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”

Shouldn’t it be 3 = 6?

Ah, but that’s what “they” want you to think. But in my universe, three does not equal six — three equals three. ;-)

I think the answer should be 6 …

8 × 7 = 56

7 × 6 = 42

6 × 5 = 30

5 × 4 = 20

4 × 3 = 12

3 × 2 = 6

Alba, yeah, I see the pattern. What grates on me is how they misuse the equals sign. The first four lines make four false statements, but in a pattern that can be inferred. If one is willing to make one more false statement in the same pattern, then you are correct (yet wrong…) to say 3 = 6.

I rebelled against making a false statement, and gave the literally correct statement of 3 = 3.

The only problem with this argument is, that the 4 = 12 isn’t there, that is just something that is assumed. The only pattern you

cansee, is that the difference between the numbers after = is, that the difference to the numbers above is equal to 2x the numbers before the =. Which means that the correct answer is 3 = 14!Bent, I like it! (‘Course, I’m still distracted by the use of the equals sign to mean something other than equals…)

3 = 3.

I’m having a great time watching people try to work out all the possible answers. Or complain about the misuse of the equals sign.

Greg, I think we’re on the same page. Great minds, and all. ;-)

The answer is 9. The multiplier is the trick, nothing more. Each multiplier is one more than the one before it: 3 x 3, 5 x 4, 6 x 5, 7 x 6, etc.

Jon, that pattern works, too! It’s amazing how many different patterns this sequence of numbers supports.

The answer could also be 3 = 4 based on the following pattern:

8 = 56 (sum of all 3 digits is 19)

7 = 42 (sum … 13)

6 = 30 (sum … 9)

5 = 20 (sum … 7)

3 = 4 (sum … 7)

The difference between the sum of the 3 digits decreases by 2 each time: 6, 4, 2, 0. It’s a ‘zero sum’ pattern.

Wow, Ryan.

Anotherpattern that works!Brent, although I agree with your comment that 3 = 3 despite a number of prior false statements, my inclination (purely on aesthetic grounds) is to state that:

3 = (insert any number but 3)

Thus we end up with a list of false assertions, as opposed to some false followed by one true.

Simon, I admit there is a symmetry to continuing the false statements. I’m not convinced, “That’s the way we’ve always done it” is a good enough excuse to knowingly be wrong, though. There is no improvement without change… ;-)

Haha, thanks for this post. It just came through my LinkedIn today and it was driving me nuts.

I feel vindicated that someone felt the same as me 3 = 3!

Great minds, Dan. Great minds… ;-)

Great, I am not alone. My answer is 3.

For sure 3 equals 3; 3 = 3.

The statements before are all logically wrong – they just there to change the readers mind. They would be correct if the equal symbol would be replaced by congruence relations (symbol by THREE lines) and the congruent modulo would be a part of a mathematical sequence (sentential logic symbol required). But even the sequence would be incomplete (missing 4)- so there are misleading statements, and most of the persons do interpret a sequence and congruence relation – and they confirm their wrong result as correct on the basis of previous wrong given results. IF someone thinks that 3 = 9, I would like to give him/her 3 Euros and I want to have 9 Euros back – it would be fair, because it is equal!

Markus, you are my kind of people. Nice explanation. And no, I’m

notgoing to take you up on the 3 = 9 Euro trade. ;-)Great discussion that improves our brain function. I love it!

Markus, I had mentioned 9 as the answer on LinkedIn, as everyone were answering 6… Anyways can you and Brent pls explain as how is the Answer 3 ….and yes I do like brain storming.

Cheers Gautam.

Gautum, I think Markus does a pretty good job of explaining our position: the equals sign has meaning. To be true to its meaning, the answer mus be “3 equals 3.” All other answers ignore the mathematical meaning of the equals sign and treats it like a generic symbol dividing two columns of numbers.

I do not like the 3 = 14 pattern. It does not make mathematical sense. It sounds good until you attempt to prove it mathematicallyâ€¦

8 = 56

7 = 42 (56 – 42 = 14 = 2 Ã— 7)

6 = 30 (42 – 30 = 12 = 2 Ã— 6)

5 = 20 (30 – 20 = 10 = 2 Ã— 5)

3 = 14 (but 20 – 14 = 6, not 14 so the pattern becomes unstable, lending support to 3 = 6).

3 = 4 in a zero sum is interesting, though, as is 3 = 9 (though it assumes the 4 is not missing which, I suppose, is fair), but 3 = 6 is by far my favoriteâ€¦just because of the pure mathematical pattern. In a puzzle situation, it is safe to assume a portion of the formulae is missing. That is what makes it a puzzle.

Those who think 3=3 just have no sense of the beauty and romance in numbers, lol. You are far too pragmatic.

I’m too pragmatic? I don’t sense the beauty and romance in numbers?

Au contraire, mon frere. I <3 3. ;-)

I saw this today and immediately I was tempted to say 3 = 6. But looking at it closely I realised 4 = 12 is not among the sequence and hence we cannot prove 3 = 6 unless we make the assumption that 4 = 12 which would be wrong.

My answer is 3 = 12.

Luetkemeyer made some good analysis but I think 3 = 12 would be better suited with that analysis.

8 = 56

7 = 42 (56 – 42 = 14 = 2 Ã— 7)

6 = 30 (42 – 30 = 12 = 2 Ã— 6)

5 = 20 (30 – 20 = 10 = 2 Ã— 5)

3 = 12 (20 – 12 = 8 = 2 Ã— 4)

Looking at it you see that the difference between the numbers on the right are reducing by 2.

Dal, it looks like your analysis ignores the numbers on the left side of the equals sign. Hmm… I’m not sure that’s appropriate. Does it bother you?