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I might be in trouble with this one (homeschool funny)

Amber in SJ

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If there is a long way to do a math problem I will find it. 

My 11 yo ds runs full speed ahead through math and only occasionally stops to ask me a question.  Today was one of those rare moments.

This was the math problem that had him stumped:

"E has a room with 100 light switches numbered 1-100. All light switches are off. E invites 100 friends and gives them each a number between 1-100. Friend #1 flips each switch that is a multiple of 1 (all of them.) Friend #2 flips each switch that is a multiple of 2. Friend #3 flips each switch that is a multiple of 3. This continues until all 100 friends have flipped switches. Ending with friend # 100 flipping only switch #100. After all the flipping which switches are off & which are on?"


There are no other directions.


This is the last question on a page about finding factors.  Remember those factor trees?

We stare at this problem for a while and talk about it. We notice things like prime numbers will only be flipped twice We notice that friends 51-100 will only get to flip their own numbers, but none of this helps us solve the problem.

I decide to go the long route & print out 2 hundred charts & we start marking them up. I dutifully mark my switches up and down and once I am all finished I use a purple marker to mark those that are on & a blue marker to mark those that are off. It takes a long time. Ds did 1-16 and then left to jump on the trampoline.

Once I was done this happened:

Me: Aren't you going to finish?
DS: I did.
Me: What? Your chart isn't done.
DS: It all depends on if the number has an odd or even number of factors. If it has an odd number of factors it is on and if it has an even number of factors it is off. Only perfect squares have an odd number of factors so 1, 4, 9, 16, 25, 36, 49, 64, 81 & 100.
Me (looking at my color coded chart): Yep.

He is 11. Does anyone else think I am in trouble?

Amber in SJ


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