### The Mad Monkey Locker Mess

Imagine you are at a school that still has student lockers. There are 1000 lockers, all shut and unlocked. Suppose the monkey goes along and opens every locker.

Then he goes along and shuts every other locker beginning with locker #2.

Then he goes along along and changes the state of every third locker beginning with locker #3.

In other words, if the locker is open, the monkey shuts it and if the locker is closed, the monkey opens it.

Then the monkey changes the state of every fourth locker beginning with locker #4.

If this continues until the monkey has followed this pattern 1000 times, which lockers will be open and which will be shut at end?

Why?

Then he goes along and shuts every other locker beginning with locker #2.

Then he goes along along and changes the state of every third locker beginning with locker #3.

In other words, if the locker is open, the monkey shuts it and if the locker is closed, the monkey opens it.

Then the monkey changes the state of every fourth locker beginning with locker #4.

If this continues until the monkey has followed this pattern 1000 times, which lockers will be open and which will be shut at end?

Why?

Labels: The Mad Monkey Madness

## 14 Comments:

At 3:15 PM , zach said...

It is 90 open lockers and 910 closed at the end and I got that by go by and find how many BEGGING 2's are in 100 and and times it and did it with the rest and the switch after the 2;and thats how I got it

(I can't wait to do this in class)

At 5:57 PM , Evil Motion said...

Haii. This is going to be fun. Baii.

Evil Motion,

doing her job.

Haha.

At 9:28 PM , dallas said...

I think its 500 open and 500 closed

At 11:10 AM , Anonymous said...

Hey Mr. Stuart this is Sandeep Singh and I say 1 lockers will be open and 999 will be shut. Why, becuase the way I saw it was that when they said he shut every locker exept one locker. So if he keeps shutting all but one 1000 times 1 will be open and 999 will be shut. Bye and that's my answer.

At 11:10 AM , Briana M. said...

Why do you make our homework so hard? It makes my brain hurt and my mom doesnt get it when i show it to her, but thank you for giving us hard work because now i know how hard it is when your a adult. From Briana M.

At 11:27 AM , Mahrukh said...

Hey,This is Mahrukh.

I think the Monkey ended right were he started.

And the odd numbered lockers are opened and the even numbered ones were closed.

At 11:32 AM , Anonymous said...

From:Wintwin

The 2nd Q was hard but we had some help and we got it right. Also we can't wait 4 the next Q. It was really challenging and took ALOT of thinking out of the box.

Thanks Bye!

At 1:38 PM , skyler & nicx said...

we think its.................................................................................................................................................................................................................................................................................................?+?= the number #2, and nicx thinks its every other number.

At 2:47 PM , Anonymous said...

I enjoy being challenged with higher level thinking problems but can we do the problem over in class so I can understand what I put, why I put what i put and why or why not it was or wasn't right.

A.J.

At 2:49 PM , Anonymous said...

My answer is 2/3 will be closed and 1/3 will be open. A.J.

At 2:49 PM , Anonymous said...

My answer is 2/3 will be closed and 1/3 will be open. A.J.

At 8:58 PM , haseeb said...

I think it is 500 open and 500 closed

At 8:58 AM , Anonymous said...

hi it,s malcolm for the monkey locker thing I think it,s 142.

At 4:05 PM , corey said...

Hey!!! I actually know this, actually the truth is every perfect square will end up open with all of the others closed...Perfect squares, are numbers such as

1, 4, 9, 16, 25, 36, 49, 64, 81 Etc..

any number when taken a square root of will give u an even integer

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