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Math Riddle II: What is Your Answer?

Math Riddle II: What is Your Answer?

A graphic shows a series of numbers and asks readers to fill in the final blank. How would you solve this equation and what answer do you think is best?

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Let’s take a look at the problem and some possible solutions.

As seen in the image below, the following riddle provides the following problem:

If:
2 = 6
3 = 12
4 = 20
5 = 30
6 = 42
Then:
9 = ??

How would you solve this quiz?

Our Answer: 90

The answer of 90 is achieved if we multiply the number on the left by one number higher than itself. Thus:

 # # +1 Product 2 x3 6 3 x4 12 4 x5 20 5 x6 30 6 x7 42 9 x10 90

It has also been presented as squaring the number and then adding the number, so for example: 2×2 = 4 + 2 = 6.

Other Answers

We’ve seen others come up with answers such as 72 and 56, using different methods than above.

An answer of 72 is reached if 9 is multiplied by 8. The reason for 8 would be that it is next incrementally in the middle column. (3, 4, 5, 6, 7, 8).

A few people have claimed it should be 56 by looking at the pattern formed by the right column. We hesitate to make assumptions that the right column would continue following the pattern before it while the left column does not.

Your Turn

Which solution did you come up with? Let us hear from you in the comments below.

Updated June 14, 2015
Originally published April 2013

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• Carlo Braganza Paras

If your answer like that, then there are 2 answers 5 and 30 because 5=30

• Nathan

What is 3/12= ?/

• OscarTheCat

I had 54! I added 6 to get the 12, then I added 8 to get the 20, added 10 to get the 30 added 12 to get the 42 and added 14 to get 54.

• LFC_BOON

X1, 2
X2, 3
X3, 4
X4, 5
X5, 6
X6, 7
……
X?, 9

• RavensRayne78

60 must solve by right because that is the “answer”. 2=6 3=12(6+3×2) 4=20 (12+4×2) 5=30 (20+5×2) 6=42 (30+6×2)
9=60 (42+9×2)
12-6=6=3×2
20-12=8=4×2
30-20=10=5×2
42-20=12=6×2
60-42=18=9×2

• samiha asif

Logically…answer is 90…u r ri8

• LMAW Podcast

72 is the obvious answer but…

The left column goes 2 3 4 5 6…….9. So it’s 90.

You could say it was 56 if you believe the missing digits aren’t a trick meant to foul you up and you were just trying to determine the pattern on the solution side of the equal sign. 56 is the next number in that sequence.

BUT!

If you wanted to have a LOT of fun and burn your brain out your could assume that these are ciphers telling you that 2’s are to be replaced with 6’s and so on. So:

2 = 6 stays this way but
3 = 12 becomes 3 = 16 because the first cipher says 2 = 6. Eventually you end up with:

2 = 6
3 = 16
4 = 60
5 = 160
6 = 606
9 = ?

At this point you have to kick your brain into overdrive because there IS a pattern here, but determining it really would take a genius. You have to assume based on the arrangement of the digits what 7 and 8 would equal so that you could figure for 9.

Ready?

The answer is:

2 = 6
3 = 16
4 = 60
5 = 160
6 = 606
7 = 1606
8 = 6060
9 = 16060

But 6 has a cipher so…

9 = 160,606,060

If you don’t understand that pattern work it backwards:

Imagine that the 6 in 2=6 is actually 2 = X6XXX. The X numbers are simply “out of view” or obscured. Then, from the bottom of the whole problem, move the entire number to the left and remove the first digit:

16060 moved to the left with the first number removed (or obscured) = 6060

Now move 6060 to the right and remove the last number, but bring the first number back into view.

6060 moved to the right with the last number removed and the first number coming back “into view” is 1606.

keep doing this, removing a digit from the total number every two sets, and you wind up at 6.

The problem with the cipher way is that once you hit 6 the entire problem becomes a circular argument you can’t finish; because you’re always going back to previous ciphers to adjust for what 6 equals.

But it’s super fun anyway grin emoticon

Have a SMART day!

• Pozest

This is exactly how I got my answer!! 58 🙂

• Rick

You are right, exept you are too smart for this problem. You are making the assumption off of what would make sense. There is no x to play with. They are saying apples are oranges and oranges are apples. Apples cannot be oranges, and 2 by itself cannot = 6 in any form of math without an x in there somewhere. This is a psychology test, not a math problem.

• Shelley

My first answer was 90 as expected, but after a chat with my genius Dad, I realize it can also and actually more satisfyingly be solved by multiplying the number by itself, then adding the same number to that answer:
2 = (2×2)+2 or 6
3 = (3×3)+3 or 12
4 = (4×4)+4 or 20 etc, to
9 = (9×9)+9 or 100

• Arnaldo (Italy)

Another answer is 81.
Because N1 is always the square root of (N2-N1) subtraction

6-2=4 (2×2)
12-3=9 (3×3)
20-4=16 (4×4)
30-5=25 (5×5)
42-6=36 (6×6)
56-7=49 (7×7)
6-2=4 (2×2)
72-8=64 (8×8)
90-9=81 (9×9)
110-10=100 (10×10)

• Bernard Ingram

5=30 and not 5=25

• Jennifer Smith

9×9=81 81+9=90 not 100

• Bernard Ingram

Oh dear, how embarrassing! 81+9=90. Thank you genius dad. And it still means that the simplest answer is multiply each number with the one that follows it directly. No genius powers required.

• SexyShonda

90 (9×9)+9
81+9=90

• Rae

My mind just automatically divided the sum by the appearing number to obtain the missing factor, but maybe I’m not a genius after all.

• Cc

I don’t understand why people don’t see this simple pattern. From the top, all numbers are being multiplied by the number below each other to get top answer. So 8 is omitted and 7, but if you factor what is multiplied by 6 = 42, it’s 7. Then 7 multiplied by the next number which is 9 = 63. I’ve seen this pattern before I think on an IQ test.

• Bernard Ingram

Don’t attempt algebra…

• Adam

I’m the only person coming up with 60. I don’t understand that. The pattern to me is obvious. I am working with the given information. The formula works and I am not assuming anything that’s not presented. 2 = 6. (2×3) + 6 = 12. (2×4) +12 = 20. (2×5) + 20 = 30. (2×6) + 30 = 42. (2×9) + 42 = 60. You simply double the next number and add it. When you start from the beginning, it works every time.

• Indrajit Kundu

Most easy.

• Brandon C

We are given 2=6 as a starting point, so we’re either dealing with a fallacy or an alternate universe. If a fallacy, then 9=9 because all previous assumptions are unreliable. If it’s an alternate universe in which these equivocations follow a very odd formula then it is 54, because 9 multiplied by the number above it, 6, yields the correct response. Neither of these answers are in the 98% of you who guessed 90 and 72, so I posit that mine solutions constitute the only viable answers that also satisfy the original requirement that 98% will get it wrong.

• JG

9 = 58

Right Side Pattern 6, 12, 20, 30, 42, 58 (+6, +8, +10, +12, +16)
Left Side Pattern 2, 3, 4, 5, 6, 9 (+1, +1, +1, +1, +3)

• \$cott

That’s not a pattern.

• Harrison Gross

The major problem of course is that the people who developed this problem wanted it for lay people to show how smart they were to one another, but didn’t want to use mathematical notation which would have been very useful for this problem.

Namely, if they had used either function notation e. g. f(2)=6 or sequence notation e. g. a_2=6 then this problem would have been much more interesting.

As it stands however, you are partially correct, in that when given the statements above, you quickly get in to nonsense. If 2=6, then 2-2=6-2 or 0=4. But if 0=4 then 0+0=4+4 or zero is now also every multiple of 4, and we are now working in the integers mod 4. But then we also get 3=12. 12=4+4+4=0+0+0=0, so 3=0. If 3=0 and 4=0, then 1=4-3=0-0=0, and then all integers can equal anything. So everyone who answered any answer were in one sense correct, in that based on the syntax 9 could be equal to at minimum any integer.

If they were to use function notation or sequence notation, the typical answers would be f(x)=x^2+x or a_n=n^2+n. Given x=9 or n=9 we get the “expected” answer of 90. But it is also true that while it fits a pattern for those terms, it could literally be any sequence.

For example, if I define a function to be f(x)=x^2+x + (x-2)(x-3)(x-4)(x-5)(x-6) then:
f(2)=6
f(3)=12
f(4)=20
f(5)=30
f(6)=42
f(7)=116
f(8)=432
f(9)=1350

This seems insane, but it satisfies the initial conditions.

• Sebastian Ogden

You and I are the only ones who have come up with 60. What was your methodology?

• Evie

Me to 60. I guess our minds work differently.
2=6
3=12 twice3=6 added to 6 above makes 12
4=20 twice 4-= 8 added to 12 = 20
5=30 twice 5 = 10 added to 20 = 30
6=42 twice 6 = 12 added to to 42 = 60
Therefore 9=60

• karie hart

2=6
3=12
4=12
5=30
6=42
9=?
ok so I really only think 90 works if you continue to show the 7 and the eight without it I would say the answer is this

2=6
3=12
4-20
5=30
6=42
9=72

if the riddle continued to show the 7= and the 8= 90 may work otherwise I think its 72

• choppame

9 should =0 or x there are no numbers before or after it right ? X is the unknown

• Beth

If you include the 7 and 8…
2+X=6 X=4
3+X=12 X=9 Take the 6 from the previous problem and add the 3.
4+X=20 X=16 12 from the previous problem and add the 4.
5+X=30 X=25 just take the answer from the previous problem and add the number you have and it will equal the X. This is the pattern.
6+X=42 X=36
7+X=Y X=49 Y=56
8+X=Y X=64 Y=72
9+X=Y X=81 Y=90

HOWEVER if you do NOT include the 7
and 8…
9+X=Y X=51 Y=60

• askandy

The answer is 72… You cannot ASSUME 7 & 8 are skipped… Or that there are numbers before the first equation. You are GIVEN the numbers and equations just the way they are… and must work with what is GIVEN to determine the next sequence. And because these are EQUATIONS, you cannot just look at the left column or just the right column… You need to ask how each EQUATION increases… In this answer, each multiplying number is increased by +1 after starting with 3:

2=6………. 2 (x3) = 6
3=12…….. 3 (x4) = 12
4=20…….. 4 (x5) = 20
5=30…….. 5 (x6) = 30
6=42…….. 6 (x7) = 42
9=??………. 9 (x8) = 72

• Bernard Ingram

Patterns follow logic. You cannot count logical from 1 to 10 by leaving out some numbers. If that is true, then mathematics is a lie.

• Deepak

I think ans is 0, see below pattern

2=6 (2*03) = 2 * second digit from 03 i.e. 3 so 2*3 =6
3=12 (3*04)
4=20 (4*05)
5=30 (5+06)
6=42 (6+07)
7=56 (7+08)
8=72 (8+09)
9=90 (9+10)

like wise 9 * 0 = 0

• A Adewale

But the sequence is broken that 2,3,4,5,6 and then 9. Why should the result for 9 follow the sequence? Therefore, there is a question mark for the answer being 90. Also notice the number 1 is not in the sequence.

• Todd in Seattle

1 is not included because there is no multiplication factor. 1 X 6 = 6, 1 X 10 = 10, etc.

• Pablo Rodríguez López

I swear I have not looked, I promise by snoopy 🙂

• Pablo Rodríguez López

in the previous:
x=y
x1 = x*x1+y = y2
x2 = x*x2+y2
in the above I have seen no equal, we almost equal

• Pablo Rodríguez López

I have given 8 possible solutions, do you want more?

• Pablo Rodríguez López

2=6
3=2*3+6=12
4=2*4+12=20
5=2*5+20=30
6=2*6+30=42
7=2*7+42=56
8=2*8+56=72
9=2*9+72=90
well, this yes if mathematic.

• Pablo Rodríguez López

It all depends on in as you approach the problem, if you consider it a problem of mathematics or as a problem of sequences, I for example am very bad at math, just I have knowledge, but however I have abstraction ability, why I believe that I have given so many replies, I’ve taken me as a problem of sequences, much easier for my.

• Michael Ballard

What if the question is not a math problem but a sequence problem? This question is all over the internet and I have yet to find the original answer. If this question is from an I.Q. test the answer could be 56…and here is why this pattern would work.
6 plus 6 = 12 (skip 7) 8 plus 12 = 20 (skip 9) 10 plus 20 = 30
(skip 11) 12 plus 30 = 42 (skip 13) 14 plus 42 = 56
In this answer it dose not matter what the numbers are in the left column, it’s the sequence in the right column that will give you the answer. I have taken I.Q. tests that have asked similar questions so that’s how I came up with this non mathematical solution.

• Pablo Rodríguez López

7=511, 8=67, 9=75, And 10=85 And 11=915 the final response?

7=40, 8=50 y 9=74 the final response?

7=56, 8=70, 9=94, y 10=126 the final response?

(the 2 too count).

3 FINAL RESPONSE I BELIEVE THAN CORRECTS.

others alternatives:

7 = 56, 8=64, 9=74, 10=86.

2=06, 3=12, 4=20, 5=30, 6=42, 7=56, 8=62, 9=70, 10=80, 11=92.

2=06, 3=12, 4=20, 5=30, 6=42, 7=50, 8=60, 9=72

if are corrects,the problem is very easy, it isn’t for geniuses

• Pablo Rodríguez López

x = 6
y = 4
-1= x*-2 + y*-3= -24
0 = x*-2 + y*-3= -24
1 = x*-1 + y*-1= -10
2 = x*1 + y*0 = 6
3 = x*2 + y*0 = 12
4 = x*2 + y*2 = 20
5 = x*3 + y*3 = 30
6 = x*5 + y*3 = 42
7 = x*6 + y*5 = 56
8 = x*6 + y*6 = 60
9 = x*7 + y*6 = 66
10 = x*9 + y*8 = 86
sorry about so much change, and if the two sequences are definitely correct that of the x and the y, good for negative numbers as 0 and -1 give the same result, is a match, if not for numbers positives will also later

• Pablo Rodríguez López

I lied I have one last grinding because I’ve noticed that did not follow the sequence x?
x = 6
y = 4
0 = x*-2 + y*-1= -16
1 = x*0 + y*-2= -8
2 = x*1 + y*0 = 6
3 = x*2 + y*0 = 12
4 = x*2 + y*2 = 20
5 = x*3 + y*3 = 30
6 = x*5 + y*3 = 42
7 = x*6 + y*5 = 56
8 = x*6 + y*6 = 60
9 = x*7 + y*6 = 66
10 = x*9 + y*8 = 86

• Pablo Rodríguez López

the previous not correct, THIS IS CORRECT
x = 6
y = 4
0 = x*-2 + y*-1= -16
1 = x*0 + y*-2= -8
2 = x*1 + y*0 = 6
3 = x*2 + y*0 = 12
4 = x*2 + y*2 = 20
5 = x*3 + y*3 = 30
6 = x*5 + y*3 = 42
7 = x*6 + y*5 = 56
8 = x*6 + y*6 = 60
9 = x*9 + y*6 = 78
10 = x*10 + y*8 = 92?

• Pablo Rodríguez López

you can delete the 4 above, the latter is correct
x = 6
y = 4
0 = x*-2 = -12
1 = x*0 = 0
2 = x*1 = 6
3 = x*2 = 12
4 = x*2 + y*2 = 20
5 = x*3 + y*3 = 30
6 = x*5 + y*3 = 42
7 = x*6 + y*4 = 52
8 = x*6 + y*5 = 56
9 = x*9 + y*5 = 76
10 = x*10 + y*6 = 84

• MARK

First time I got 90 as right answer by myself.

But after sometimes I got an other formula to get an other answer:

two times of left number + upper right number : (2*X) + Y . So: If we assume that 1=2 => (2*2) + 2= 6 (2=6) and others will be:

(2*3) + 6 = 12 (3=12)
(2*4) + 12 =20 (4=20)
(2*5) + 20 =30 (5=30)
(2*6) + 30 = 42 (6=42)
Therefor (2*9) + 42 = 60 (9=60)

What are your ideas ?

As in the question not mention that 7 & 8 are exist in this number serie.

• Jay

The pattern i see is: x^2+x

2^2 + 2 = 4+2 = 6
9^2 + 9 = 81 + 9 = 90

Answer = 90

• Knic

I beg to differ on why 72 is NOT the correct answer.

The solution you presented does follow the pattern of adding one number higher, however you also have to consider why “9” is the number given to solve. It should follow that the number “9” is derived from a pattern.

“9” was the number to solved to form the series of sequential numbers. (3,4,5,6,7,8).

So, 72 is as much a correct answer as 90. It just depends on which pattern you adhere to.

Are you person who assumes that there is more data missing (which gives the answer 90), or are you the person that assumes that all you the data you’ll need is in the puzzle.

• waffles

It wasn’t really looked at it as having skipped numbers, but a row of problems of a number squared plus 1.

• Amanda

1=2
2=6=(2+4)
3=12= (6+6)
4=20=(12+8)
5=30=(20+10)
6=42=(30+12)
7=56=(42+14)
8=72=(56+16)
9=90=(72+18)

• David

9
I have no indication that I am to look for patterns. As far as I know, the person working the first equations is an idiot. 9=9!

• jose

But there is an “if” and a “then”. So, IF we take that equality presented, THEN we can reaply the same PATTERN and achieve a matching RESULT.

• Eric Raymond

FINALLY someone gets it. Those are EQUAL signs. Everything above the 9 = question is a lie. 9 can only equal 9, nothing else.

• Stephen Smith

I did it another way:
2^2+2=6
3^2+3=12
4^2+4=20
5^2+5=30
6^2+6=42
9^2+9=90

• Sylar

Thats how I did it too 🙂

• Big Rob

Problem: Answer:

9=72 72-56=16
8=56 56-42=14
7=42 42-30=12
6=30 30-20=10
5=20 20-12=08
4=12 12-06=06
3=06 06-06=0

• Nothing

2=((2+3)+1)6
3=((2+6)+(3)+1)12
4=((3+12)+(4)+1)20
5=((4+20)+(5)+1)30
6=((5+30)+(6)+1)42
9=((6+42)+(9)+1)58

• KADAB

2(3)=6
3(4)=12
4(5)=0
5(6)=30
6(7)=42
7(8)=56
8(9)=72
9(10)=90

• The Purple Phantom

I got what Chelle came up with.

• Chelle

This is the pattern I saw: Take the previous answer and add the next even number to it
1=2
2=6 (2+4)
3=12 (6+6)
4=20 (12+8)
5=30 (20+10)
6=42 (30+12)
7=56 (42+14)
8=72 (56+16)
9=90 (72+18)

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