# 6

Discussion in 'Off Topic' started by Vihzel, Apr 28, 2011.

?

## 6÷2(1+2) = ?

94 vote(s)
54.3%

77 vote(s)
44.5%

2 vote(s)
1.2%

Jan 22, 2010
11,821
3,411
923

#76
2. ### novox77 Leeeroy Jennnkinnns! Rank:  #75 Points: 413 Posts: 3,965 Joined: Jul 7, 2010

Jul 7, 2010
3,965
3,257
413
It was a great thread, no doubt.

However, I personally like the problems where there actually is a clear-cut correct answer and yet all the bigshot PhDs of the world can't agree on a right answer. Such was the case for:

1) The Monty Hall problem

2) The plane on a treadmill runway problem

#77
3. ### Vihzel Destroying Balls Everyday Thread Starter Rank: None Points: 333 Posts: 5,364 Joined: Apr 8, 2010

Apr 8, 2010
5,364
1,055
333
NYU Student & Real Estate Agent
Manhattan, NY
The thing is... my answer is as good as anybody else's. I don't have like the FINAL ANSWER THAT MUST BE OBEYED!!!!!!!! lol

I personally believe it's 9 and that's the answer I would put on the math test to save my life. hehe

I interpret it as 6/2(1+2) is not the same as 6/[2(1+2)], so one answer would come up 9 and the other one as 1.

It's really amazing to see how even really intelligent people can argue for days on this and not come to an agreement on other equivalent problems to this.

#78
jroc likes this.
4. ### dan330 Android Expert Rank:  #26 Points: 923 Posts: 11,821 Joined: Jan 22, 2010

Jan 22, 2010
11,821
3,411
923
so.. there is no scientifically "right/correct" answer???? there must!

math at this level is very exact...

#79
5. ### novox77 Leeeroy Jennnkinnns! Rank:  #75 Points: 413 Posts: 3,965 Joined: Jul 7, 2010

Jul 7, 2010
3,965
3,257
413
In case no one has bothered to wiki this subject yet...
Order of operations - Wikipedia, the free encyclopedia

And the part of interest:

Gaps in the standard

There exist differing conventions concerning the unary operator &#8722; (usually read "minus"). In written or printed mathematics, the expression &#8722;3^2 is interpreted to mean &#8722;(3^2) = &#8722;9, but in some applications and programming languages, notably the application Microsoft Office Excel and the programming language bc, unary operators have a higher priority than binary operators, that is, the unary minus (negation) has higher precedence than exponentiation, so in those languages &#8722;3^2 will be interpreted as (&#8722;3)^2 = 9. [1]. In any case where there is a possibility that the notation might be misinterpreted, it is advisable to use brackets to clarify which interpretation is intended.
Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x). Again, the use of brackets will clarify the meaning and should be used if there is any chance of misinterpretation.

The takeaways are highlighted.

RED: neither 9 or 1 is correct or incorrect. The person posing the problem (not you Vihzel) is WRONG for not being explicit.

GREEN: if there is the possibility of ambiguity of INTENT, use parentheses!

#80
Ichapp likes this.
6. ### alostpacket Over Macho Grande? Rank: None Points: 513 Posts: 7,973 Joined: Nov 29, 2009

Nov 29, 2009
7,973
3,603
513
Android App Developer
NY
So the Android compiler/Java was right
Code (Text):
1. 6/2(1+2)
2. Syntax error on token "2", * expected after this token.
heh

#81
7. ### EarlyMon The PearlyMon Rank:  #1 Points: 5,218 Posts: 57,632 Joined: Jun 10, 2010

Jun 10, 2010
57,632
70,418
5,218
New Mexico, USA
I guess we're ready, people have shied away.

Uncle.

#82
8. ### novox77 Leeeroy Jennnkinnns! Rank:  #75 Points: 413 Posts: 3,965 Joined: Jul 7, 2010

Jul 7, 2010
3,965
3,257
413
Bob's sequence is how the second, minute, hour hands cross the numbers 1-12 on a clock.

Again a "Blink" answer. I haven't had time to even think if that makes sense or not. Gotta run to the doc's office. be back in a few hours with some more thought on it.

#83
9. ### EarlyMon The PearlyMon Rank:  #1 Points: 5,218 Posts: 57,632 Joined: Jun 10, 2010

Jun 10, 2010
57,632
70,418
5,218
New Mexico, USA
Sure?

My understanding was that the same number was next for both sequences, for the same reason.

I based my answer on a cycle I thought I saw.

#84
10. ### apavolka Android Enthusiast Rank: None Points: 43 Posts: 495 Joined: May 15, 2010

May 15, 2010
495
30
43
Plumbing Supply House
Flagstaff, AZ

#85
11. ### Knifethrower Lurker Rank: None Points: 5 Posts: 1 Joined: Apr 29, 2011

Apr 29, 2011
1
0
5
@BobMaxley The bell tolls. 15min single or thirty min single

#86
12. ### RiverOfIce Banned Rank: None Points: 313 Posts: 1,715 Joined: Mar 30, 2010

Mar 30, 2010
1,715
1,254
313
In exile
LOL. 2 pages over this?

That answer is 9, could not be anything else. Regardless of how you read it.

I guess you want me to prove it right?

Ok, easy.
6/2 (1+2)= 6/2 is what you do with them. (1+2) is what they are, so....

You have to make a dog house, you have 3 (1 pine +2 fir), six foot long, boards to do it with. Plans say your dog house must be 2 feet tall. The boards are exactly 6 foot long and you must cut them at 2 feet. (6/2=3)

How many boards do you have after you finished cutting them?

1 six foot long board cut at every 2 feet, is exactly 3 boards

You have 3 six foot long boards, after you cut them all you have 9 exactly equal boards. 3x3=9

You can not take 2 feet out of 3 boards equally, which is what the multiplication is telling you, until you know the actually feet of the boards,which is what the division is telling you. The parenthesis make it clear what is the object and what is the operation. Because the operation tells you what to do with the object.

All you have to do is look at it as real things, not just numbers.

#87
13. ### DaSchmarotzer Blame it on me Rank: None Points: 313 Posts: 3,087 Joined: Mar 10, 2010

Mar 10, 2010
3,087
1,568
313
Studying
Qu
I still think my explanation is less confusing.

6

#88
EarlyMon and novox77 like this.
14. ### novox77 Leeeroy Jennnkinnns! Rank:  #75 Points: 413 Posts: 3,965 Joined: Jul 7, 2010

Jul 7, 2010
3,965
3,257
413
no i was not sure. and now that i think about it, i can't get it to fit my hypothesis, so never mind

#89

Jul 7, 2010
3,965
3,257
413

#90
16. ### Usta Android Expert Rank: None Points: 333 Posts: 2,585 Joined: Jul 8, 2010

Jul 8, 2010
2,585
1,374
333
The Netherlands
Allow me to take another stance...
If 6

#91

Jan 22, 2010
11,821
3,411
923

#92
18. ### EarlyMon The PearlyMon Rank:  #1 Points: 5,218 Posts: 57,632 Joined: Jun 10, 2010

Jun 10, 2010
57,632
70,418
5,218
New Mexico, USA
A*B*C = A*C*B

It's not operator location that implies precedence - it's only operator type and parens that set that.

Probably the only reason the confusion ever existed is because at some point around 20 years ago compilers popularly ended up whenever there was code like this and evaluating multiplications first, then divisions - leading to computation tools that enforced the thinking that leads to the wrong conclusion.

6
--------
2(1+2)

and

6(1+2)
--------
2

are both correctly hand-written notations of two different problems.

6/2(1+2) is machine-form (the typewriter) notation - and so only the conservative and strict rules may apply, to free from compiler confusions.

A * B * C = A * C * B
A / B * C = A * C / B

Therefore = 9.

#93
krouget, Ichapp and DaSchmarotzer like this.
19. ### dan330 Android Expert Rank:  #26 Points: 923 Posts: 11,821 Joined: Jan 22, 2010

Jan 22, 2010
11,821
3,411
923
but the way it is represented... there is an implied reason for the location....

so there is an implied () around the first part = (6) ..
and an implied () around the second part = (2(1+2))..

you can not change what is inside or outside ().

NOTE: that is my interpretation of "implied"... i can be wrong.
is there an expert / professor here that can state the facts?

#94
20. ### Roze Hiding behind a mystery Rank: None Points: 333 Posts: 9,814 Joined: Jan 20, 2010

Jan 20, 2010
9,814
2,183
333
Where the Sakura grows
...dear lord of the butterflies...the answers have gotten much more confusing >_>;;; I think I got confused when letters started appearing in the equations.

#95
jroc likes this.
21. ### EarlyMon The PearlyMon Rank:  #1 Points: 5,218 Posts: 57,632 Joined: Jun 10, 2010

Jun 10, 2010
57,632
70,418
5,218
New Mexico, USA
Well, if you don't find me expert enough (I'm peer-reviewed published in higher math for signal processing, nuclear reactor stuff, hydrodynamics, and radar among other things, and have lectured on and taught related stuff at the post-grad level), or DaS, another cool guy in the science biz - then just use the wiki info that novox 77 kindly copied:

Similarly, care must be exercised when using the slash ('/') symbol. The string of characters "1/2x" is interpreted by the above conventions as (1/2)x. The contrary interpretation should be written explicitly as 1/(2x).

Substitute (1+2) for x and it's case closed.

#96
alostpacket and dan330 like this.
22. ### DaSchmarotzer Blame it on me Rank: None Points: 313 Posts: 3,087 Joined: Mar 10, 2010

Mar 10, 2010
3,087
1,568
313
Studying
Qu
There is not such thing as "implied" when it comes to mathematics, since it would change the result. Rigor is important in sciences for that precise reason. Also, I consider EarlyMon to be an expert. Well, I also consider myself an expert for many things but that's a whole different story.

Also, both Mathematica (it's the same as Wolfram Alpha) and Maple say 9. Computers can't assume stuff (unless it's coded in ). If you ever start programming (maybe you do), you will truly understand what I mean by that.

PS: Roze, what a disappointment.

EDIT: Wow, I wrote that before EarlyMon had posted again.

EDIT2: Note to self: Using a lot of smiley faces sure doesn't help my credibility.

#97
krouget and dan330 like this.
23. ### dan330 Android Expert Rank:  #26 Points: 923 Posts: 11,821 Joined: Jan 22, 2010

Jan 22, 2010
11,821
3,411
923

ok.. i aint no expert. so i will bow to expert interpretation....

there is no implied () and
if in doubt...
left to right ...

x = 9

#98
24. ### EarlyMon The PearlyMon Rank:  #1 Points: 5,218 Posts: 57,632 Joined: Jun 10, 2010

Jun 10, 2010
57,632
70,418
5,218
New Mexico, USA
My reply was turning into another EarlyMon War+Peace special , so I deleted it, hoping you might post the clear path.

Doesn't hurt it any.

Often, information has to be expressed in multiple ways before clarity occurs.

This is true at all times and at all levels.

I once spent a decade solving a single equation - final proof took 30 pages of trig. After lecturing on the results and implications, and engaging in 5 years of feedback, I found while sitting in an airport, pretty smug over the day's lecture, that by considering all arguments for over a decade that the entire matter reduced to a simple progression of merely 4 clear and simple equations.

Illustrating for me for all time the positive need and positive benefit for us all to argue our way through things - you just never can be sure until the process completes how things might end up.

One of the reasons I like the people here.

Multiple people came to the same conclusion, all for the right reason.

#99
jroc likes this.
25. ### alostpacket Over Macho Grande? Rank: None Points: 513 Posts: 7,973 Joined: Nov 29, 2009

Nov 29, 2009
7,973
3,603
513
Android App Developer
NY

I'm no professor, but this is what I think it comes down to: To change the order of operations around the adition part (1+2) you need to add a parenthesis to make that go first, we all agree there.

But it shouldn't (and doesn't in my mind) make any sense that I should have to infer that a number that is near a parenthesis should have it's order of operation changed too. The parenthesis should change only what's inside it, with the innermost being evaluated first.

Basically some other problems to illustrate:

we clearly know that 6 * (1+2) = 18

And that 6 * 1 + 2 = 8

And that 6 / (2(1+2)) = 1 <- this is clear and obvious

^ So how is it we can infer 6 / (2(1+2)) from 6/2(1+2) ?

Unless there's some clear exception to the order of operations rule, we should not make assumtions that require additional parenthesis (imo)

Though my own argument can be used against me here too because the opposing argument could be how can you infer (6/2) * (1+2) ?

IMO,the reason you can infer the second (6/2) * (1+2) is because 6/2 doesn't need parenthesis normally, as it would natually come first in the order of operation.

6/2*3 is certainly clear enough I think. Once the parenthesis have been evaluated, they shouldn't affect the rest of the equation.

Also, I think It's pretty clear that:

EarlyMon/Rose(dan330+usta)=nova777 (imo)

And that's my final proof. Irrefutable! Just be sure to evaluate the (imo) first.

jroc likes this.