# One corner oriented wrong



## jtoc (Apr 21, 2010)

Hi all,

I'm a high school math teacher, and I use a cube whenever possible in discussing mathematics with my students. Last week I allowed some students to scramble my cube for me to solve, and came across a curious problem. There is one corner oriented wrong on my cube. It's not a matter that it just needs to be turned once or twice; it's backward. That is to say, going clockwise around it, this piece should be blue/orange/yellow, and instead it's blue/yellow/orange. The rest of the cube is correctly completed.

Obviously, I can't just pop the piece off and put it in correctly. So my questions are:
(1) What did my students do to my cube?
(2) What can I do to fix it?
(3) What should I do to the students who commit such a crime against mathematics?

Thanks for your help!


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## miniGOINGS (Apr 21, 2010)

My guess would be that the stickers were removed in some way.


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## ~Phoenix Death~ (Apr 21, 2010)

Peel the stickers off and put them back on right.
Give them lines.


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## RyanO (Apr 21, 2010)

Sounds like there was some sticker rearangement going on.


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## Andreas737 (Apr 21, 2010)

"I will not peel the sticker's off my teacher's cube"
"I will not peel the sticker's off my teacher's cube..."


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## FatBoyXPC (Apr 21, 2010)

You should tell them you won't make them do detention if they give you those sentences, one for each possible combination the cube can be. I'm not sure how advanced of a math class you teach (probably not very advanced or they wouldn't cheat like that, they'd probably be more intrigued on how to actually do it), but most students when I was in high school would have jumped to the conclusion of 54 sentences and called it a day. I would then explain to them when they turn in these sentences how they are nowhere close to done, and then explain how to calculate the total combinations haha.


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## janelle (Apr 21, 2010)

We're you watching them scramble it? They most likely moved a sticker since most people say " I just move the stickers" other than "I popped the cube then put it together correctly."

And you could just fix it and explain to them how it's impossible to have a piece like that without someone messing with it.


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## iChanZer0 (Apr 21, 2010)

Make the students learn how to solve the cube then move the stickers on there cubes.


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## goatseforever (Apr 21, 2010)

People always make jokes about peeling the stickers off a cube and reapplying them for the win. Where can I find such stickers? Last time I tried to peel off my Cubesmiths to reapply on a different cube it didn't end well.


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## Dene (Apr 21, 2010)

~Phoenix Death~ said:


> Peel the stickers off and put them back on right.
> Give them lines.



LMAO! Yes make them do lines! HAHAHAHA LINES!!


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## megaminxwin (Apr 21, 2010)

Let's start the lines off.

I will not peel the stickers off my teachers cube.
I will not peel the stickers off my teachers cube.
I will not peel the stickers off my teachers cube.

And no, before you ask, Ctrl-V is not allowed.


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## qqwref (Apr 21, 2010)

Either the stickers were removed (likely) or you have a four-dimensional student who accidentally flipped the corner and brought it back into threespace (unlikely).

I suggest asking your students to do some cubing-related homework as a punishment (as a reward?). You could start them off with easy questions like explaining why you can't have something like a red-orange edge, and then go onto possibly harder ones like explaining why you can't flip just one edge.


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## Toad (Apr 21, 2010)

Andreas737 said:


> "I will not peel the sticker's off my teacher's cube"
> "I will not peel the sticker's off my teacher's cube..."





megaminxwin said:


> Let's start the lines off.
> 
> I will not peel the stickers off my teachers cube.
> I will not peel the stickers off my teachers cube.
> ...



I think lines are better when written with correct English grammar...

"I will not peel the stickers off my teacher's cube."


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## riffz (Apr 21, 2010)

goatseforever said:


> People always make jokes about peeling the stickers off a cube and reapplying them for the win. Where can I find such stickers? Last time I tried to peel off my Cubesmiths to reapply on a different cube it didn't end well.



The stickers on old Rubik's cubes were different though. You could actually pull them off and reposition them and it would stick fine. My dad left his in his backpack and put his warm laptop in beside it. When he got home from work the stickers had slid off the cube because the heat had caused the adhesive to melt a bit. He just stuck them back on and they are all still fine.



randomtoad said:


> Andreas737 said:
> 
> 
> > "I will not peel the sticker's off my teacher's cube"
> ...



Nazi.


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## JTW2007 (Apr 21, 2010)

jtoc said:


> (1) What did my students do to my cube?
> (2) What can I do to fix it?
> (3) What should I do to the students who commit such a crime against mathematics?



1. What did you expect? You're a high school math teacher.
2. www.cubesmith.com
3. 50 lashes? Or, in the case of qqwref's four-dimensional student, have them sent to a secret facility in a remote location and kept there for further studying.


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## jtoc (Apr 24, 2010)

Thanks for the advice, everyone. I feared that it was stickers; this is probably a 5-year-old cube which has been, shall we say, well-loved. If I peel stickers off, I'm afraid they won't stay stuck on afterward. (Apparently my students have the secret for that.) Thanks for the advice on the replacement tiles, too.


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## peedu (Apr 24, 2010)

There must be (at least) one student in that class who knows that you will not be able to solve the cube after sticker switching trick. There must be more he/she knows about the cube.


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## Luigimamo (Apr 25, 2010)

Give them FREE TIME !!
School's supposed to be fun !


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## gibbleking (Apr 25, 2010)

as im vindictive i would give them a maths problem for homework that was unsolvable........hehehehehehe that would teach them.


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## RubiksDude (May 18, 2010)

gibbleking said:


> as im vindictive i would give them a maths problem for homework that was unsolvable........hehehehehehe that would teach them.



Good idea. What's the math problem?


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## Feryll (May 18, 2010)

RubiksDude said:


> gibbleking said:
> 
> 
> > as im vindictive i would give them a maths problem for homework that was unsolvable........hehehehehehe that would teach them.
> ...



x = x + 1


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## SuperNerd (May 18, 2010)

Feryll said:


> RubiksDude said:
> 
> 
> > gibbleking said:
> ...



Wow, you made my head aspload.

I'd give them √-1.


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## Kenneth (May 18, 2010)

SuperNerd said:


> I'd give them √-1.




√-1 = √ [-1,0] = [0,1]

Or 

√-1 = √ [-1,0] = [0,-1]

Both are correct, but also this:

√-1 = √ [-1,0,0] = [0,1,0]
√-1 = √ [-1,0,0] = [0,-1,0]
√-1 = √ [-1,0,0] = [0,0,1]
√-1 = √ [-1,0,0] = [0,0,-1]

And this:

√-1 = √ [-1,0,0] = [0,cos(45 degree),sin(45 degree)]

Or any point that is on a circle around the x-axis with radius = 1

Moving to 4D it is any point on a "sphear" around the x-axis with radius 1.

In 5D it is any point on a ???? (what is it??) around the x-axis and so on.


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## ~Phoenix Death~ (May 18, 2010)

RubiksDude said:


> Feryll said:
> 
> 
> > RubiksDude said:
> ...



That problem is easily solvable, what's wrong with you?


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## gibbleking (May 18, 2010)

sorry fella ...its just been solved by a hermit who wont accept the prize money..


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## mrCage (May 18, 2010)

jtoc said:


> Hi all,
> 
> I'm a high school math teacher, and I use a cube whenever possible in discussing mathematics with my students. Last week I allowed some students to scramble my cube for me to solve, and came across a curious problem. There is one corner oriented wrong on my cube. It's not a matter that it just needs to be turned once or twice; it's backward. That is to say, going clockwise around it, this piece should be blue/orange/yellow, and instead it's blue/yellow/orange. The rest of the cube is correctly completed.
> 
> ...


 
If you do not know anwer to 1 and 2 then dont be a math teacher

Per


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## megaminxwin (May 18, 2010)

And now it's time to actually make a contribution in this thread.

1. Switch stickers.
2. Switch them back.

OR buy tiles so they can't switch the stickers 

3. Teach them calculus:
'Why do we need to learn this, sir/miss?'
'Why did you switch the stickers on my cube?'
'But we -'
'Anyway...'


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## canadiancuber (May 22, 2010)

RubiksDude said:


> ~Phoenix Death~ said:
> 
> 
> > RubiksDude said:
> ...



what's the answer? 


my guess 



Spoiler



i don't have one......MONKEY


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## ThatGuy (May 22, 2010)

x - x = x + 1 - x
0=1 
All numbers are solutions
which is true because:
For notational purposes let a = b
a^2 = ab
a^2-2ab = ab-2ab = -ab
a^2 - 2ab + a^2 = -ab + a^2
2a^2 -2ab = -ab +a^2
2(a^2 - ab) = a^2 - ab
divide both sides by a^2 - ab
Yes I did divide by 0.
2 = 1
2 -1 = 1-1
1=0
transitive property 
0=1
put anything discovered in spoilers. like why this works.


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## adimare (May 22, 2010)

ThatGuy said:


> x - x = x + 1 - x
> 0=1
> All numbers are solutions
> which is true because:
> ...





Spoiler












I have a better one:

1 = 1
1 + 1 = 1 + 1
since 1 = √1
1 + 1 = 1 + √1
1 + 1 = 1 + √(-1 x -1)
since √ab = √a x √b
1 + 1 = 1 + √-1 x √-1
1 + 1 = 1 + i x i
1 + 1 = 1 + i^2
1 + 1 = 1 - 1
2 = 0


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## miniGOINGS (May 22, 2010)

adimare said:


> 1 + 1 = 1 + √-1 x √-1
> 1 + 1 = 1 + i x i
> 1 + 1 = 1 + i^2
> 1 + 1 = 1 - 1
> 2 = 0



(-1)^2 =/= (-1)


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## CubesOfTheWorld (May 22, 2010)

Peeled the stickers like the non-cubers they are.


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## TrollingHard (May 22, 2010)

Easy:

It doesn't happen.
It's similar to proving that you can divide by zero: all math would be incorrect.


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## adimare (May 23, 2010)

miniGOINGS said:


> adimare said:
> 
> 
> > 1 + 1 = 1 + √-1 x √-1
> ...



I never wrote that (-1)^2 = -1
I wrote that i^2 = -1


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## qqwref (May 23, 2010)

Even better: http://mzrg.com/math/0=1.shtml


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## Forte (May 23, 2010)

adimare said:


> since √ab = √a x √b



Not when a and b are both negative 



qqwref said:


> Even better: http://mzrg.com/math/0=1.shtml



Is it that you didn't factor in the constant from the integrals? (the +C)


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## adimare (May 23, 2010)

Forte said:


> adimare said:
> 
> 
> > since √ab = √a x √b
> ...


You got me



Forte said:


> qqwref said:
> 
> 
> > Even better: http://mzrg.com/math/0=1.shtml
> ...


You got him. If you're going to abuse integration by parts, 1/x works just as well.

\( \int{\frac{1}{x}dx} \)
\( u = \frac{1}{x} \) and \( dv = dx \)
\( du = -\frac{1}{x^2}dx \) and \( v = x \)

\( \int{\frac{1}{x}dx}=\frac{x}{x}-\int{-\frac{1}{x^2}xdx} \)

\( \int{\frac{1}{x}dx}=1+\int{\frac{1}{x}dx} \)

\( 0=1 \)


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## Rinfiyks (May 26, 2010)

Let x = -1/(-1/(-1/(-1/(-1/(-1...
x = -1/x
x^2 = -1
x = ± i
± i = -1/(-1/(-1/(-1/(-1/(-1...


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## Forte (May 26, 2010)

Rinfiyks said:


> Let x = -1/(-1/(-1/(-1/(-1/(-1...



That can't exist because each time you do the -1 thing, you're flipping it from 1 to -1, so it's "divergent" (it never settles onto one number). I think that's what it is


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## Rinfiyks (May 26, 2010)

Forte said:


> Rinfiyks said:
> 
> 
> > Let x = -1/(-1/(-1/(-1/(-1/(-1...
> ...



It converges from the "bottom" of the infinite fraction though
\( 
\frac{-1}{0-\frac{-1}{0-\frac{-1}{0-\frac{-1}{0-\frac{-1}{...}}}}}
\)
(I put the zeroes in there so it's easier to see)


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## Lucas Garron (May 27, 2010)

Okay, enough fun, but this is puzzle theory. If anyone posts more unrelated math nonsense, it will be deleted.


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## InfernoTowel (Jun 1, 2010)

jtoc said:


> Thanks for the advice, everyone. I feared that it was stickers; this is probably a 5-year-old cube which has been, shall we say, well-loved. If I peel stickers off, I'm afraid they won't stay stuck on afterward. (Apparently my students have the secret for that.) Thanks for the advice on the replacement tiles, too.



If just one corner is oriented wrong, rotate a layer with that corner in it 45 degrees, pop out an edge piece, and turn the corner. Then (with the layer STILL TURNED 45 DEGREES, OR YOUR CUBE WILL BREAK) pop your edge back in.


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## Rpotts (Jun 1, 2010)

InfernoTowel said:


> If just one corner is oriented wrong, rotate a layer with that corner in it 45 degrees, pop out an edge piece, and turn the corner. Then (with the layer STILL TURNED 45 DEGREES, OR YOUR CUBE WILL BREAK) pop your edge back in.



lol at trying to help. I'm pretty sure he remedied his problem over a month ago.


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## InfernoTowel (Jun 6, 2010)

Rpotts said:


> InfernoTowel said:
> 
> 
> > If just one corner is oriented wrong, rotate a layer with that corner in it 45 degrees, pop out an edge piece, and turn the corner. Then (with the layer STILL TURNED 45 DEGREES, OR YOUR CUBE WILL BREAK) pop your edge back in.
> ...



xD sorry, I assumed it was a new thread because it was at the top of the forum and there aren't a ton of pages.


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