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.**

__TASK 1__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?

__TASK 2 (similar problem)__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.

(d) Identify at least 2 methods to solve this problem.

(e) Is there a particular topic in maths that analyses such problems?

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?

(C) 5X12=60

ReplyDelete12X5=60

30X2=60

Trial and error

(D) 3x5x12=180

Um...common sense?

(E) Factors and Multiples

Benedict wong

Siddharth

Sean

Jun Jie

(c)LCM of 5,12,30=60

ReplyDelete(d)Solve by LCM and ???

(e)Yes.Factors and Multiples.

Darren

Deepika

Charmaine

Nicole

Rhea

This comment has been removed by the author.

ReplyDelete1st 30x2=60 60/5-correct 60/12-correct so 60

ReplyDelete2nd 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

There the answer is 60

Darren

Deepika

Charmaine

Rhea

Nicole

Math Locker Problem:

ReplyDeleteAfter 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