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## A math problem for the wise

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Jul 1, 2019, 17:5007/01/19

Kiki47 said:

1 !

Those who know maths - know the maths! ;-)

Your answer implies two conditions...those that know and those that don't. I consider this applicability in error. There are 4 conditions implied...those that know, those that don't, those who think they are correct in spite of being wrong, and those who could care less either way!

The problem is, when given opportunity, some of those who are wrong will contest this finding and engage in convoluted justifications to their error...and miss the moon and be lost in space. Those who are correct will pay no heed, land on the moon, and come home to raucous applause and accolades.

So, Kiki47, how does it feel to be a space wanderer?
Jul 4, 2019, 02:5607/04/19
Jul 4, 2019, 05:13(edited)

8    /   2   (1+3)

First the long explanation:

Note: The parenthesis coming directly after the 2 means that the amount within the brackets is to be multiplied by 2 . There is no nothing there to separate them.  i.e. 8 / 2(1+3)  is not the same as 8 / 2 x (1+3) . If you inserted the symbol you added something that was not part of the original equation in the question. Even then there would need to be brackets around the (8/2) in order for the 2 not to be distributed over the (1+3).

Everything after the division sign in this particular equation must be dived into the 8.

The proof first.

lets say x = 1 and y = 3  too make it easier to see for now.

=      8  /   2 (x+ y)

Solve for x and y:

Divide all by 2:

becomes

= 4 / (x+y)

OR:

4

=  _________

(x+y)

Multiply all by (x+y) to get x+y on one side of the equation and isolate the sub-equation.

becomes   (x+y)  =  4  x ( (x+y)/(x+y))

since anything divided by itself is 1 becomes simplified as

---->(x+y)  = 4 (1)

Divide all by 4:

becomes:  (x+y) /4 = 4/4

simplified is   (x+y) / 4 = 1

which when we substitute back in the 1 for the x and 3 for the y is

(1+3)

_____  = 1   TRUE Statement

4

gives us 1 = 1    ---- > Hence the correct answer is one. (1)

Brackets when incorporated in math equations denote superiority and must be dealt with first. The leading 2 in front of the brackets without a multiplication symbol indicates the integer or whatever  must be distributed over the contents inside the brackets. The 2 in this case.

2(x+y) == 2x + 2y  proof put the numbers back in temporarily  2(1+3) == 2 x 1 + 2 x 3    OR   2(4) == 2+6   ==>    8 = 8  See...

Let's proceed.

So a faster method:

8 / 2 (x+y)

= 8 /(2x +2y) ;            You must distribute the 2 across the contents inside the brackets.

WHY? Rules. Don't add something not there. You are dividing 8 by 2 groups of (x+y) or (1+3) in this case.

=   8 /((2x1) +(2x3))   ; you can't lose your outside brackets when distributing be careful as you are basically breaking

the brackets down here. It is the opposite of fusing runes.

= 8 / (2+6)

= 8/8

= 1

You cannot add symbols to an equation which will change the equation do what you would like it to be.

8 / 2(1+3) is not the same as 8 / 2 x (1+3)

The answer in the first case is 1.

The answer in the second case is, you guessed it, 16. Which is not the one we were being asked about.

8/2(1+3)  is NOT equal to  8 / 2 x (1+3) where the 8 gets divided  by only the  2.

People get sloppy with equations and writing their symbols. Don't let that happen to you. Write what you mean.

Jul 4, 2019, 07:3707/04/19
Jul 4, 2019, 07:38(edited)

Just for the geniuses in this thread. Multiplication is associative, division is NOT:

https://en.wikipedia.org/wiki/Associative_property

Thus,

8 * 0.5 * 4 == (8 * 0.5) * 4 == 8 * (0.5 * 4) => 16

You cannot swap the order of division and multiplication, it is not associative:

(a / b) * c != a / (b * c)

The whole problem comes down to interpretation of 2(3 +1). Plarium have ommited the '*' sign to confuse people. Previous poster seems to think that lack of '*' implies parenthesis around the whole '2(3+1)' expression. That is highly subjective imho. Please site a source which indicates that lack of '*' implies ordering of operations. Until such time, the answer can only be 16.
Jul 4, 2019, 20:2007/04/19
Jul 4, 2019, 20:22(edited)

I remain surprised at the steadfastness of this topic, so I have just looked at the internet as to the correct solution to this problem.remembering the L R, (left to right) rule and following BODMAS, or as some say PEDMAS, which are effectively the same thing, the answer as 1.

Explanation.

8÷2(1+3)=?

First you had to do B=P=( ), ie what is inside them.

1+3 = 4 but the ( ) remain, so the equation becomes

8÷2(4) =? so the operation connected to the ( ) retains superiority,over anything else,so the equation becomes

8÷8=?,which is 1.

though ( ) and x ,are effectively the same operation,the equation does not become

8÷2x4

If this was the case,where division,and the left to right rule takes priority, the equation would become,

Jul 4, 2019, 23:2707/04/19
Jul 5, 2019, 00:08(edited)
DeathMiser said:

The most amazing thing is to read those with the wrong answer, who profess how all those with the correct answer are wrong!
lol ... maybe people should go to an online calculator and type it in exactly as written in the op (which means you need one where you can put in parenthesis) with an = at the end and then "those with the wrong answer" can argue with the online calculator
Jul 5, 2019, 00:2507/05/19
CIM said:

DeathMiser said:

The most amazing thing is to read those with the wrong answer, who profess how all those with the correct answer are wrong!
lol ... maybe people should go to an online calculator and type it in exactly as written in the op (which means you need one where you can put in parenthesis) with an = at the end and then "those with the wrong answer" can argue with the online calculator
I found his posts ironically amusing too, considering his bluster and incorrect answer.
Jul 5, 2019, 00:5107/05/19
KROW said:

I found his posts ironically amusing too, considering his bluster and incorrect answer.
Jul 5, 2019, 01:0807/05/19
Jul 5, 2019, 01:35(edited)

I decided to check on your advice and look on the internet.As you described it is difficult to ask the question.

On typing  8÷2(1+3) on a browser the internet converts the question to (8÷2)×(1+3)= ? Answer to (8÷2(1+3) is 16,

As to WDYWTNTF  according to several web tutorials  hosted by whom appear to be maths teachers,there is no need for the double brackets, as the bracket would  not appear to disappear after you have completed the operation inside. So CIM what is your answer?

Given the internet's different appraisal the argument continues!?

Did Plarium steal the puzzle  directly from the internet, where the answers given are as similarly contradictory ?

Jul 5, 2019, 01:3507/05/19
Jul 5, 2019, 05:52(edited)

It isn't how I described t it is how the OP described it. And yes it is not the best way to write it which is what makes so much "doubt" about it.  However I was able to type it right into calculators just as written ...

https://www.desmos.com/fourfunction

This is a variation of 6÷2(1+2) = ? which there is a lot on the internet on that.

WDYWTNTF did what a few others did also ... what is INSIDE brackets comes first but what is connected to the brackets which is an implied multiplication doesn't necessarily have "superiority" over the division.

Some set up the equation in fraction form with differences in their set up and then differences in their results.

Anyways here is some links for discussion concerning the 6÷2(1+2) = ? that might "help"

Jul 5, 2019, 01:3607/05/19
Alice Vytsenets said:

Hello Jarls!

We have an exercise for you that seems easy only at first glance. Can you solve it and explain your answer? Just to show again this is how it was written in the OP ...
Jul 5, 2019, 01:3707/05/19
Jul 5, 2019, 01:45(edited)

Yes I have just found that question,  6÷2(1+2) = ? as well, when I did more searching.Its effectively the same situation.

Jul 5, 2019, 01:4407/05/19
Jul 5, 2019, 01:44(edited)
KROW said:

Yes I have just found that question,  6÷2(1+2) = ? as well, when I did more searching.Its effectively the same dilemma.

Those two links then I posted above concerning that equation should be helpful.
Jul 5, 2019, 01:4607/05/19
Well fury has killing invaders and ghosts in my home kingdom now as bonus ... so ... lol ... I decided to finally chime in here and well I was waiting for there to be a number or responses before I did ...
Jul 5, 2019, 01:4907/05/19
CIM said:

Oh I changed my post above to give you an online calculator that you can just type it into ...

https://www.desmos.com/fourfunction

That puts the cat amongst the pigeons, The link gives the answer as 16.
Jul 5, 2019, 02:0107/05/19
KROW said:

CIM said:

Oh I changed my post above to give you an online calculator that you can just type it into ...

https://www.desmos.com/fourfunction

That puts the cat amongst the pigeons, The link gives the answer as 16.
I had to look that saying up ... I had no idea what it meant ...
Jul 5, 2019, 02:4207/05/19
Jul 5, 2019, 03:40(edited)

Now how surprising is that?

There is an argument that the puzzle is not solvable.

We all seem to agree that you have to complete the brackets first  (1+3)=4.

We can all agree 8÷2 =4 but there are no instructions given as to what should be done with the  two fours.

4 ? 4 =?

If you then argue that brackets become a multiplication then 4 x 4 =16, but if you drop the brackets as soon as you do the addition there are no brackets, therefore no multiplication can be implied, if you then say keep the brackets, and call it multiplication instead, then you have to admit that the brackets/parenthesis contents, takes priority over the Left to Right Division scenario,so the answer has to be 1.

Revision after doing more research.

In spite of internet calculators appearing to give the answer as 16, I have come to the conclusion that the problem isn't really solvable as written, as explained above.

Simplified (hopefully) here,

if you drop the brackets which seems to be the modern way of doing things there is no operand for  the product of 1+3,

if you keep the brackets and say they become multiplication which I seem to remember perhaps erroneously used to be the case,

8÷2(1+3)=? becomes 8÷2(4)so you must do the brackets content first.  Answer 1.

if you drop the brackets for multiplication 8÷2(1+3)=? becomes 8÷2 x 4.Answer 16.

I cannot find any reference or rules that brackets change to x, multiply, after completing anything inside the brackets

Jul 5, 2019, 07:1607/05/19
Jul 5, 2019, 07:18(edited)

What do you mean "drop" the brackets?  8÷2(4) ... how do you just "drop the brackets" ... and how can there be "no multiplication"?  There HAS to be multiplication.  Question is does the multiplication that happens with the (4) happen with the 2 or with the results of 8÷2 ...

And if you say you are going to do 8÷2 and it equals 4 then the only thing left to do with the other 4 is multiply it ... what do you want to do another divide (since you already did 8÷2) ... ???  That doesn't make any sense at all ... this 4?4=? ... this isn't a "possibility" ...

It is either 8÷8=1 OR 4x4=16 ... there is no 4?4=?

So I see you have done some revisions to that post so the above was wrote before that revision.  Again no one is talking about "drop the brackets" ... and you seem to be in your revision proposing that 1 MUST be the answer.

Jul 5, 2019, 10:0807/05/19
Jul 5, 2019, 11:01(edited)

To Summarize:

The answer 1 and 16 can be given and support can be produced for each of them ... the equation should not really be written like it is ... if I had to give only one answer and couldn't explain it I would give 16.  And if I could explain it I would also give 16.  But it isn't the "only" possible answer if proper explanation is given since we don't have a universal standard for dealing with it.  To make it clear it needs more parentheses/brackets.

------------------------------------------------------------------

Using PEMDAS/BODMAS/BEDMAS you have:

8÷2(1+3) =

8÷2(4) =

4(4) =

16

------------------------------------------------------------------

If we use an outdated way of dealing with this where everything on the left side of the divide sign is divided by the right side of the divide sign we have:

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

This is outdated for many reasons ... first let us look at what would happen here ... this was done in the past for some simple equations where people were trying to convey what the answer here shows ...

2+3÷3+2 =

5÷5 =

1

However this is so far away from PEMDAS/BODMAS/BEDMAS which would be

2+3÷3+2 =

2+1+2 =

3+2 =

5

So everyone who used this way of doing 8÷2(1+3) = 1 do you want to also say 2+3÷3+2 = 1 ???

And when there are multiple divisions to be done in an equation well I think you could start getting confused ... what would you do with ...

2-4÷6+7x5+3÷17x5-3÷6÷12+3 =

yea I guess it could be done ... but again wouldn't be PEMDAS/BODMAS/BEDMAS and well it isn't how it would be done these days or I think even in the past

------------------------------------------------------------------

Then we have a modified form of PEMDAS/BODMAS/BEDMAS which is used by mostly physicists ... it has to do with implied multiplication having higher precedence over explicit multiplication and division.  Parentheses can be one way for multiplication to be implied but it is not the only way.  So it is not because of the parentheses but because of the implied multiplication caused by the parentheses that would give you this.

8÷2(1+3) =

8÷2(4) =

8÷8 =

1

I would think if you gave the reasoning that PEMDAS/BODMAS/BEDMAS requires you to do parentheses (brackets) first and the 2 is part of the brackets you wouldn't get full credit for this ... if you said that implied multiplication has higher precedence over explicit multiplication and division you have a good chance to get full credit.  Some calculators have implied multiplication having higher precedence than explicit multiplication and division and will give the answer 1 to the OP equation as posted.

So let's look at another equation and see what you would come up with SINCE parentheses (brackets) are not always necessary for implied multiplication.

A ÷ BC =

Where A = 3 , B = 2, C = 30 ... what would be your answer?

If you say 0.05 then you are being consistent with the modified form of PEMDAS/BODMAS/BEDMAS and with an answer of 1 for the OP, since in the equation BC is implied multiplication it needs to be done first.

3 ÷ 60 =

0.05

If you say 45 then you are being consistent with the "normal" PEMDAS/BODMAS/BEDMAS and with an answer of 16 for the OP.  Here division and multiplication are done in the order from left to right that they appear with no precedence for implied multiplication.

1.5 x 30 =

45

Big difference between 0.05 and 45 ... and yes I tried to make it simple to illustrate the difference between PEMDAS/BODMAS/BEDMAS and the modified form of PEMDAS/BODMAS/BEDMAS.  I will see if I can get better examples ... but you see this has nothing to do with parentheses (brackets) but with whether the multiplication is implied and not explicit.

------------------------------------------------------------------

And it's been over 36 hours since I have had any sleep so I hope I didn't mess any of that up and I hope I explained adequately.  The answer 1 and 16 can be given and support can be produced for each of them ... the equation should not really be written like it is ... if I had to give only one answer and couldn't explain it I would give 16.  And if I could explain it I would also give 16.  But it isn't the "only" possible answer if proper explanation is given since we don't have a universal standard for dealing with it.  To make it clear it needs more parentheses/brackets.