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”

Those “thingies” on the left side of the equals signs already are symbols. Unlike the letters you’re putting on the right side, numbers have a fixed value. Once you equate the letters to the numbers, you’re assigning fixed values to them as well (at least for this context). I’m not convinced you’re solving my original (and somewhat facetious) issue.

I’m more interested what logic you’re using to determine that the question mark should be replaced with 12.

3 never could be 6, becoz if u got the answer pattern accordingly to the statement given, 6 is already = 30, so 3 cannot be 6 anymore.

the answer is 6 correct

Vasu, what method are you using to reach your conclusion?

8 × 7 = 56

7 × 6 = 42

6 × 5 = 30

5 × 4 = 20

3 × 3 = 9

answer is

3 = 9

Wrong.. These things intentionally omit numbers. To assume “what if” is not Logical.. There is always a MOST logical conclusion without hypothetical added numbers.. The correct answer is 12

Answer … This formula stays consistent using only the Logic provided without assuming anything. The left numbers mean absolutely nothing in finding the answer other than validating the Proven Facts… SO, using ONLY the right side numbers follow this formula the validate with the left corresponding number >>> 56 – 42 = “14” then 42 – 30 = “12” then 30 – 20 = “10” then ?? from 20 will get the next in sequence figure? Note the factors reduce in perfect order will give to you the next in sequence figure of “8”? Note 14 / 12 / 10 / 8 <>> 3 x 4 = What??? Bingo TWELVE (12) … 12 is the only logical answer.

If you will only see, the Left corresponding number multiplied by the next Left side number gives to you the right side number . You will see the 4 was omitted. However in the last row, the $ is called in as the next adjacent multiplication factor… Thus 3 x “4” = 12. The absolute most logical conclusion can only be 12 as the answer

If 8 is the next in succession then at all above, validate by subtracting that 8 from twenty

I see your pattern, but it seems to ignore that the last step for numbers on the left decreased by two. It doesn’t seem that it matters for your pattern (and maybe it shouldn’t…).

Thanks for dropping by!

Hmm… If ignoring the numbers on the left is valid, then your answer clearly makes sense.

Look the results :

Results for the left-hand numbers: 5, 4, 3, 2, ?; ? and the right numbers for 6, 2, 0, 0,?,?

To see if the numbers are based on logic; the size of the result is 6, because

8 × 7 = 5 6

7 × 6 = 4 2

6 × 5 = 3 0

5 × 4 = 2 0

4 × 3 = 1 2

3 × 2 = 6

2 × 1 = 2

1 × 1 = 1

results number – left rows numbers : 5, 4, 3, 2, 1; right: 6, 2, 0, 0, 2, 6

So the result is number 6

:)

I’ve read your comment a bunch of times, and I still can’t quite figure it out. Six is probably the right answer; I just don’t see how you got there.

Simplest is: x = x*x – x

When you assume ‘what if 8 = 56’ etc.

The answer is 6 also when you visualize numbers so that the number on right is divided by the number under it on left, e.g. 56/7.

So, you get this:

8 = 56/7

7 = 42/6

6 = 30/5

5 = 20/4

4 = a?/3

3 = b?/2

a = 12

b = 6

And proof is: x = x*(x-1)/(x-1)

E.g. 6 = 30/5 or 6 = 6*5/5

Meaning x = x

;-)

And if you want to be strict with the puzzle then the most correct answer is that…

3 = any number but 3

…because all statements are wrong, so to make your right you have to keep it wrong so all answers are in ‘harmony’ (same ‘logic’).

But if I have to pick a wrong number then it is 6, because it is beautifully wrong to state 3 = 6 in context of this interesting thought-provoking puzzle.

“3 = any number but 3”

Ha! :-D I can see your logic, and frustratingly so, it works.

The rest makes complete sense.

Thanks for dropping by. ;-)

Hi Brent! Was a pleasure to find your blog and see your answer and that of others. Just shows how differently different people approach the same thing :) Technically speaking yours is most correct…

7 + 7 = 14 – 56 = 42

6 + 6 = 12 – 42 = 30

5 + 5 = 10 – 30 = 20

3 + 3 = 6 – 20 = ///14///

Dimas, interesting pattern. I like how it doesn’t worry about there not being a row starting with the number four. Unfortunately, it doesn’t explain where the 56 comes from, while the n × (n – 1) pattern does.

Thanks for dropping by and writing a comment. :-)

I lost what I mistakenly thought was a friend over this puzzle, she tried to bully me into saying the answer was 6. That may be the most popular but not necessarily the right answer, not the way I see it.

I see it as 0, used to think it was 12.

8 = 56

7 = 42

6 = 30

5 = 20

4 = 12

3 = 6

2 = 2

1 = 1

0 = 0 with the answer being 0.

Math makes my head hurt; but I love how you guys have an obvious love for it. I wish I understood it better.

Norma Jean, because the question is “3 = ?” it seems to me that you’re answering 6, not 0. Did I miss something?

jess2248, doing a quick run through the names, I’d guess we’re not all guys. There are some gals in the group. :-)

And yes, math is fun. Math is a language and a tool to understand how the world works, in so many ways. And even though I like math, it can still make my head hurt. ;-)

Totally agree with you, 3 = 3.

I have seen this so many times. A particularly popular post at the time on my own blog is “A Little Problem for the Holidays” where you will see I commented on the misuse of the = sign.

3 = 3 only in base 10.

3 does not necessarily equal 10 in other bases.

For example 3 = 11 in base 2.

So I was thinking the problem could be solved by induction??

Ronnie, that’s a great idea, but it doesn’t work out. There is no integer base n where 5

_{10}= 20_{n}.I am not mathematical, but I am logical. What I got when I looked at this was 15. To me the pattern went like this:

15

8 = 56; (56/8 = 7)

7 = 42; (42/7 = 6)

6 = 30; (30/6 = 5)

5 = 20; (20/5 = 4)

3 = 15; (15/3 = 3)