After posting Trending: Only for genius ?? 3 – 3 x 6 + 2 = ?? yesterday, I had to post a follow up article with the correct answer.

Even with the hint about remembering the order of operations, people still got it wrong on my poll. If you haven’t done the poll yet, click on the link above and respond.

The question was

The correct answer is as follows:

- Question: 3 – 3 x 6 + 2
- Multiplication first: 3 – 18 + 2
- Left to right: -15 + 2
- Answer: -13

**So what do you get if you type it into a calculator (physical or app)?**

That depends on if the calculator is simple and calculates as you type, or if it is smart and waits for the entire equation to be entered and the equals button pressed.

On my Windows 10 Mobile phone, the calculator app can behave in both ways.

In Scientific mode, it allows the entire equation to be entered and so correctly calculates the answer as -13 using the “Order of Operations” rules (same as above).

In Standard mode, it calculates as you type and so incorrectly gives the answer as 2. The way to think of it is that it inherently presses equals each time you press an operation button. This is just left to right calculation and ignores the “Order of Operations” rules.

- 3 = 3
- 3 – 3 = 0
- 0 x 6 = 0
- 0 + 2 = 2

If your calculator behaves in this simple way, you would need to apply the rules yourself. Here are the buttons to press:

- 3 x 6 = MS
- 3 – MR + 2 =

If your calculator has brackets or parentheses buttons you can use them instead of the Memory buttons to achieve the same effect.

- 3 – ( 3 x 6 ) + 2

Looking at the poll results from the previous article, there are a number of incorrect answers being selected, so I thought I would try to identify the **actual** equations that would give those incorrect answers (changes highlighted in red):

- -17 = 3 – ( 3 x 6 + 2 )
- 0 = ( 3 – 3 ) x ( 6 + 2 )
- 2 = ( 3 – 3 ) x 6 + 2
- 8 = 3 – 3 + 6 + 2
- 13 = – 3 + 3 x 6 – 2
- 17 = – 3 + 3 x 6 + 2

Hope this all makes sense. Here endeth the lesson.🙂

Have a look at the other posts in the series:

- Trending: Only for genius ?? 3 – 3 x 6 + 2 = ?? With Poll and Order of Operations
- Answer: Only for genius ?? 3 – 3 x 6 + 2 = ?? This article
- Conclusion: Only for genius ?? 3 – 3 x 6 + 2 = ?? Breaks down solution into steps
- The Last Word: Only for genius ?? 3 – 3 x 6 + 2 = ?? Explains ordering of DM and AS

Enjoy

David

This article was originally posted on http://www.winthropdc.com/blog.

If you go by pemdas your supposed to add before you subtract… giving you -17

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Hi Mindy

PEMDAS means Parentheses, Exponents, (Multiplication/Division), (Addition/Subtraction). The Multiplication and the Division are performed at the same time and but before the Addition and Subtraction which are performed at the same time.

However, even if I perform the addition first, the answer is still -13.

3 – 3 x 6 + 2 = 3 – 18 + 2 = 3 – 16 = -13

because -18 + 2 = -16 not -20

Think of the sum as 3 + -18 + 2 if that helps.

Please see the third post in the series which discusses this further:

https://winthropdc.wordpress.com/2016/02/15/conclusion-only-for-genius-3-3-x-6-2/

David

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Yes. I showed it to an engineer at lunch today and he said -17. However, that was after he said 2, which is what I say. This is not how you measure IQ anyway. A person with high IQ figures the problem out without knowing any pre-existing rules.

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Hi Sandy

Can I suggest you ask your engineer to read this blog article and its comments?

David

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hi Mindy!

you’re right, PEMDAS is the rule in every equation which means

3 – 3 X 6 + 2 =

3 – (3 X 6) + 2 =

3 – 18 + 2 =

-15 + 2 = -13

because -18 + 2 = -16 and not -20

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To prove you’re a genius, you have to figure the problem out without prior knowledge of the rules. Going left to right, the answer is 2. You may have the right answer because you know the “rule” but that doesn’t make you a genius.

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Hi Sandy

I just took the image from the internet which had the wording “Only for genius” already on it. I do agree that figuring out the problem is important.

However, there are some basic maths rules which are needed to make it work.

For example: If you reorder the equation, what answers do you get when calculating left to right?

3 – 3 x 6 + 2 = 2

2 + 3 – 3 x 6 = 12

2 – 3 x 6 + 3 = -3

–3 x 6 + 2 + 3 = -13

If you follow the order of operation rules ALL of the above equations give the same answer = -13.

David

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Hi Sandy

Try this:

You are an apple farmer. You can sell apples individually or in a carton of 6 apples.

You have 3 apples available when a shop asks for 3 cartons to be supplied.

You give the individual apples you have to the shop and promise to supply the rest.

2 more apples are now ready for picking and so you also supply those to the shop.

How many apples do you still owe to the shop?

David

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3-3×6+2= -13

I see 3×6=18

But how does it turn to -15

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Hi Ed

I could not work out how to get -15, but it was in the list of answers I saw on the original Facebook post. I think it comes down to just not being able to do addition.

David

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hi Ed!

-15 derives from adding the first number which is 3 to -18 which derived from (-3 X 6) where when you add 2 with -15 will give you -13 as the answer.

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Why the two ??

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Hi James,

The two question marks are on the image that was doing the rounds on the internet. I did not create it and don’t know who did. If you can identify the creator you can ask them !!🙂

David

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A teaser. What if ? represents x in algebra

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-13=??

-13=?squared

?=square root of -13

?=3.60555126 i

Or impossible because you can’t have the square root if a negative number.

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Hi Clancy, The creator of the original image got over excited with the question marks, but I am glad you have solved for a single question mark. The use of imaginary numbers based on the square root of -1 (represented as i) is allowed.🙂

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Why would you do the subtraction before the addition of the addition comes first in order of operations? I came up with -17 by doing the addition first.

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Hi John

The order of operations mnemonic is designed to ensure that you perform the multiplication and division before the addition and subtraction. The actual order of multiplication and division (or division and multiplications) will not affect the answer. Also the actual order of addition and subtraction (or subtraction and addition) will not affect the answer.

Your calculation error is covered in my final post on the topic: https://winthropdc.wordpress.com/2016/02/29/the-last-word-only-for-genius-3-3-x-6-2/

Basically you jumped from 3 – 18 + 2 to 3 – 20. The mistake is that -18 + 2 is not -20, it is -16. When you add to a negative number, you make it less negative. See my post above for a full explanation.

David

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Why don’t you apply “BODMAS” rule?

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Hi Thabiso

I did apply BODMAS. The answer is still -13.

Note that Division and Multiplication can be performed at the same time as long as they are executed before Addition and Subtraction, which can also be performed at the same time.

However, if I do it exactly in BODMAS order you still get -13.

3 – 3 x 6 + 2 = 3 – 18 + 2 = 3 – 16 = -13

I suspect you are thinking I did the addition wrong, but when you add -18 + 2 you get -16 not -20. Just draw a number line and move 2 places right from -18 to -16.

Did you look at the other articles in this series which explain why the answer is always -13? Especially the “Last Word” article.

Yours Mathematically

David

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in my opinion it should be 0 because in badmas rule. first + ad – is solved then * and /.

no matter what the order is.

until u use brackets and explain the question.

why we are suppose to solve the * first. we must not as the brackets are not present

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Hi Muhammad

You have two “a”s in your mnemonic. The second letter should be I (indices), O (orders) or E (exponents).

Mulitiply and divide are always performed before addition and subtraction.

Look at the other articles, especially the last one which has links to online sites solving the sum.

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I understand why it is -13 but using the same method used to get -13 if you do the addition then the subtraction you get -17

3 – (3×6) + 2 =

3 – 18 + 2 =

3 – 20 = -17

And you can’t say that right to left the answer is -13 because saying that is -18 is to assume

3 (-18)+2 or

3 – (-18) + 2

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Hi RicknMorty (great show)

Ok, you agree that you need to do 3×6 first to get 18. Except that it is actually -3×6 = -18.

So 3 – 18 + 2 = -15 + 2 = -13

Or 3 – 18 + 2 = 3 – 16 = -13

Or 3 – 18 + 2 = 5 – 18 = -18 + 5 = -13

Regardless of the order you do the addition and subtraction the answer is the same -13.

If you think about it as the following it might make it easier, especially if you use a number line:

3 – 18 + 2 = 3 + -18 + 2

Don’t subtract 18. Add negative 18.

Regardless as long as you do multiplication and division before addition and subtraction the answer will always be -13. The order that you do the multiplication/division in is not important: 3 x 6 = 6 x 3 = 18. The order that you do the addition/subtraction in is not important: 2 + 3 = 3 + 2 = 5 or 3 – 2 = -2 + 3 = 1.

David

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I just want to know how you know that it is negative 3 because i see it as 3 minus 3??

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Hi Keith

The order of operations rules say that you must perform multiplication and division BEFORE addition and subtraction. So even though there are no brackets you must treat it as though there are brackets around multiplications and divisions.

3 – 3 × 6 + 2 = 3 – (3 x 6) + 2 = 3 – (18) + 2 = 3 – 18 + 2

Now have a look my previous comment response to see how 3 – 18 + 2 = -13

Also look at the other articles in the series which provide more details.

David

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I will be

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3 – 3 × 6 + 2 = ????

3 – 3 = 0

6 + 2 =8

Now 8 × 0 = 0

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Hi Rumi

Sorry but your answer is incorrect.

Mathematical principles say you MUST calculate the Multiplication and Division before Addition and Subtraction.

David

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But of there are no brackets don’t you skip that part?

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Hi Yoshi. Order of operations says multiply and divide before addition and subtraction. No brackets needed.

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(3-3)*(6+2)=0

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Sorry Raj but that was not the question asked and so is not the correct answer.

If you must put brackets/parenthesis around part of the equation then it must be around the multiplication as Multiplication and Division must always be performed before Addition and Subtraction.

3 – (3 x 6) + 2 = 3 – 18 + 2 = -15 + 2 = -13

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Why is it not 3-18+2 = 3-(18+2) = 3-20?

You do the addition before subtraction. So you add 18 and 2.

You do not add -18+2 as the minus sign should be outside the brackets. You only use it once so you are taking the sun of (3×6)+2 away from 3.

If it is (-3×6) then suddenly your sum becomes 3 (-3×6)+2. This would be -54!

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Hi Ian

Order of operations says that Multiplication and Division should be completed before Addition and Subtraction. However, Multiplication and Division can be performed at the same time as can Addition and Subtraction.

3 x 4 / 2 = 4 / 2 x 3 = 6

3 + 4 – 2 = 4 – 2 + 3 = 5

The order is not important. if you really need to add parenthesis/brackets:

3 – 3 x 6 + 2

= 3 + -3 x 6 + 2

= 3 + (-3 x 6) + 2

= 3 + -18 + 2

= -15 + 2

= -13

David

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I thought using bedmas addition would be first so 3×6+2-3=17??

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Hi Cameron

The sum you state does calculate to 17, but it is NOT the sum in the question.

3 – 3 x 6 + 2 = 3 – 18 + 2 = -15 + 2 or 3 – 16 = -13

In your bedmas, division and multiplication are performed together before addition and subtraction are performed together.

The issue is that -18 + 2 is -16 not -20.

David

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Why wouldn’t you solve like this: 3-[(3*6)+2] ?

Don’t you have to do Addition before Subtraction?

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Hi Nick

3-[(3*6)+2] is not the question.

3+[(-3*6)+2] is the question if you add brackets.

Please see https://winthropdc.wordpress.com/2016/02/29/the-last-word-only-for-genius-3-3-x-6-2/ which explains that the order of Addition & Subtraction and Multiplication & Division is irrelevant as long as Multiplication & Division is performed before Addition & Subtraction.

Doing Addition before Subtraction or Subtraction before Addition will ALWAYS give the same result if you do it correctly.

David

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The answer cannot be -17 it is -13 and the reason is because of pedmas. Parenthesis exponent division multiplication addition then division. So 3-3×6+2=? U start with -3×6 which gives you -18 so the new equation is 3-18+2=? Next we go -18+2 =-16 New equation is then 3+-16=-13. If we say 3-3=0 is it not the same as 3+-3 = also 0. Another way of looking at it is 3-3×6+2 is the same as 3+-3×6+2=? Same operation -18 +2=-16 3+-16 still equals -13. That’s where the confusion lies because you can’t do 3-3×6+2=? And think you do 18+2= 20 therefore 3-20 = -17 it makes no sense that way because you forget it is already -3 to begin with not 3

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Why not: 3 (-3×6)+2? =-52 how do you know whether it’s just 3 not -3?

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Hi Danielle

The question is 3 – 3 x 6 + 2 = ?, which could be written as 3 + -3 x 6 + 2 = ?

This is not the same as 3(-3×6)+2=? as you have effectively written 3x(-3×6)+2=? which changes the + sign after the first 3 to a x sign.

If you must add unnecessary brackets then the question is either

3 – (3 x 6) + 2 = ? or 3 + (-3 x 6) + 2 = ? both of which give the answer -13.

David

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Do none of you realise the order is Brackets, Order, Division, Multiplication, Addition, Subtraction in that order?

So, as it should go is as followed:

Multiplication: 3×6 = 18

Addition: 18+2 =20

Subtraction: 3-20= -17

That is straight forward mathematics that is taught to 11 year olds in schools….

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Hi Dwayne

You are correct on the order, but forgot to note that Addition and Subtraction can be performed together, or any order and the answer will always be the same… if you do it correctly.

Your issue is that you changed the sign of the -3 value.

Multiplication: -3×6 = -18

Addition: -18+2 = -16

Subtraction: 3-16 = -13

or

Multiplication: -3×6 = -18

Subtraction: 3-18 = -15

Addition: -15+2 = -13

Try solving 3 + -3 x 6 + 2 as this is the same as 3 – 3 x 6 + 2 but will help you keep the sign.

Multiplication: -3×6 = -18

Addition: 3 + -18 = -15

Addition: -15 + 2 = -13

Look at https://winthropdc.wordpress.com/2016/02/29/the-last-word-only-for-genius-3-3-x-6-2/ as it shows that Google and Bing say -13 is the answer.

David

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How can the subtraction sign be used twice in this equation?

3-3×6+2

Not only are u using the subtraction as a minus for the 3-3 part but then you’re subtracting 3.. so really shouldnt it be written as 3 take -3 ×6 +2?

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Hi Jake

I only see one subtraction sign in the original equation 3-3×6+2.

Subtracting a number changes the sign, so 3 take -3 x 6 + 2 will change the original equation to 3 – -3 x 6 + 2 which becomes 3 + 3 x 6 + 2

Adding a negative number is the same as subtracting a positive number, so 3-3×6+2 can be written was 3 + -3 x 6 + 2 without changing the equation.

Just solve the original equation, do the multiplication first, then do addition and subtraction together from left to right.

3-3×6+2 = 3-18+2 = -13

If you want to add brackets, try (3 – (3 x 6)) + 2 = (3 – 18) + 2 = -15 + 2 = -13

David

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I don’t get why the number is negative, it’s just the subtraction symbol?

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Hi Mr Me

What is the difference between 10 – 5 and 10 + -5?

Nothing, the answer is 5 for both.

Because, subtracting a positive number is the same as adding a negative number.

David

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Thank you for the challenge of my brain😀

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Hi.

Okay. I understand that you did the multiplication first, which left the equation as:

3-18+2=

What I don’t understand is why you then reverted to “left to right”. When I was at school, we would not have then gone “left to right” after the multiplication. We would have continued to apply BODMAS (Brackets, Of, Division, Multiplication, Addition, Subtraction). That means we would then have done the addition 18+2. That reduces the equation to:

3-20.

Ergo, the answer is -17.

Was I taught incorrectly or has the process changed over the years?

Thanks,

Peter.

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Hi Peter

The mnemonic is actually BO[DM][AS] as the Division and Multiplication can be done at the same time as can the Addition and Subtraction. That’s why some people know the mnemonic as BOMDAS.

Either way, your maths is incorrect, The addition is -18+2 = -16 then 3-16 = -13

I think that people believing the addition must be done before subtraction combined with ignoring the fact that 18 is a negative number is why so many people incorrectly get -17.

3-18+2 will always equal -13 regardless of the order you do the calculations.

3-18+2 = -15+2 = -13

3-18+2 = 3-16 = -13

3-18+2 = 5-18 = -13

3-18+2 = -18+5 = -13

David

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14

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Hi Surjyamani

I have no idea how you got the incorrect answer of 14. Please tell us what you did, so we can work out your error.

David

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