## A math problem for the wise

106 Replies
User
23 April, 2019, 6:01 AM UTC

I can see how it is tempting to turn

8/2(1+3) into 8/2(4)

but then it would  become 4(4) = 16  working left to right.

I also so see how it looks like an algebra equation and everything outside the brackets should be multiplied by what is inside them.

This would turn

8/2(1+3) into ((8/2)×1)+((8/2)×3)

which becomes (4×1)+(4×3) = 4 + 12 = 16

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2
User
23 April, 2019, 11:42 PM UTC

42

eh … OK then. 16.

Could also be written in a more classical way like:

8                   8 ( 1 + 3 )      8 + 24      32
--- (1 + 3) = -------------- = ---------- = ----- = 16
2                          2                  2             2

One could of course also take the simpler / more direct? approach with normal precedence and associativity, (here from K&R p. 53 (p. 66 in PDF)) * Parenthesis have highest precedence in the given exercise

* Division and multiplication have same, and are applied left to right

8 ∕ 2 × (1 + 3)
= 8 / 2 × 4
= 4 × 4
= 16

or, if you like:

8 ∕ 2  × (1 + 3)
= (8 / 2) × (1 + 3)
= 4 × 4
= 16

or:

8 ∕ 2 × (1 + 3)
= 4 × (1 + 3)
= 4 + 12
= 16

etc.

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2
User
25 April, 2019, 5:22 PM UTC

The ANSWER IS 16!! 😜

1 plus 3 is 4, and 8 multiply / divided by 2 is 4, then 4x4=16!
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User
25 April, 2019, 5:54 PM UTC

Interesting puzzle.  This type of ambiguous math question has been widely discussed.  And the big problem - is the ambiguity.

Order of operations as taught by mnemonic device, in schools, states the answer would be 16.

BUT the math community at large could instead state that the question is inherently ambiguous, and if a single answer is required, the ambiguity should be resolved by adding parenthesis, before requesting an answer.

The answer can be 16 (commonly), but it could also be argued to be 1.   Both could have valid arguments.  If I were pressed to give an answer to this ambiguous equation -- the answer would be 16 (with x degree of probability) or 1 (with y degree of probability).  Since Math describes situations - both answers could be correct.

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User
26 April, 2019, 2:10 AM UTC
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? UTC +0:00
0
User
26 April, 2019, 11:15 PM UTC
It’s 16 because when you divide 8 from 2 and you get 4 and then once you add 3 to 1 and you get 4 and then multiply those to answer together and you get 16
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User
27 April, 2019, 3:04 PM UTC

First, congratulations to everyone who got it wrong... Keep trying skippy.

Order of operations is important, so is grouping.

8 + 2(1+3) = ?

rewrite this equation as a division problem

8               4              4

_____   =  _____  =  _____  =  1

2(1+3)       (1+3)          (4)

Either way you choose to write it, the (1+3) need not be evaluated until it is used.

2(1+3)  IS the number.  just as if it were represented by a variable X.

So, to use the apple example, you have 8 people and 2 apples.  The two apples are cut into (1+3) pieces.

The now 8 slices of apple is divided between the 8 people, so each gets 1 slice of apple.

If you use any other logic to solve this simple problem...this is why bridges collapse.

Throw the box away, there is a big wide world out there to think in.

Now, to prove the point...

8 + 2(1+3) = 16    |   8 + 2(1+3) = 1

rewrite:

8 + 2(4) = 16        |   8 + 2(4) = 1

Multiply by 8

2(4) = 128            |   2(4) = 8

Divide by 2

4 = 64                   |   4 = 4

Simplify

1 = 16                   |   1 = 1

Any Questions?

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User
27 April, 2019, 7:17 PM UTC

8\2(1+3)=16

1+3=4

8/2=4

4*4=16
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1
User
28 April, 2019, 9:35 AM UTC

2 + 6=8. divided by 8=1 one is the answer

44519293
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User
28 April, 2019, 6:00 PM UTC

Parenthesis first-- THEN Division/Multiplication from LEFT to Right:

Therefore:

8÷2(1+3)

rewritten as:

8÷2×(4)

The only way to get 1 is if the equation was

8÷(2(1+3)).

UTC +5:00
2
User
1 May, 2019, 5:19 AM UTC
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? UTC +0:00
0
User
4 May, 2019, 1:39 PM UTC

Please Excuse My Dear Aunt Sally

Parenthesis, Exponents, Multiplication, Division, Adding, Subtraction

(1+3)=4, 2x4=8, 8÷8=1

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1
User
25 May, 2019, 10:40 PM UTC
Easy 4(4) parenthesis is multiplication come up 16 it’s basic
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1
User
25 May, 2019, 11:19 PM UTC

8            8           8
--------  = -------- = ------- = 1
2(1+3)      2(4)        8

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User
27 May, 2019, 4:18 PM UTC

8/2(3+1)= 16

for 1 miss ()  8/(2(3+1))=1
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User
27 May, 2019, 4:22 PM UTC

Can we have the answer to this from admin please?

Jarls clearly have two ideas for the answer and it would be nice to know which half of the community is correct.

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UTC +1:00
1
User
27 May, 2019, 10:19 PM UTC

I am surprised this thread has lasted so long, but you are right it would be nice as to which is the right answer,according to the administrator who posed the question.

However, I suspect that wouldnt be the end of it, as both answers are correct, depending on which ever system you use to solve it ,which I think was the whole point of the riddle.

Lots of mathematical and scientific information has been refined over the years such that old definitions strictly speaking no longer apply,though those outside these fields still probably might remember them or use them.

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User
30 May, 2019, 2:39 AM UTC
The most amazing thing is to read those with the wrong answer, who profess how all those with the correct answer are wrong!
Live through the blood of your foes! Exalt in the lamentations of their women and children!
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1
User
13 June, 2019, 12:25 PM UTC

BEDMAS

8/2(1+3)

8/2(4)

4*4

=16

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1
User
13 June, 2019, 8:59 PM UTC

1 !

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