# Fun Maths Riddle: If 1 + 4 = 5; Then 8 + 11 = ??

Look at the equations and find the value of the missing number in the last equation of this riddle.

If;

1 + 4 = 5

2 + 5 = 12

3 + 6 = 21

Then;

8 + 11 = ?? So were you able to solve the riddle? Leave your answers in the comment section below.

The logic followed by the equations are as follows;

1 + 4 = 1 x (4 +1) = 1 x 5 = 5

2 + 5 = 2 x (5 + 1) = 2 x 6 = 12

3 + 6 = 3 x (6 + 1) = 3 x 7 = 21

Therefore we can find the missing number as;

8 + 11 = 8 x (11 + 1) = 8 x 12 = 96

Too much discussion on this riddle… feedback is always welcome.

## 151 Replies to “Fun Maths Riddle: If 1 + 4 = 5; Then 8 + 11 = ??”

1. Pam Gould says:

1 + (4×1) = 5
2 + (5×2) = 12
3 + (6×3) = 21
Now there are 2 possibilities, depending on the pattern you are following:
The multiplication factor is the next consecutive number i.e. x4, regardless of the first number = 8 + (11×4) = 52
Or you the first number dictates the multiplication factor = 8 + (11×8) = 96

1. Satish Dwivedi says:

Correct answer is 1+4=5 because this the only right sum others are false

2. Nitin says:

But we can do with another trick and from my trick it’s answer is 92. Like 4×1+1=5
5×2+2=12
6×3+3=21
Similarly,8×11+4=92

3. Sukumaran says:

If 1+4=5
2+5=12
3+6=21
8+11=?
Here it has only one answer ie (11*8)+8=96

It can never get any other answer ….,40 is wrong why?
Because ,If you change the pattern of question as given below
2+5=12
3+6=21
1+4=5
8+11=? Then also there is only one answer 96 and not 40 or any other number .

Moreover it is not by adding (8+11) to the previous no 7+10=77 as pointed out by some one . If it is considered like this ,then question arises how you get 1+4=5 ?

4. wesley says:

1+4=5
2+5=12
3+6=21
8+11=?

So, I have one function that could work here: f(x)=f(x-2)+x. The only problem is that f(3) has to equal 0.

f(1+4)=5
f(2+5)=12
f(3+6)=21
f(8+11)=?

f(5)=f(5-2)+5=5
f(7)=f(7-2)+7=12
f(9)=f(9-2)+9=21
f(19)=f(19-2)+19=?

f(5)=f(3)+5
f(5)=0+5
f(5)=5

f(7)=f(7-2)+7
f(7)=f(5)+7
f(7)=5+7
f(7)=12

f(9)=f(9-2)+9
f(9)=f(7)+9
f(9)=12+9
f(9)=21

I could show that f(19) aka f(8+11) is equal to 96, but that would take up a lot of space.

1. SAKIR AHMED CHOUDHURY says:

1+4=3 3+2=4 9+8=13 4+1=?

2. Jim Burgess says:

Sukumuran, I disagree with you saying that you can determine how the pattern goes by simply looking at 1+4=5! You could just add the numbers or as you said multiply and add 1×4+1=5, hence you have to look at other patterns to see what fits!!

Jim Burgess math teach

3. AB says:

1+4=(1+4)=5
2+5=(2+5)+5=12
3+6=(3+6)+12=21
8+11=(8+11)+21=40

5. HeVi says:

1+4=5; 2+5=12; 3+6=21; 8+11=?
Reformulating the riddle: we search a function F(x,y,z)=0, where
F(1,4,5)=0; F(2,5,12)=0; F(3,6,21)=0;
and we search third number for F(8,11,N)=0 (N here stays for ?-mark)
Sollution for N: any number
My function is (just one from endless possibilities):
F(x,y,z) = [(1-x)+(4-y)+(5-z)] * [(2-x)+(5-y)+(12-z)] * [(3-x)+(6-y)+(21-z)] * [(8-x)+(11-y)+(N-z)] = 0
And You can use similar sollution for any riddle of this kind.

6. shashank says:

How to solve this question of 1st no is 3 and 2nd is 6 and 3rd is 45 then what will come after this no..

7. giddalti says:

I answered your problem when I ran across it on Facebook, but I used a different formula to reach the same answers (which is typical in math).

I multiplied the first number times the second number, then added the first number. I pasted my method using your equations below.

(1 x 4) + 1 = 5
(2 x 5) + 2 = 12
(3 x 6) + 3 = 21
(8 x 11) + 8 = 96

Thanks for the fun problem. I like to solve these problems. I call it “Crazy Math.” Ü/

1. Dee says:

That’s the equation I used as well ….. but I’m trying to figure out how people are coming up with 40 for the answer ….

1. Arash says:

add the answer of the previous line to the numbers in the next line. 21 + 8 + 11 = 40

1. Dj LiquidE says:

See that’s what I was thinking also. But was told I was wrong!! Well shit. I did it the way you did it. I don’t isn’t see where to multiply it!! Oh well glad someone else thought of 40 WOOOOOT!! I may be wrong but damnit I don’t care I’ll go down in a blaze of glory!!

8. Mr Shahid says:

pls solve this
? + ?=8
+ +
? – ?=6
= =
13 8

1. nidhi verma says:

3.5+4.5=8
+ +
9.5-3.5+6
=13 =8

9. pratap damor says:

1 + 4 = 5

2 + 5 = 12

3 + 6 = 21
8 + 11 = 52

1+4×1=5
2+5×2=12
3+6×3=21
8+11×4=52

10. anjaly says:

1. vijay dubey says:

96 and 40 both are right answer

11. Gláucio Duarte says:

1 + 4 = 5 -> 1 + (1 x 4)
2 + 5 = 12 -> 2 + (2 x 5)
3 + 6 = 21 -> 3 + (3 x 6)
8 +11= 96 -> 8 + (8 x 11)

1. Bee says:

FUNNY, functions??? What if the instruction would read to simply ad the result of the previous to the result of the current equation? Anybody consider that? Or would that be too far fetched??? I find it hard to tell without instruction….

12. Anushka says:

My answer is 57. The pattern I see is:
1+4=5
2+5=12
3+6=21
7+10=38
8+11=57
9+12=78

13. The correct answer is 19, because 8 + 11 = 19, while 2+5=12 is wrong! 😉

1. Davidb says:

8+11=19, it’s hard to believe how many people keep trying to change the equations to fix what is wrong with it.

1. agreed! moral of the story, don’t believe everything you’re told. Because someone says it, doesn’t make it true…….

14. Tomas says:

I see: 1 + 4 = 5
next: 2 + 5 = 12 I read: 2 + 5 = 7 (7 + last answer 5 = 12)
next: 3 + 6 = 21 I read: 3 + 6 = 9 (9 + last answer 12 = 21)
next: 4 + 7 = 32 I read: 4 + 7 = 11 (11 + last answer 21 = 32)
next: 5 + 8 = 13 I read: 5 + 8 = 13 (13 + last answer 32 = 45)
etc
next: 8 + 11 = 19 I read: 8 + 11 + 19 (19 + last answer 77 = 96)

1. marco says:

wrong, the correct answer is 32.

2. hillinvestmentdesignsllc says:

40 or 96 are correct

1. manu weber says:

!

3. EDDIE LANSANG says:

REAL FORMULA: a x b + a = c (Let a = any number; b = a + 3)

0 + 3 = 0
-5 + (-2) = 5
100 + 103 = 10,400
64,000 + 64,003 = 4,096,256,000
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
4 + 7 = 32
5 + 8 = 45
6 + 9 = 60
7 + 10 = 77
8 + 11 = 96 🙂

1. Dan says:

Eddie: Agreed. Your formula gives a^2 + 4 x a = c (answer). (^2 denotes squared).

Interestingly, the difference of consecutive squares is the series of odd integers;

2^2 – 1^2 = 3
3^2 – 2^2 = 5
4^2 – 3^2 = 7
5^2 – 4^2 = 9, etc.

Notice that the difference of the consecutive Answers above (12 – 5 and 21 – 12) are also the series of odd integers ( . . 7, 9, . .). This gives us the clue needed to conclude that the Answers are related to consecutive integers squared. Adding some additional equations:

.
.
-6 + (-3) = 12
-5 + (-2) = 5
-4 + (-1) = 0
-3 + 0 = -3
-2 + 1 = -4
-1 + 2 = -3
0 + 3 = 0
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21
4 + 7 = 32
.
.

This uncovers the series of numbers that represent the Answers ( . . 60, 45, 32, 21, 12, 5, 0, -3, -4, -3, 0, 5, 12, 21, 32, 45, 60, 77, 96, . . ) where we have made use of the fact that the difference of consecutive Answers ( . . -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, . . .) are the odd integers.

Noticing the symmetry in the Answer series of numbers, there is an obvious choice for the zero-th element, (-4).

We can denote the Nth number in the series as A(N) and the zero-th element as A(0) which equals -4. Also, due to the symmetry and our choice of the zero-th element, we now have that A(N) = A(-N).

The first number in the equation you called “a”, so that in the equation 1 + 4 = 5, “a” was equal to 1. This relates to the variable “N” as [ a + 2 = N ].

N a equation
-1 -3 -3 + 0 = -3
0 -2 -2 + 1 = -4
1 -1 -1 + 2 = -3
2 0 0 + 3 = 0
3 1 1 + 4 = 5
4 2 2 + 5 = 12

And we see that A(N) = N^2 – 4 For example :

A( 100) = 100^2 – 4 = 9996 = 98 + 101
A(-100) = (-100)^2 – 4 = 9996 = -102 + (-99)

and finally, considering the requested answer,

A( 10) = 10^2 – 4 = 96 = 8 + 11 or
A(-10) = (-10)^2 – 4 = 96 = -12 + (-9)

so, we see that 8 + 11 actually equals -12 + (-9)

2. Rahul says:

1×4+1=5
2×5+2=12
3×6+3=21
4×7+4=32
5×8+5=45
6×9+6=60
7×10+7=77
8×11+8=96

15. IamLupo says:

Convert a + b = c to c = round(sqrt(exp(b) – floor(30 – a^4))).

in the end we have:
round(sqrt(exp(4) – floor(30 – 1^4))) = 5
round(sqrt(exp(5) – floor(30 – 2^4))) = 12
round(sqrt(exp(6) – floor(30 – 3^4))) = 21
round(sqrt(exp(11) – floor(30 – 8^4))) = 253 <—

Ok, let this math geek show you how the PUREST answer is 201 …. not kidding …..

Here – let a math geek blow your mind … as Meghan Trainor will tell you, it’s all about the BASE … 🙂 … and, when it’s all about the BASE, the answer is 201 and you don’t have to go making up any operations ! Ha !

To simplify:
1 + 4 = 5 is correct in base-6
2 + 5 = 12 is correct in base-5
3 + 6 = 21 is correct in base-4
8 + 11 = 201 in base-3

1. Joel Ewing says:

This is what I independently arrived at as well, and stumbled on this particular discussion when I searched to try to determine the true origin of the puzzle. Whether or not 201₃ was the intended answer by the one who first posted the puzzle, “201₃” is by far the most elegant and simplest solution to anyone with a mathematical mindset (and hence by the Occam’s Razor argument used by someone else’s reply, must be the “correct” answer). All the other answers totally ignore the well-established mathematical meaning of “=” and simply ignore the fact that their solution and interpretation of the puzzle would make the last three equations into mathematical nonsense — madness with a pattern, but still madness. It’s much simpler if you just assume the equations are indeed true and not just a intentional falsehood..

1. Douglas Vernon says:

Pff.. whatEVER.. simplest? And you’re using bases and multiplication and all this stuff but the statement has only addition. If you ASSUME that all statements are true and have to find an answer that supports them, Occam’s Razor says the only possible answer will be 40. without using any fancy math, add the first line.. take that answer and add it to the second line. Take that answer and add it to the third line, take that answer and add it to the fourth line and you get 40.. It’s the simplest math trick ever.. Fibonacci Sequence.. I can’t believe you all didn’t see that.

1. Davidb says:

Seriously, you think the simplest answer with the least amount of math is 40. if you want to use Occam’s Razor you would immediately acknowledge that instead of trying to alter the equations in the fashion you tried to use, In base-10 math 2+5 does not equal 12 and 3+6 does not equal 21. So the simplest answer would be 8+11=19.

as for changing the bases all I can say is that 201 in base-3 is 19 in base-10 which kind of defeats the purpose of changing the bases all together, other than proving the two middle equations

17. bnmcc1 says:

1. Heeeere's Johnny says:

1. Douglas Vernon says:

No, he typo’d I think and meant to suggest 19 as THE most simple solution, had the problem said solve for line 4. Since it did not, only the top and bottom lines are congruent, leaving half the problem unsolved or unREsolved, anyway.. Occam’s Razor tells us to take it to the next most logical answer, and that would be to add the sum of the preceding line to the next and come up with 40 for your answer. No re-writing, no coding, no base, no multiplication, no paper equals simplest answer.. I agree, and my brother is arguing 19, and with that I’ll spread my hands and say, okay.. that would be acceptable for the trick question, but the problem as written tells us to ASSUME that the answers are correct.. then what? How can we justify it the way it’s written.. and then the above happens.

1. The question is do you assume because someone writes something (online or anywhere) that it is true, even though it violates absolute logic? Politicians do this all the time and people follow blindly. Otherwise, the base-3,4,5, 6 solution is intriguing but requires extreme inferences. I would have to think the first equation should logically be base 1…

2. Douglas Vernon says:

You are my HERO, man! So simple, it’s the Fibonacci Sequence. Add the answer from the preceding line to the next and you get 40. I solved this in 12 seconds and started a 24 hour debate on my fb page that is still going on and I’ve even posted your very scientific explanation and proof and they still do not believe. Silly people.

1. Maria says:

Lol i also find 40 and the others laugh with me!!!they find 96!wtf why can i calculate something that did not exist??

3. Hom says:

1(1+4)=1{1 +(1+3)}=5
2(1+5)=2{1+(2+3)}=12
3(1+6)=3{1+(3+3)}=21
4(1+7)=4{1+(4+3)}=32
If it’s n
n{1+(n+3)}
So if it’s 8
8{1+(8+3)}
8{1+11}
8×12=96
formula is
n{1+(n+3)} where n = {1,2,3………….}
From
Sequence and series

1. wesley says:

Wow, this is great

18. James Nicholas says:

If you are looking for patterns, given the initial information, there are three: the first being, 1, 2, 3, 8. The next being 4, 5, 6, 11. The third being 5, 12, 21, &?.
The commonality of the first two series is that you have to add 5 to the 3 in1, 2, 3, to get 8. (3+5=8), and add 5 to the 6 in 4, 5, 6 ( 6+5=11) – but then, the last column would not have any relationship to the first two columns. If you add 5 to 21, your answer would be 26 (21 + 5). In that case, you would be ignoring the first two numbers in column three, which differ by seven (the amount between 5 and 12), and the next two numbers 12 and 21 (which differ by nine [two more in difference than the first two numbers]). The next number in the third column, if the pattern is to continue, will have to be two more than the difference of the last two numbers, or 11. The difference between that number will have to be 13, then the next number will have to be 15 more than the previous number. Tthe sequence in last column would have to be:
5,

The logic to solving this puzzle presumes and assumes that the sequence of each column has a pattern, the first column being 1, 2, 3, 4, 5, 6, 7, 8, (adding one to each of the previous numbers, ending in 8). This is a set of perfectly logical consecutive numbers.

The second column is a naturally logical consecutive pattern of adding one to each of the previous numbers: 4, 5, 6, 7, 8, 9, 10, 11.

To me, their can not be any answer, but 96. The puzzle must have all consecutive and logical sequences, so the missing numbers must be assumed, in order to have a correct solution, otherwise, I believe that it would be unsolvable.

1. bnmcc1 says:

why do ýou dismiss the context and mathematical syntax of the indivdual equations and settle on finding a pattern that requires missing elements to provide the one answer that ive seen computated with multiple differing strstegies but all creating the same number by ignoring the syntax and functions to arrive at this answer 96… if your right then its not 1 in 1000, its almost inevitable that 99% of the people will get this same answer… inversley that makes the 1% who don’ t arrive or settle on 96 very interesting, if the claim is true that only 1 out of a 1000 people get this problem right, then something is out of place, or exagerated!

2. Lynn Morris says:

You are all making the problem so hard you cannot stick stuff in there that was not there to begin with. 1+4=5 2+5=7+5=12 3+6=9+12=21 8+11-19+21=40

1. Heeeere's Johnny says:

But you yourself are sticking stuff in there that was not there to begin with. Why u adding 5 and 12 and 21?

3. Douglas Vernon says:

No, it does not. you are re-writing the problem.. solve it by putting a number in the box that justifies the rest. You can’t do it with any other number than 40. Add the answer from the above line to the line following it and you will come up to 40 using simple addition.

19. Joe Dobbs says:

Each line uses this Mathematic Equation: (A * B) + A = X. Therefore 8 + 11 = 96.

(8 * 11) + 8 = X
88 + 8 = X
96 = X

20. Asuquo Queen says:

The answer is 96, which ever way you may arrive at the answer,when it comes to quantitative reasoning, the answer remains 96. 8+11= 8*11=88+8=96

21. Edwinhills says:

1+4=5
2+5=12
3+6=21
8+11=?

(1×4)+1=5
(2×5)+2=12
(3×6)+3=21
(8×11)+4=92

1. FELIMON says:

8+11=40

1. FELIMON says:

1+4=5
2+5=7+5=12
3+6=9+12=21
8+11=19+21=40

22. Angie says:

I get 218

1+4=5
2+5=7+5 from answer above = 12
4+7=11+21 form answer above = 32
5+8=13+32= 45
6+9=15+45=60
7+10=70+60=130
8+11=88+130=218

1. Vrtak says:

I get 165
1 + 4 = 5
2 + 5 = 7 + 5 = 12
3 + 6 = 9 + 12 = 21
4 + 7 = 11 + 21 = 32
5 + 8 = 13 + 32 = 45
6 + 9 = 15 + 45 = 60
7 + 10 = 17 + 60 = 77
8 + 11 = 88 + 77 = 165

2. Jim says:

You should check your addition… 7+10 is 17 not 70… and 8+11 is 19 and not 88

3. Stan Smith says:

1+4=1×4+1=5
2+5=2×5+2=12
3+6=3×6+3=21
4+7=4×7×4=32
5+8=5×8+5=45
6+9=6×9+6=60
7+10=7×10+7=77
8+11=8×11+8=96

1. Cheryl says:

I got 96 also

2. Asuquo Queen says:

This is the correct method to the answer

1. Mona says:

Yeppp!!! Lol

23. Anon says:

Considering that the originator of the question has stated that the answer is 96, debating anything other than that is moot.

1. Naomi says:

Kin 40

2. Bee says:

In that case, here is a question for you!
(Is there a mistake, if so reveal it, or is math irrelevant?)
a=b
a+a=a+b
2a=a+b
2a-2b=a+b-2b
2(a-b)=a+b-2b
2(a-b)=a-b
2=1

24. Abdul Haleem says:

1 + 4 = 5. → 1×4 + 1= 4+1=5
2 + 5 = 12. → 2×5 + 2 = 10 +2= 12
3 + 6 = 21. → 3×6 + 3 = 18 + 3 = 21

Similarly,

8 + 11= 96. →8×11 + 8 = 88 + 8 = 96.

1. Coral Jackson says:

96

25. Cindy says:

I think the correct answer is “not enough information”

26. Phil france. says:

To respect the logic of 40 , you must add the result of the previous operation in the first line , 1 + 4 = 5, you add 0 , but it is impossible to obtain it by addition of 2 integers respecting the gap 3. the number to be added on the front line can not be zero (but 4 for me), and as the result 5 need zero, the operation is different between the first and subsequent lines , we can not validate all lines by the same operation, so the result is false.

27. McKidd says:

1+4=5
2+5=12
The difference between 12 & 5 is 7 and the 2+5=7
3+6=21
The difference between 21 & 12 is 9 and 3+6=9
8+11=40
Because the difference between 40 & 21 is 19 and 8+11=19

1. Lisa Lee says:

I agree

2. ROBERT HOLMES says:

True

3. Donato Arredondo says:

1+4=5
2+5=12
3+6=21
4+7=32
5+8=45
6+9=60
7+10=77
8+11=96

28. Rick Reed says:

When I was in school, I was often told to take the question as is, assume nothing, to come up with the answer. So…

The first line is as is. The 2nd line is the 2 numbers to add plus the previous answer to get the answer. 3rd line is the 2 numbers to add plus the previous answer. That’s how I got 40: 8+11=19; 19+21 (previous answer) =40.

It works this way if one takes the question at face value, adding and assuming nothing else.

That’s the answer i got was 40

2. Walter R Williams says:

If you take it as written, no where does it ask for the next number in the sequence or progression… therefore lines 1-3 are irevelant and the answer is 8+11=19.

3. Pete says:

Each equation is of the form x+y = (x*y) + x

so 8 + 11 = 98*11)+ 8 = 96

Therefore, using your logic, both answers are correct . Either 40 or 96

29. Dave Jerrard says:

If you take the puzzle as an actual math problem the answer is 19, because that’s what 8+11 equals. The first line is correct, and the next two are not. It doesn’t actually ask you to match what they are doing, so figure out the one equation that is missing a solution.

However, if you treat this as a logic puzzle, where the numbers and functions could just be variables, the best answer is 96.

You can use the idea that you do the math in the given line, and then add the previous answer, which works, but you have to go through each iterations to find the next value, which is clunky. A simpler solution is xy+x, where you multiply the two values, then add the first. This works regardless of what line you’re on, and you don’t need to solve previous lines to get the answer. So, 8×11+8=96.

You also have to note that the sequence of numbers jumps at the last line, which is an indication that something is missing – four lines to be precise. This rules out 40 as the answer because that relies on ignoring several patterns that are present in the first three lines. Those are:
1. The first digit always increments by 1. This graphs to a straight line.
2. The second digit also increments by 1. This also graphs to a straight line
3. The solutions shown increment by an odd number that increases by 2, starting at 7, then 9. The next steps would be 11, then 13, then 15, etc. This graphs to a straight line as well.
4. You can solve each line by taking the previous answer, adding the difference between it and the one prior to it, and adding two.
5. The solution to each line always works out to the two values multiplied together, plus the first value.

So, right away, we have five graphs that form straight lines, which makes everything simple. The next increment values are easily determined for all steps in the sequence, in both directions. This gives us 4+7, 5+8, 6+9, 7+10, 8+11, 9+12, etc…
https://www.dropbox.com/s/0o6wj01j89eds7d/First3Entries.png?dl=0

From the three entries here, it’s easy to predict what the next steps should be, except for the solution, but that can be figured out from the rest.

Trying to use 8+11 as the next step in the sequence breaks every one of these patterns, and gives you a series of numbers that no longer form any pattern, and thus, do not allow you to predict what any other entries in the sequences would be. Prediction is one of the basic defining traits of patterns, along with the fact that they follow a repeating, well, pattern. For the first number in each line you get 1, 2, 3, 8. That’s not a pattern, and there’s nothing to hint what the next value would be. The same with the second value; 4, 5, 6, 11. If you graph these, you get a weird broken hockey stick looking thing for each line:
https://www.dropbox.com/s/7bquznsm5ees8mh/WrongSolution.png?dl=0
There no way to predict what the next entries should be with this; there are no patterns that can be extrapolated. Sure, you can try to wedge things like different base systems, but even those fail to provide any sense of consistency. The last line is clearly not the next one in the sequence, so it should not be treated as such.

Now, using the simple xy+x formula, we get something that is very predictable. If we graph it out over twelve steps, we get five straight lines, and we see an elegant looking curve developing for the solutions:
https://www.dropbox.com/s/vq5yomyv0hq3bpn/Correct12steps.png?dl=0

Wait a minute. That looks awfully similar to a…
https://www.dropbox.com/s/jmmndu0mjgg67nw/Correct40steps.png?dl=0

Yep! A parabola.

So, the xy+x solution fits every pattern perfectly, in both directions, and it doesn’t get much more elegant than a parabola. From this it’s pretty safe to assume the creator of the puzzle had this in mind. The answer has to be 96.

1. James Lenac says:

Dave a thought for you. Your first paragraph is the key. If this is a maths question how can we prove the answers to the first three lines are correct and therefore find the correct answer for line four. Everyone is working in the decimal counting system if we think outside of this we can get the answers to fit. Each answer is in a decending base starting with 6, then 5, then 4 and final 3

So line one is 1 + 4 = 5 which is correct if the base is 6
Line two 2 + 5 = 7 which is expressed as 12 in the base of 5
Line three 3 + 6 = 9 which is expressed as 21 in the base of 4
Line four 8 + 11 = 19 which is expressed as 201 in the base of 3

It’s a different approach how you like it.

30. Corey Cavalier says:

I solved it this way:
1 + 4 + (prev sum 0) = 5
2 + 5 + (prev sum 5)=12
3 + 6 + (prev sum 12) = 21
4 + 7 + (prev sum 21) = 32
5 + 8 + (prev sum 32) = 45
6 + 9 + (prev sum 45) = 77
8 + 11 + (prev sum 77)= 96

1. Lisa says:

But that is not what the problem shows, there is no 4+, 5+, or 6+, it jumps from 3+6=21 to 8+11 answer is =40

1. Milan says:

That’s the same answer I got. But they said the answer was 96? What gives!??

31. Vickie Bush says:

40 if you just solve the problem as seen
96 if you follow the pattern
19 if you just solve 8+11=?

32. Billy Vance says:

Answer is 36. Sorry, guys. Turns out I’m the only genius in this bogus debate lol

1. Haha YOU fool turns out your not even close….haha rotflmao. TRY AGAIN!!!! Lol

33. Marilyn says:

If you multiply the second digit by sequential numbers beginning with 1 and the first number, the final answer should be 52.

1+ (4×1) =5
2+ (5×2) =12
3+ (6×3)= 21
8 +(11×4) = 52.

1. Witchy425 says:

That’s what I thought too. Doesn’t seem to be a very popular answer.

1. Razi says:

You have to follow the order you are forgetting to add 4-7:
1+(4×1)= 5
2+(5×2)= 12
3+(6×3)=21
4+(7×4)= 32
5+(8×5)= 45
6+(9×6)=60
7+(10×7)=84
8+(11×8)=96

1. Dave Jerrard says:

I missed this pattern! I used a couple others; multiple the two values then add the first, as well as add the two, plus the previous solution. This is yet another pattern than all the other ‘solutions’ break.

The interesting part is when you have the correct solutions, they all form a parabola.

2. Kathy says:

Razi…following your method which is how I did it…you have one mathematical error…look at 7+(10×7) =84…shouldn’t it be 77?

2. Josh says:

Your chosen math seemed to skip the fact that 4-7 would have absorbed the 4-7 you want to use which is why you received your 52 answer.

1+ (4×1) =5
2+ (5×2) =12
3+ (6×3)= 21

4+ (7×4)= 32
5+ (8×5)= 45
6+ (9X6)= 54
7+ (10×7)= 77

8 +(11×8) = 96

1. 11Eleven11 says:

Josh, your assumption is that it is a sequential mathematical series that has simply left out the steps 4-7. Solving only for the presented information, 52 is an acceptable answer. Without further parameters, such as a fifth line fully solved like lines 1-3, there is not enough information to rule out that answer or the answer of 96.

2. Janet Doolen says:

21 + 19= 40.

3. Janet Doolen says:

21 + 19= 40. You start with 4+1=5 then 2+5=7 plus 5=12, then 3+6=9+21.then8+11=19+21=40.

1. Milan says:

I hear ya Janet! That’s what I did, and came up with the same answer… 40.

4. Gina says:

That is what I did as well. To me the pattern is to multiply by the next number then add the other digit. It is all in what you think the pattern is. I see the 1,2,3,8 as random numbers. I also see the 4,5,6,11 as random numbers the only true pattern would be the pattern of the answer multiplied by the next number and then added. Ex. 11×4+8= 52

5. Steve says:

Agreed. 52. Must use ONLY what’s given, and can’t assume missing elements. All the “96” answers are based on an assumption for which there is no basis provided.

34. Char says:

The solutions 40, 96 and 19 are correct.
If you take the previous row solution and add it to the sum of the next row, the solution is 40.
If you take the 1st number, add it to the 2nd number then multiply that sum by the 1st number the solution is 96.
If you just add the last row you get 19.

It all depends upon how you view the equation.

1. Shane says:

Not sure how it can be 19… the second row is 2 + 5 = 12 and that’s not regular addition like 8 + 11 = 19 is.

1. Luke Lovekin says:

Actually the only valid answer is 19. 8+11=19 regardless of what pattern of incorrect answers come before it.

35. Dawson says:

U times them both then add the first number to wat u got. It applys to all of em, to big of a coincidence to be wrong: 1×4=4+1=5, 2×5=10+2=12, 3×6=18+3=21, 8×11=88+11=99 so my answers 99 but thats with my deduction skill, idk of im right

1. Tom says:

I came up with the same equation and got 96. 8×11=88+8=96. You added the 2nd # instead of the first

2. Dave Jerrard says:

Close. You do multiply the two values, but you add the first again, not the second, so you get 96 for 8+11; xy+x. This is the correct method because all the correct answers are on a parabolic curve.

36. ryan says:

1+4=5

37. Daos says:

I suppose it is positional numeral system with usual rules of arithmetic.
I suppose left side of all equations is in radix of 10.
I suppose right side of all equations is in different radix.
First is in radix of six, second is in radix of five, third is in radix of four, four is in radix of three.
For every next equation radix is lowered by one.

2 (rad 10) + 5 (rad 10) = 12 (rad 5); 5^1 * 1 + 5^0 * 2 = 5*1 + 1*2 = 5 + 2 = 7 (rad 10)
3 (rad 10) + 6 (rad 10) = 21 (rad 4); 4^1 * 2 + 4^0 * 1 = 4*2 + 1*1 = 8 + 1 = 9 (rad 10)
8 (rad 10) + 11 (rad 10) = 201 (rad 3); 3^2 * 2 + 3^1 * 0 + 3^0 * 1 = 9*2 + 3*0 + 1*1 = 18 + 0 + 1 = 19 (rad 10)

Hi, i had the same reflexion, but since 1+4 = 5 in any radix higher than 5, why absolutly take 6 ?
5+2 = 12 is only right with radix of 5 and 6+3=21 in radix of 4.
so i used the Lagrange Polyomials from equation f(5,2)=5 and f(6,3) =4 to deduce the simplest radix to take in consideration is 28 for 4+1=5, wich works because 28>=5, and thus, the simplest radix to use for 11+8 is 98. So the simplest way to solve this problem is “11+8=19 in radix of 98”.

Do the math for the polynomials, it’s easy since there are just 2 équations to take in account.

38. seth says:

I’m sorry but Whatsapp is wrong again, as I will clearly demonstrate. Everybody who answered 96 or 40 were fooled by the fact the lines 2 and 3 in the puzzle are incorrect . This caused them to seek out patterns to justify these wrong answers. They got 96 by choosing multiplication operators that aren’t even in the equation. They got 40 by adding horizontally with operators that are not in the equation. But none of this changes the fact that 8 +11 is 19. That is pure truth. It doesn’t matter what incorrect answers precede it. They are incorrect. And them being incorrect does not justify giving a wrong answer to 8 +11 no matter what imaginary patterns they find based on being derailed by wrong answers.. 3 wrongs do not make a right. 8 + 11 is always 19.

1. Renee says:

Yes! Finally someone talking some sense!!

2. chris says:

You are correct. It is amazing how this riddle truly stumps. Folks are overthinking. The only question asked is, 8 + 11 = ?. The answer is always 19. I responded to a shared FB posting. The vast majority answered 96 or 40.

1. R says:

You’re answers are SOLEY based on the assumption that its a trick question. The problem states that IF 4+1= 5 AND 5+2= 12 AND 6+3=21, Then solve for 8+11. The problem is stating that there are conditions by saying”IF” this pattern Is used, what is the answer for 8+11.

1. H says:

So true! They are taking it so literally! Thats y a lot failed in logic exams…

2. M says:

The word “IF” does not appear anywhere in the problems. In fact, all the convoluted-arithmetic answers assume it is a trick, or a puzzle to be solved. Why should wrong equations affect one’s thinking about future equations using standard numbers and symbols?

If you fed these into lines of code on a computer (with appropriate syntax), you’d get back Boolean answers for the first 3: “true” “false” and “false” and the final one would result in the completion of the equation and would result in the answer of “19”.

3. Anon says:

8 + 11 is not always 19. That only holds true for some numbering systems.
As a matter of fact, 8 + 11 is equal to 20 if the numbers are based on powers of nine.
Your “truth” is relative, pure or not. The FACT of it is another matter entirely.
The other solutions present a consistent logic within the context of the problem, while yours chooses to disregard the given information which does not conform to your hypothesis.

Anon is correct here – 8 + 11 is not always 19 …. in a base-3 numbering system it is 201

39. Josep Mas Colell says:

1+4 = 5
2+5= 12
3+6 =21
4+7=33
5+8=46
6+9=61
7+10=78
8+11=97

1. Trying to be helpful says:

I think your answer would be 8+11 = 96. Since 4+7 = 11, then 11 +21 = 32. That makes all your following numbers +1. Unless I am misreading something.

40. Wojtas says:

n=1
1+4n=5 1+4×1=5
2+5(n+1)=12 2+5×2=10
3+6(n+2)=21 3+6×3=21
8+11(n+3)=8+11×4=52

41. marcos lopez says:

HOLA QUERIA SABER QUE PASO CON MI RESPUESTA

42. marcos lopez says:

el resultado es 57 esta es la lógica
1+4=5
2+5=12
3+6=21
como ya tenemos los primeros 6 números(1.2.3.4.5.6=21) sumados vamos por los siguientes
6 números(7.8.9.10.11.12=57) sumados los dos grupos del (1.2.3.4.5.6.7.8.9.10.11.12=78)
7+10=38
8+11=57
9+12=78
en conclucion tenemos que el problema nos habla de la sumatoria de los primeros 12 números (1.2.3.4.5.6.7.8.9.10.11.12) formado por 4 grupos, primer grupo(1.2.3) sumado al segundo(4.5.6)
y el tercero(7.8.9) sumado al cuarto grupo(10.11.12)

43. ROBERTO MATA says:

The result is 201 is the only one that respects the signs of addition and equality.

We are so accustomed to the decimal number system that we sometimes forget that it is not the only one there. The problem is solved as follows: first look 1 + 4 = 5 apparently everything is normal, so we go to the second line 2 + 5 = 12, and we wonder what universe 7 = 12? in our course, rather the question is to what numbering system seven is represented by the symbol 12? in the numbering system with base 5.

Those who have not understood me yet: our numbering system is called decimal that has 10 symbols (including zero) to represent all numbers there, so when you get to nine we just all symbols and to represent the ten use a figure and we repeat representing it as 10.

However, in the numbering system with base 5, to reach four symbols are finished and we represent with five symbols 10, for that 6 = 12, 7 = 12; understanding that the problem in what is left of the equal sign (operations) are in the decimal system and the right (result) on another system.

In the third line 3 + 6 = 21; It is in the number system with base 4 because in this system 1 = 1, 2 = 2, 3 = 3, 4 = 10, 5 = 11, 6 = 12, 7 = 13, 8 = 20, 9 = 21.

After observing all this, we realize that in the first line the result is in the numbering system with base 6 and as in this system five is represented as 5 as in the decimal makes us believe that in that line does not pass nothing weird.

And we have the sequence: the first line is numbering system with base 6, second base 5 row, third base 4 line, so in the fourth line, where the question is asked, it is with base 3.

In the numbering system based on March 19 it is represented as 201.
1 = 1, 2 = 2 3 = 10, 4 = 11, …, 17 = 122, 18 = 200, 19 = 201.

1. Bruce says:

Brilliant pattern to see, but who says we need to respect the equal signs and plus signs, when so many other of these riddles on the internet certainly imply some other function besides standard operations as we know them?

Also you are wrong about that being the only way to still respect the plus signs and the equal signs anyway. Simply assume the numbering system on the right side of the equal signs is a numbering system such that for any non negative number Z in that system, Z is equivalent to a value on our decimal system of 2*SQRT(4+Z) – 1

That will also make each equation correct and preserve the meaning of the equal signs just as well as the descending base numbering system will. Then the answer to 8+11 is 96 in this defined numbering system, and that is 19 in our own defined decimal system. So, it works out well.

1. Daos says:

If there is more than one correct answer then why we must prefer or even consider much more complex solution over much more simple? I believe simple solution is always better than complex if they are both correct.
http://www.cs.elte.hu/~ewkiss/jokes.html

1. John Brittain says:

201 is the plainest answer you can get by simply reading the equations as is. You only change your perception of the representative numerals.

2. Lawrence says:

If this was a base 5 system, we would have to omit numerals 6-9 sir.

44. Cách giải đơn giản nhất:
1 + 4 = 5
2 + 5 = 12
3 + 6 = 21

”4 + 7 = 33
5 + 8 = 46
6 + 9 = 61
7 + 10 = 78”

8 + 11= 97

Kết quả 97
Đó là 1 logic số đầu 1.2.3.4.5.6.7.8+………..
Lấy 2 số cộng với nhau cộng cho kết quả liền kề trước đó.
*Chú ý đây là bài toán đánh lừa 🙂

45. Shawn says:

The first answer 5+2+5=12 … 12+3+6=21…. 21+8+11=40

The pattern is simple, where the hell did all this multiplication come from? There are only addition symbols in this puzzle.

1. Deloris Paige says:

46. Shane Cheesman says:

I got 96 due to sequential theory.

1 × 4 + 1 = 5
2 × 5 + 2 = 12
3 × 6 + 3 = 21
4 × 7 + 4 =
5 × 8 + 5 =
6 × 9 + 6 =
7 ×10+ 7 =
8 ×11+ 8 = 96

1. zhan says:

it’s 40

47. Shane Cheesman says:

I got 92 due to sequential theory.

1 × 4 + 1 = 5
2 × 5 + 2 = 12
3 × 6 + 3 = 21
4 7 4
5 8 5
6 9 6
7 10 7
8 ×11+8 = 96

48. Robo says:

The answer is 21. This comes from 1+4=5 base 10, 2+5=21 base 3, 3+6= 21 base 4, 4+7=21 base 5, 5+8=21 base 6, etc base 7, base 8, 8+11=21 base 9. It’s not completely tidy for 5 (base10) but it seems the only answer.

49. teejay says:

I solved it this way:
1 + 4 = 5
2 + 5 = (5+2) =12
3 + 6 = (12+5+2+2) = 21
4 + 7 = (21+5+2+2+2) = 32
5 + 8 = (32+5+2+2+2+2) = 45
6 + 9 = (45+5+2+2+2+2+2) = 60
7 + 10 = (60+5+2+2+2+2+2+2) = 77
8 + 11 = (77+5+2+2+2+2+2+2+2= 96

1. Jksoft says:

2 + 5 = (5 + 5 + 2 ) = 12

50. Sare says:

There of course is 40 as well
2+5= 12 ( 5+2+5)
3+6=21 (12+3+6)
8+11=40 (21+8+11)

51. Dave says:

It has to be 19. All of the symbols have precise meanings. 8 is always 8. 11 is always 11. + always means addition. = always means equals. There is no multiplication indicated. No matter if the two incorrect equations before the 8+11=? give the false impression that there is something more complicated going on, 8 + 11 always equals 19.

1. Gary James says:

Dave;

I agree with you and others that the riddle, as stated, is essentially mis-stated. Rather than showing the simple “additions” where the second and third ones are obviously incorrect, the riddle should really be stated as:

If a = 1 and b = 4, then x = 5
if a = 2 and b = 5, then x = 12
if a = 3 and b = 6, then x = 21
If a = 8 and b = 11, then x = ?
Solve for ?

a + (b)a = x will produce the results, as will a + (a+3)a = x.

Of course, as Einstein would point out, the following would also produce the results when “a” is 1, 2, 3, or 8, but would produce higher results when “a” is any other number: (a-1)(a-2)(a-3)(a-8) + a + (b)a = x.
In fact, we could insert any expression in place of (a-1)(a-2)(a-3)(a-8), no matter how complex, as long as it resolves to zero when “a” is 1, 2, 3, or 8.

52. Gary James says:

I believe the formula n + (n+3)n = x produces all the results shown without any convoluted logic.

This reminds me of reading years ago about Einstein causing his math professors grief when he kept telling them that their exam questions had no single correct answer because they could have multiple answers. A simple example was determining the next number in the sequence 1, 2, 3, 4, 5. Two possible answers were 6 and 126. The formula x = n + (n-1)(n-2)(n-3)(n-4)(n-5) will produce 1, 2, 3, 4, 5 when n is one of those numbers because the string of multiplied numbers will have a zero in it. But for n = 6, the formula produces x = 6 + (5)(4)(3)(2)(1) = 6 + 120 = 126. For n = 7, the result is 7 + 720 = 727.

1. Good info Gary
Thanks for sharing 🙂

53. Bill says:

The answer to 8 + 11 = ? will always be19 no matter how many equations came before (or whether they were solved correctly or not).

1. Howard Baker says:

Finally someone who understands math. I see so many people trying to make sense of this simple addition while violating every math principle known to man (ok maybe not every principle but you get my drift)…LOL

1. Daos says:

It seems you are wrong.
What we see in our example? Set of symbols, not more, not less.
Then we must decide – are that symbols numbers?
If they are numbers then we must check is it positional notation?
If it is then we must find radix.
Then we must check whether “+” sign means “addition” and “=” sign means “equal”.
And only after such steps we may try to solve that puzzle.
What if that puzzle is fake after all and has no right answer?
Anyway, it may be done just for loolz 🙂

54. Neillusion says:

The most reasonable single answer is 201. Your answer involves a lie, the + is telling us to add. An equal sign is used & regular numbers are used. The level of ‘trickery’ goes beyond what is considered fair and challenging in a rational reasonable way to construct a puzzle. This would open the gates for stupid puzzles with multiple answers.
For decent puzzle making, esp of this kind, only one, reasonable answer should be possible, having an elegance that suggests simplicity in logic, yet devious, convoluted or obscure procedure. The solution you have admits other possibilities, not only 96 but 40 and others.
Where two answers are possible using similar contrivance, then, under the premise suggested by the question or suggestion to ‘share IT when you get it’, that there is one answer, then neither of the two answers can be right.
So the reasonable single answer involves the numbers on the left to base 10 yet the numbers on the right to bases 6 down to 3 in the last equation. Adding 8 to 11 gives 19base 10 which is 201base 3. Numbers to different bases that are not shown, do not involve other operators or numbers that are missing or in error. If the answer is as you gave, 96, then this is a sloppy excuse of a puzzle, will only cause suffering of those genuinely attempting to answer a genuine bona fide puzzle. You have a duty of care, honour it in the puzzle industry

1. Robo says:

My answer is 21, eg 1+4=5 base 10, 2+5=21base 3, 3+6=21 base 4, 4+7=21 base 5, etc to 8+11=21base 9. The 1+4=5 base 10 is not very tidy when the progression is 10,2,3,4,5,6,7,8,9. Maybe you could give a better answer.

1. jacquemes says:

la base de 10 n’équivaut pas à une base 1 ? dans ce cas c’est parfais.

2. Robo says:

Oh and 2+5 also = 12 base 5.

3. Marius says:

I totally agree with you. 201 is the least complicated answer that explains the pattern, respects the standard interpretation of addition and the equal sign. It also shows that most people forget that a Base 10 representation of numbers is an arbitrary choice.

55. Ronald Turpin says:

If I work for you on Monday for 8 hours, and I work for you on Tuesday for ll hours, and you pay me \$1 per hour then you claim you would pay me \$96 for working 19 hours?? I think you would be out of business with this math very soon. Can you explain in a more logical way than: 8 + 11 = 8 x (6+1) ? Sounds like liberal government accounting! Pardon my sarcasm because I would really like to learn, but this seems to defy the basic tenant of math that the formulas clearly convey the work, not leave the reader to fill in blanks that are not clearly defined.