## 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. (C) 5X12=60
12X5=60
30X2=60
Trial and error
(D) 3x5x12=180
Um...common sense?
(E) Factors and Multiples
Benedict wong
Siddharth
Sean
Jun Jie

2. (c)LCM of 5,12,30=60
(d)Solve by LCM and ???
(e)Yes.Factors and Multiples.
Darren
Deepika
Charmaine
Nicole
Rhea

3. This comment has been removed by the author.

4. 1st 30x2=60 60/5-correct 60/12-correct so 60

2nd Prime factorisation method.
2I_30_12_5
2I_15_6_5
3I_15_3_5
5I_5_1_5
I_1_1_1
so 2x2x3x5=60

Darren
Deepika
Charmaine
Rhea
Nicole

5. Math Locker Problem:

After 1st student pass, all lockers are closed.
Open: All
Closed: None

After 2nd student pass, all lockers with the factor of 2 is closed
Open: All lockers not the multiple of 2
Closed: All lockers the multiple of 2

After 3rd student pass, All lockers with the factor of 3, and with the factor of 2 is open, without, is closed.
Open: Multiples of 3 and 2, and other lockers not the multiple of both 3 and 2
Closed: Multiples of 3 not 2, and other lockers not the multiple of both 3 and 2
THE NUMBERS WITH AN ODD NUMBER OF FACTORS AND ODD TIMES OPENING!!!

THUS, SQUARE NUMBERS( Multiples of 1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9 1,10) ARE THE ONLY ONES.

All square numbers will be open, 1x1 2x2 3x3 4x4 5x5 6x6 7x7 8x8 9x9 10x10
1 4 9 16 25 36 49 64 81 100

Shaun
Mason
Kevin
Keming