, a fourth for every fourth locker and so on, all the way to the 100th locker.
source:  seas.gwu.edu
The goal of the problem is to determine which lockers will be open at the end of the process.

Working in pairs, explain your thinking to the following problems clearly. Be sure to use appropriate mathematical language and methods. Post your answers in the comment and indicate both of your names.
(a) Which lockers remain open after the 100th student has passed?
(b) If there were 500 students and lockers, which lockers remain opened after the 500th student has passed?

3 droplets of water fell at the following rate, droplet A at every 5 minutes interval, droplets B at every 12 minutes interval and droplets C at every half an hour interval.
source: unreasonablydangerousonionrings.blogspot.co
(c) When do you think all the droplets, that is A, B and C will fall at the same time on the ground?
(d) Identify at least 2 methods to solve this problem.
(e) Is there a particular topic in maths that analyses such problems?

1. 1a) 10 lockers remain open.
1b) 22 lockers remain open.

2a) 60 minutes after they first drop together.
2bi) Lowest common multiple.
In this case, the numbers used are 5, 12, and 30. The lowest common multiple of these numbers is 60.
2bii) The table method.
This method, as its name says, uses a table.

2. Task 1a lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Task 1b lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484
Task 2a They will fall at same time at the 60th minute/1st hour
Task 2b Method 1: Find the common multiple of 5, 12 and 30.
Method 2: Make a graph and list out all the times that each droplet drops.

3. 1a) 10 lockers remain open
1b) 22 lockers remain open
2a) 1 hour after their first drop
2b) Lowest Common Multiple
Algebra/ Guess and Check
2c) HCF and LCM: Highest Common Factors and Lowest Common Multiples

Members: Carissa, Valery, Chelsea, Wei Qin

Find the square roots of the numbers which is under 100 for a and 500 for
Task 2a:They will fall at same time at the 60th minute/1st hour
Method: algebra/guess and check
Task 2c:highest common factors and lowest common multiples

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Method:Find the square roots of the numbers which is under 100 for A and 500 for B.
Task 1d.Lowest Common Multiple and Guess and Check
Done with Darshan

7. 1a)10 lockers:1,4,9,16,25,36,49,64,81,100
1b)22 lockers: 1,4,9,16,25,36,49,64,81,100,121,144,169,225,256,289,324,361,400,441,484
2a)1 hour after their first drop
2b)Lowest Common Multiple
Method:Guess and Check
2c):Highest Common Factors and Lowest Common Multiple

Task 1b) 1,4,9,16,25,36,49,64,81.100, 121, 144, 169, 196,225,256,289, 324, 361, 400,441, 484

Group Members: Bowen, Ryan Lai, Sherwin

9. Task 2 a) 60 min
b) find common multiples and use guess and check
c) factors and multiples

10. i'm stuck at task 1 anyone help me

11. Task 1a) 10 lockers: 1,4,9,16,25,36,49,64,81,100
Task 1b) 22 lockers: 1,4,9,16,25,36,49,64,81.100,121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

Task 2b) Find the smallest common multiple of 5, 12 and 30
Task 2c) List out the time past as the waters drip, making a list

Method:Find the square roots of the numbers which is under 100 for A and 500 for B.
Task 1c: After 1 hour time
Task 1d.Lowest Common Multiple, Guess and Check
Task 1e. Patterns Done with Wai Kit

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14. Task 1a) 1,4,9,16,25,36,49,64,81,100 (10 lockers)

Task 2b) Find the smallest common multiple of 5,12 and 30/ Guess and Check

15. 1a) lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
1b) lockers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484

2a) 60min
2b i) Find the smallest common multiple of 5,12 and 30(60)
2b ii) Make a table
2c)Multiples and factors

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17. Task 1a 10 lockers: 1,4,9,16,25,36,49,64,81,100

Task 2b LCM and Guess and check

18. I did it with Praveen

19. Task 1: A)10 lockers that are>1,4,9,16,25,36,49,64,81,100(square numbers)
B)all square numbers from 1 to 500>1,4,9,16,25,36,49,64,81,100,121,144...
D) FIRST METHOD: find the lowest common multiple of all the numbers using 30mins as the reference.
SECOND METHOD: unsure
E) this years first unit: factors and multiples

20. ^^^did with sheares

21. Task 1a 10 lockers: 1,4,9,16,25,36,49,64,81,100