Friday, February 8, 2013

Solve if u r a genius !

I was strolling through facebook and happened upon a chance encounter with the equation below. At most I saw other people giving two answers. This is what my mind ended up with before I cut it short. I actually tried to post it in a reply but it either got deleted or cut off due to excess length..etc. I thought it explained my mind well. Its entirely out of order and lacking structure, but all the elements are there. With the possible exception of a more complete and definitive link between the relationship between answers and the relationship between patterns. Im already aware there are a couple possible theoretical answers I over looked. Oh what my mind could accomplish if I could increase my memory, recreate my structure and train my mental blackboard to hold more information again like it once did.

I am seriously debating writing an entire book revolving around this very math problem and the typical responses people have. I just looked through approximately 3,000 comments/answers in response to this and at most other individuals had 2 responses. 99% of which did not backup their answers with any details or facts. I only saw two comments that claimed it couldn't be solved with the amount of information given and/or that it needs a 3rd point.


The 'question': Solve if u r a genius !
11 x 11 = 4
22 x 22 = 16
33 x 33 = ???

The correct answer (if you asked any lawyer) would be, "It depends". In a typical math class, I would have to say "More information is needed" or as  I would care to say "There is a flaw in the question".

Under normal rules it should read..

11 x 11 = 121
22 x 22 = 484
33 x 33 = 1089

But who says we are using normal math? Obviously it just doesn't add up as is. So let us look at the simple facts as we know them. x = mulitplication and = equals a balance with the other [half, for lack of a better word]. They say there are two types of people in this world, Those that can extrapolate.

For the sake of argument, we will assume there is an answer (because well, there has to be one, the only question is really context or type of answer). This is presented as a related group and as math, so naturally it would have some type of consistent, logical structure. If we find enough truths, enough factual information, we can deduce the rest.

So lets simply look at the information given and figure out the possible patterns shall we?

It can't realistically be truncation or rounding.

(More information needed, where/how? between the numbers), +?
1+1 x 1+1 = 4
2+2 x 2+2 = 16
3+3 x 3+3 = 36?

Missing information/needed information: Spaces.
When two numbers are beside each other with no relevant number, one usually multiples them.
1x1x1x1 = 4? Doesn't add up.. no point in continuing the rest.

Looking only at the answer. Why? Its a related pattern. If the answers are based on the question (which all math, well all questions and answers really) then it is based on a system. Each answer is based on the same system as the last so the answers themselves should hold this same pattern as the question. So we should be able to figure out all the possible answers without using the question initially. it would be [1?], 4, 16, 64? (multiplications of 4) with every increase of the number..

Based on the previous answer in the pattern.
(1)x4, (4)x4, (16)x4 = 64

So we have +4, x4, 4^ = 65536.

So now that we have all the theoretical answers, we have to plug them in and test the math. Going backwards after you have the answer and formula to try and figure out the math, but frankly that's too much work to derive a convoluted formula of no meaning. It turns into a disturbing algebraic equation.

Missing information, lack of signs. A progressive formula? But here we have a divergence, is the rule that the two aspects must maintain separation [between the two halves of x] or not? So we split the two possibilities.

Adding the same consistent sign

(1+1) x (1+1) = 4
(2+2) x (2+2) = 16
(3+3) x (3+3) = 36

Adding mixed signs to make it true (solving one unfinished equation then the next, look at them more separately)
(1+1) x (1+1) = 4
(2x2) x (2x2) = 16
(3x3) x (3x3) = 81

(1+1) x (1+1) = 4
(2+2) x (2+2) = 16
(3x3) x (3x3) = 81

After addition and multiplication is exponents..

Missing information, lack of signs.
(1+1) x (1+1) = 4
(2x2) x (2x2) = 16
(3^3) x (3^3) = 729

But what if the answer to one question changes the next question somehow? What if we are coming into a problem thats already been partially solved? Who said we are starting this process at the beginning? What if part of the equation has already been balanced or modified somehow?

11 x 11 = 121 1+2+1 = 4
22 x 22 = 484, 4+8+4 = 16
33 x 33 = 1089 1+0+8+9 = 18

But then comes another problem. If they didn't add the proper symbols and/or explanation, mathematically speaking it must be flawed by design. If I am to consider that an imperfect source created this and errored, than why would I only stop at considering adding information? I mean just looking at the grammar anyone with half an IQ point should see and understand, before the fully questioning the question itself, it questioning the source. I mean they can't even articulate using the same rules as everyone else, clearly their math is along the same lines. The first thing I find myself questioning is if I should consider myself stupider just for reading it. Perhaps they messed up in other ways? Perhaps we are meant to remove (or change) information? Maybe the other answers are wrong, Maybe the answers are correct and the question is the problem. I'll spare you all the possible combinations of ways to add or multiply out 4 and 16 to create a realistic base for the third segment. In my experience though, whether climbing a rope, predicting a number or making a realistic grounding for a tripod, You usually need sets of three at minimum.

But if we are going to randomly add or remove or change information, we are changing the nature of the question are we not? We are no longer solving that question. Even if we are solving that question still, the number of possible changes are, almost literally, endless.

So where does the genius lie? In the fact that they are asking you an open ended question with no real definitive answer. And by a definitive answer I mean a simple self evident truth. The genius is the one that looks beyond the numbers and realize they are either
A) A bored individual looking for attention or amusement
B) A genius of their own right, smart enough to educate the masses through critical thought (which sadly, is statistically unlikely)
C) This tool is an extension of the very philosophy of facebook itself designed to pull individuals of all walks of life into one place in an effort to make someone else rich. A variation of B but much more based in a different set of morals centered around ego rather community.
D) Part of a study to gather various information or test people for some weird CIA recruitment or other known reasons.
E) Some kid who is trying to win a candy bar from his teacher because he is solving this question by asking someone smarter (and thus theoretically proving that he is smarter by using the tools at hand more effectively, solving a math question without ever having to learn the math)
F) There is always the chance I haven't solved it and must consider that I am wrong
G) There is no answer.
H) The answer is all the possible answers because there is no criteria to limit it: More information, no answer, 18, 36, 64, 81, 729, 65536.
I) This is all a bet between facebook programmers or some MIT nerds or whoever to see how many collective man hours we would waste
J)... the answers go on and get more bizarre than Alice in wonder land _input own funny references here_.

As for me, if I had to choose.. I'd go with H.

(In reference to G) I also saw 12 and 256 in the comments.. my brain already hurts too much to try and figure out how they even arrived at such an answer. You can plug and play if you really want to know that badly.



  1. 1+2 is 3, 11+22 is 33, 4+16 is 20?

  2. As an alternative, you can use only the first point: 11x11 = 4
    Then you can calculate the rest of them using that first point:
    22x22 = 2x11x11x2 = (11x11)x4 = (4)x4 = 16
    33x33 = (11x11)x9 = 36
    44x44 = (11x11)x16 = 64

    Also, when you say:
    11 x 11 = 121 1+2+1 = 4
    22 x 22 = 484, 4+8+4 = 16
    33 x 33 = 1089 1+0+8+9 = 18

    The last one is incorrect... I'll try to show you why.
    We have:
    11x11 = 121, 1 + 2 + 1 = 4
    22x22 = 484, 4 + 8 + 4 = 16
    33x33 = 1089, ??? = ???

    For the last one, we would expect: 9 + 18 + 9
    But 9189 is not what we are looking for...
    The second number, 18, is bigger than 9, and we are adding one-digit numbers (0 to 9). So, we are going to keep 3 columns, like this:
    9 + 18 + 9 --> 9 18 9

    And, as 18 has 2 digits, we will subtract 10, and add one unit to the number on the left:
    9+1 18-10 9 = 10 8 9

    Now, if we put the whole thing together, we get 1089, which is consistent with 33x33 = 1089. So the answer is: 33x33 = 9+18+9 = 36

    Now, 44x44 = 1936
    Again, we expect: 16 + 32 + 16 --> 16 32 16
    We need to subtract from every column, starting from the right:

    16 32+1 16-10
    16 33 6

    16+3 33-30 6
    19 3 6

    We get 1936, consistent with 44x44 = 1936. Then 44x44 = 16+32+16 = 64

    55x55 = 3025, 25 + 50 + 25 = 100
    25 50 25
    25 52 5
    30 2 5

    We can go on with 66x66, 77x77, ....

    1. Easier to explain is using always the three columns as you said. After that u only have to make a 3rd of school table with units, tens, hundreds...and so on. So, going on the example with 55x55, we expect 25-50-25 which is the result of: 25 units+50 tens+25 cents. CONSISTENT! :-)

  3. This comment has been removed by the author.

  4. 4^1=4

    and also


  5. I agree with H,
    There is even another solution: 44
    (By keeping adding all the numbers and ignoring any signs).
    Another solution that I was thinking about is: "if you are a genius !".
    Because what is actually asked to solve?
    In this answer I solve the sentence by replacing u and r with you and are.


  6. & 20; 11*11=121= (1+1)*2=4
    22*22=484= (4+4)*2=16
    or 11+22=33; 4+16=20

  7. All this time and it's still doing the rounds. Try using a common denominator, 30.25 seems to work.

  8. the answer should be a logical 3-digit number since the 3 question marks "???" is a clue vital to eliminating the other possibilities... you have to think out of the box in solving this while putting yourself at the age of a normal 5th grader..


    1. thank you, i thought i was the only one

    2. Three question marks is the standard that you see when the answer is not known. Kind of like three periods to notate a should stray away from demeaning statements like "putting yourself at the age of a normal 5th grader" especially when you are wrong.

  9. lol, I look at it and what i see is the answer is meant to be the question? It is subjective.

  10. Another answer: 18

    11x11 = 121. Add the digits 1, 2, and 1 together and you get 4
    22 x 22 = 484. Add the digits 4, 8, and 4 together and you get 16
    33 * 33 = 1089. Add the digits 1, 0, 8, and 9 together and you get 18.

  11. superrr.., I like it...,

  12. You touched on this a bit, but I believe you are missing the most obvious answer. Based on the equation given, 33 x 33 =, the correct answer is 1,089. Because the answers given to the previous two equations are incorrect doesn't necessarily imply we need to repeat the mistakes of the past.

  13. Man, the answer is 1089. The question NEVER says follow the pattern. Obviously the first two equations are wrong, and they are meant to deceive you.

  14. good thinking. Or the answer is 28. Diff between 11x11 and 22x22 is 12, so 33x33 must be 16 + 12.

    No need to thank me, autographs after five

  15. This kind of qeustions are from the "fun" math contests, so the answer must have a "funnier" solution. Here is my logic behind my 36 answer:
    11^2=4 => 11=2
    22^2=16 =>22=>4
    33^2=x => 33= square root of x
    considerig that the equations are related in any way, the logic will tell us that the answer is 6, which makes the equations equals 36. Why 6 because we can notice that the aswers for the first 2 equations are 4 for the first one,which is 2^2( 2 being the first even number) and for the second one 16 which is 4^2( 4 being the second even number) therefore the answer must be 6 considering the logic of the numeric series( 6 being the third even number). Basically the left part of the equations(11^2, 22^2, 33^2) just tell us the rule of the calculus and the rule of the series(the first the second and the third) and you can go on for ever and ever like this). in the same maner 44x44 equals 64 and 55x55 equals 144