Solve this if you are a genius? This quiz showed up on my Facebook news feed.

8 = 56

7 = 42

6 = 30

5 = 20

3 = ?

The pattern looks pretty easy, right?

8^{2}— 8 = 56

7^{2}— 7 = 42

6^{2}— 6 = 30

5^{2}— 5 = 20

So what is the correct answer?

Here’s mine:

3 = 3 — even if it’s preceded by a bunch of false statements.

Do you agree?

**Update**. This is an *old* post and I thought it had seen all the life it was going to see. Then Angel comes and leaves a comment:

It turns out that the “?” can be whatever we want it to be!

Angel backs up his claim with math. I think we have the definitive answer.

## 106 responses to “Solve this if you are a genius”

Numbers on the right and left are not correlated.

Like you said 5 does not equal 20 so is 6 not equal to 30. The numbers on the left and the equality sign are just mere distractions and do not relate with the numbers on the right.

Ignoring the numbers on the left might not bother you, but I think the solution to this pattern needs to consider the numbers on both the left and right.

I see this pattern. What’s wrong in my thinking? I am not adding another series in it. Number is squared and then subtracted by the same number. Is this correct?

8

^{2}– 8 = 567

^{2}– 7 = 426

^{2}– 6 = 305

^{2}– 5 = 203

^{2}– 3 = 6Ding! Ding! Ding! I think we have a winner.

I

lovethis pattern.Interestingly, n

^{2}– n = (n × n) – n = n × (n – 1), which is the pattern I mentioned in my original post (minus the snarky final line…).WOW!! FUNNY ALGEBRA.

Because of this i also thought of this:

ALL NATURAL NUMBERS ARE EQUAL.

The proof starts with a formula that a

^{m}= a^{n}⇒ m = nE.g.:

Let a = 1 then … = (1)

^{-3}= (1)^{-2}= (1)^{-1}= (1)^{0}= (1)^{1}= (1)^{2}= (1)^{3}= … = 1. Then … = -3 = -2 = -1 = 0 = 1 = 2 = 3 = …Let a = -1 then … = (-1)

^{-3}= (-1)^{-2}= (-1)^{-1}= (-1)^{0}= (-1)^{1}= (-1)^{2}= (-1)^{3}= … = 1. Then … = -3 = -2 = -1 = 0 = 1 = 2 = 3 = …Let a = 0 then … = (0)

^{-3}= (0)^{-2}= (0)^{-1}= (0)^{0}= (0)^{1}= (0)^{2}= (0)^{3}= … = 1. Then … = -3 = -2 = -1 = 0 = 1 = 2 = 3 = …So always remember a

^{m}= a^{n}⇒ m = n but a ≠ -1, 0, 1Zoheb, hmmm… I’m not sure why you don’t like my algebra. Do you not agree that n

^{2}– n = n(n – 1)? Or, to use an example, 8^{2}– 8 = 8 × 7.By the way, it might not be obvious to others that you are attempting (maybe?) to link to a clearer representation of your proof here.

I completely agree!!

It’s different PROBLEM that has been addressed in that blog. I just wanted to throw that in your post so I just posted it here.

I must confess I can’t follow the math in it. It looks completely wrong to me. For example 1

^{n}= 1 and 0^{n}= 0, not n. Oh well…Interesting mental exercise. The facts are: equations in math (and chemistry) MUST be balanced otherwise our world would end.

First: Math rules state that if you perform an operation to one side of the equation you must do the same to the other side.

Second: There is no rule at the beginning of this puzzle that sets up a pattern — it doesn’t say 8 × X = 56 so assuming that is incorrect. None of the implied patterns work either because the moment you introduce an operation you are changing the equation completely.

As Brent states, all of the equations up to 3 = ? are false. 8 does NOT equal 56.

There’s no proof needed because we know that to be true.

In the scientific world many scientist perform experiments and come to answers that are later disproven. Just because someone states that 8 = 56 doesn’t make that true. In fact it’s quite interesting to note that most people’s answers do not follow any mathematical method. Most are happy to state 3 = 6. Faced with a series of incorrect data most people would continue to interpret that as true and solve a math question incorrectly.

That’s a little troubling.

So, Robert … let’s see if we can recover this. Instead of the equals sign, let’s put a meaningless divider in it’s place. Then include the instructions, “Continue this pattern.”

What would you put in place of the question mark? ;-)

3 equals the question mark :)

Ha! So they gave the answer to start with? :-D

This brings to mind the saying, “The first step to solving a math equation is admitting you have a problem.”

Thanks for dropping by. :-)

3=13

8 = 56; 56 – 8 – 7 + 1 = 42 (next result)

7 = 42; 42 – 7 – 6 + 1 = 30

6 = 30; 30 – 6 – 5 + 1 = 20

5 = 20; 20 – 5 – 3 + 1 = 13

3 = 13

Chiunti, although your answer looks different from everything before it, I don’t believe it is, plus it doesn’t explain the first pair of numbers. Here’s why I say that.

Your equation is effectively:

A

_{n}= A_{n+1}– (n + 1) – n + 1In other words, the answer for 7 is the answer for 8 less 8 less 7 plus 1. What happens if we say the answer for n + 1 is (n + 1) × n, substitute it into your proposal, and then simplify? I suggest doing this because it shouldn’t detract from your answer, and it allows us to explain the first number pair.

A

_{n}= (n + 1)n – (n + 1) – n + 1A

_{n}= (n + 1)n – n – 1 – n + 1A

_{n}= (n + 1)n – n – nA

_{n}= (n + 1)n – 2nA

_{n}= (n + 1 – 2)nA

_{n}= (n – 1)nA

_{n}= n(n – 1)What do you think?

Considering:

N1 = A1

…

Nn = An

then:

An = A(n-1) â€“ N(n-1) â€“ Nn + 1

N will never have value of 4, because it is not in the numbers listed.

I hope I explained.

Obviously the first line is the exception.

I tried to give a mathematical answer, however is a correlation in the order listed.

But that’s not the puzzle.

I get what you’re saying but then I could easily say “put a × (times) sign at the beginning preceded by variable Y and then solve.”

I must adhere to the strictest rules of mathematics. If not we are altering the results.

But to answer your question and adding elements to the equation to make it “work” then the answers would be

7 × 8 = 56

6 × 7 = 42

5 × 6 = 30

4 × 5 = 20

3 × 4 = 12 (missing)

2 × 3 = 6.

But I state again that interpreting the original data and ADDING data to find the solution is incorrect

Chiunti. There is an error in your interpretation. You forgot the â€œ4â€ line which is obviously missing from the pattern

8 = 56; 56 – 8 – 7 + 1 = 42 (next result)

7 = 42; 42 – 7 – 6 + 1 = 30

6 = 30; 30 – 6 – 5 + 1 = 20

5 = 20; 20 – 5 – 4 + 1 = 12

4 = 12; 12 â€“ 4 â€“ 3 + 1 = 6

3 = 6; 6 â€“ 3 â€“ 2 + 1 = 2

Therefore in your pattern 3 = 6 is next in the sequence preceded by 4 = 12

Following 3 you have

2 = 2; 2 â€“ 2 â€“ 1 + 1 = 0

let suppose 8 = a

7 = b

6 = c

5 = d

and 3 = e

then 3 = 12 as the series goes on, but this assumption is proved logically and there will be no questions as how 8 equals 56 so. i guess my answer is interesting.

Hmm… I’m not sure I follow what you’re trying to say. What is the benefit of assigning the numbers to letters?

if we dont assign numbers then we take them(left side numbers) as symbols only so then 4 will not be a concern then this question can be solved logically and 3 will be 12 and no issues will be their as how 8 equals 56. 7 equals 42 and so on