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## A math problem for the wise

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Apr 23, 2019, 23:4204/23/19
Apr 24, 2019, 02:25(edited)
06/14/17
90

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.

Apr 25, 2019, 17:2204/25/19
02/03/19
33

1 plus 3 is 4, and 8 multiply / divided by 2 is 4, then 4x4=16!
Apr 25, 2019, 17:5404/25/19
Apr 25, 2019, 18:11(edited)
01/18/18
1

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.

Apr 26, 2019, 02:1004/26/19
04/25/19
1
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?

Apr 26, 2019, 23:1504/26/19
04/26/19
1
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
Apr 27, 2019, 15:0404/27/19
03/27/19
1

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?

Apr 28, 2019, 09:3504/28/19
06/10/18
67

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

44519293
Apr 28, 2019, 18:0004/28/19
05/19/17
6

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)).

May 1, 2019, 05:1905/01/19
11/04/17
1
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?

May 4, 2019, 13:3905/04/19
3

Please Excuse My Dear Aunt Sally

Parenthesis, Exponents, Multiplication, Division, Adding, Subtraction

(1+3)=4, 2x4=8, 8÷8=1

May 25, 2019, 22:4005/25/19
12/31/18
14
Easy 4(4) parenthesis is multiplication come up 16 it’s basic
May 25, 2019, 23:1905/25/19
04/14/19
1

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

May 27, 2019, 16:1805/27/19
06/10/17
63

8/2(3+1)= 16

for 1 miss ()  8/(2(3+1))=1
May 27, 2019, 16:2205/27/19
10/14/18
196

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

May 27, 2019, 22:1905/27/19
May 27, 2019, 22:21(edited)
02/21/18
1162

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.

May 30, 2019, 02:3905/30/19
12/02/17
184
The most amazing thing is to read those with the wrong answer, who profess how all those with the correct answer are wrong!
Jun 13, 2019, 12:2506/13/19
06/04/19
1

BEDMAS

8/2(1+3)

8/2(4)

4*4

=16

Jun 13, 2019, 20:5906/13/19
Jun 13, 2019, 20:59(edited)
12/03/18
1

1 !

Those who know maths - know the maths! ;-)
Jun 14, 2019, 10:1506/14/19
05/18/18
12

Due to rule of BODMAS(Bracket of Division Multiplication Addition and Subtraction) it's 16