## Monday, January 18, 2010

### The Locker Issue in SST

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:

Task: In aSST, 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. The goal of the problem is to determine which lockers will be open at the end of the process.

Sample Questions:

In words, explain your thinking to the following problems clearly. Be sure to use appropriate mathematical language and methods:

Which lockers remain open after the 100th student has passed?

If there were 500 students and lockers, which lockers remain opened after the 500th student has passed?

Further Activity:

Identify another problem that uses the same method or technique to solve and post it to this blog

1. They are 100, 81, 64, 49, 36, 25, 16, 9, 4, 1.
They are 1, 4, 9, 16, 25, 36, 49, 64, ,81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484.

2. 1 4 9 16 25 36 49 64 81 100

14 9 16 25 36 49 64 81 100 121 144 169 196 225 256 289 324 361 400 441 484

3. The technique:
The pattern starts with 1. As it progresses, the difference between each pattern increases by 2 each time.

4. a) The answers are : 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 .

b) The answers are : 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , 144 , 169 , 196 , 225 , 256 , 289 , 324 , 361 , 400 , 441 , 484 .

The difference between each pattern increases by 2 each time.

5. They are lockers 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 .
As the pattern continues, the difference between each number increases by two each time.

They are lockers 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , 144 , 169 , 196 , 225 , 256 , 289 , 324 , 361 , 400 , 441 , 484 .
We continue the pattern from 100.

6. 1) 1,4,9,16,25,36,49,64,81,100
2) 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484.

7. Interesting finding.
Is there a pattern for all these number series?

8. 1. They are:
1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100

2. 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100, 121 , 144 , 169 , 196 , 225 , 256 , 289 , 324 , 361 , 400 , 441 , 443 , 484.

9. 1. they are 1,3,9,16,25,36,49,64,81,100

2. (continues from 1st pattern) 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441 and 484.

The pattern is that these numbers are all square numbers.

10. interesting point Jonan - they are all square numbers.
Is 0 a square number? after all 0square = 0 !!!

11. The pattern is like this. The first locker to be open is locker number 1 and to find the second locker, add 3, so it will be locker number 4 and to find the next locker that is open, add 2 to the previous number u added, and the sum of the 2 numbers will give you the next next number to add to the previous locker that is open.

12. 1.
Lockers:

1,3,9,16,25,36,49,64,81,100

2.
Lockers:

1,3,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,361,400,
441,484

Naveena

13. Method: Listing

1. Lockers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100

2. Lockers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441 and 484.

14. Mr Jo's comment

How is this calculation used in your CLASS TIMETABLE planning?

15. The difference starts with 3. As it goes on, the difference increases by 2.
1, 4, 9, 16, 25, 36, 49, 64, 81 and 100.

16. For the 2nd question, the pattern continues.
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441 and 484.

17. a) 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 .

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