# The Viral 1 + 4 = 5 Puzzle The Correct Answer Explained

Viral Math Problem 1 + 4 = 5, 2 + 5 = 12, 3 + 6 = 21, what is 8 + 11= ?

This video presents what many people believe to be the correct answer.

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A mathematician might take a literal approach.

1 + 4 = 5

2 + 5 = 12

3 + 6 = 21

8 + 11 = ?

The first equation is true, the second and third are false, and the answer to the equation should be 19.

But riddles like this are not about literally interpreting mathematical symbols. They are about identifying a pattern in the set of equations and applying it to the unknown.

The answer that jumped into my mind is to add the first number to the product of the two numbers to get the answer. That is:

a + b means a + ab

This works for the known equations.

1 + 4 means 1 + 1(4) = 5

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

3 + 6 means 3 + 3(6) = 21

Applying the pattern to the last equation gives the answer of 96.

8 + 11 means 8 + 8(11) = 96

The answer of 96 is valid according to this interpretation. Furthermore, many other IQ tests have this sort of pattern where you take two numbers and find a hidden equation that involves simple operations like addition, subtraction, multiplication, division, and exponentiation.

But some people interpreted the problem differently and arrived at a different answer.

Another interpretation: running total

Some people felt the pattern was a running total: add the result in the previous line to the new numbers to get the new answer.

The first line is valid mathematically.

1 + 4 = 5

For the next line, take this result of 5 and add it to the new numbers to get the new answer.

5 + 2 + 5 = 12

Do the same thing for the next line: add the previous line’s result of 12 to the new numbers to get the next result.

12 + 3 + 6 = 21

To solve the puzzle, do the same for the final line.

21 + 8 + 11 = 40

This pattern results in an answer of 40, and many people suggested this answer is more valid.

So what is the answer? Is it 40 or 96? While we cannot know for sure what the puzzle maker had in mind, there is a way to reconcile these two approaches. It turns out the running total can also lead to the answer of 96, if you decide to fill in the pattern a bit more.

Running total missing lines

Suppose the answer in each line is the running sum total of the previous result and the new numbers.

1 + 4 = 5

5 + 2 + 5 = 12

12 + 3 + 6 = 21

Notice that in each line the new numbers are incremented 1 more from the previous line. For example, 1 + 4 is turned into 2 + 5; so both the numbers 1 and 4 are increased by 1. Then 2 + 5 is increased to 3 + 6.

We can continue this pattern, so the next lines would be 4 + 7, then 5 + 8, then 6 + 9, then 7 + 10, and then 8 + 11.

What is the running total when we include these “missing” lines?

1 + 4 = 5

5 + 2 + 5 = 12

12 + 3 + 6 = 21

21 + 4 + 7 = 32

32 + 5 + 8 = 45

45 + 6 + 9 = 60

60 + 7 + 10 = 77

77 + 8 + 11 = 96