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April 13, 2006 by Vurdlak | Share  

Try to figure this one out! How is it possible that two is equal to one, when we all know that that isn’t true. Try to spot the mistake one of the twins made!

Math Optical Illusion

Comments

137 Responses
  1. Anonymous says:

    WOW….
    barring the possibility that there are little kids posting…

    if you are an adult and have gone through the education system and don’t understand the simple math like the connection between a=b and a^2=a*b you shouldn’t be allowed to have kids.

    Sorry about being harsh, because its fine to be stumped by this, its not ok to not know basic elementary school math

  2. Anonymous says:

    so really the solution is 2/0 = 1/0 ?

    And that is true…

    So the real “mistake” is saying that 2/0 = 2 and that 1/0 = 1….

    And if anyone reads this far down, get a f’in life

  3. Anonymous says:

    this is not an optical illusion,they just try to confuse you and check if you at lest remmember 6grade maths.everything that’s below line 3 is not right:
    (a+b)(a-b) will never equale the statement b(a-b)
    always (a+b)(a-b)=a2+b2

  4. Sandy says:

    There is a missing condition fot divison (as you all mentioned)
    -> a-b /= 0 =>
    -> a /= b
    which it isn't, there for you can't

  5. Andrew says:

    the mistake is in the transition from the fourth to the fifth line whereby the (a-b) on both sides is ‘cancelled’. Remembering that anything divided by 0 is undefined, divividing both sides by a-b which is really zero simply means that undefined = undefined. WOOP DE DOO. =.= , back to the drawing board.

  6. Anonymous says:

    wow some of u r in 8th grade and u cant even figure this out… and some of you have no humour, some of you think it’s a set of unrelated equations… i found the error when i was in 6th grade! and the error is that you cant divide by zero.

  7. Anonymous says:

    (a+b)=b
    not true^^^
    got me for a minute tho, hadda think it throughht
    and comment #1… (mark)
    are you saying 8th grade math is easy
    cause im in 8th grade, and im taking an advanced course, and its still hard

  8. BOBOBOBO says:

    it should come out to be 0=0
    because (a+b)(a-b)=b(a-b) equals zero
    and 2a=a which is the same as 0+0=0
    should in fact be
    0=0

  9. smartiepants says:

    so the only way the whole equation..or however they are trying to figure this out works is to ultimately say a and b equal zero. so every equation they wrote satisfys that. so 2a=a –> 2(0)=0! and (a+b)=b –> (0+0)=0!

    so the only mistake they made is at the end when they assumed that a and b were 1.

    so in lines 4 and 5 to say that they were dividing by zero so that doesn't work is stupid because they were writting random equations not following steps to get to the next problem duh :P

  10. Anonymous says:

    You can divide by zero in calculus though with L’Hospitals rule, ha ha

  11. Callum Teh Robertson says:

    They missed out the parameters – "a=b=1" (or if you prefer "a=1", "b=12)

    Need to state what a & b are ;) otherwise it is technically correct and then the last line is also wrong… you cant just assume 'a' is equal to one – needs to be stated… yes, im a uni student with nothing better to do ;)

  12. Eluem says:

    “this is not an optical illusion,they just try to confuse you and check if you at lest remmember 6grade maths.everything that’s below line 3 is not right:
    (a+b)(a-b) will never equale the statement b(a-b)
    always (a+b)(a-b)=a2+b2″

    First of all this must be corrected:
    “always (a+b)(a-b)=a2+b2″
    should read:
    “always (a+b)(a-b)=a^2-b^2″

    In this situation, this isn’t the error.
    b(a-b) is equal to ab-b^2 and since a=b this could also read a^2-b^2.

    The real error is as it has been said before, when they divide by zero by trying to cancel by dividing the (a-b) over since a=b, a-b = 0. You cannot divide by zero.

  13. qqqq says:

    if a=b , then a and b are equal, meaning that THEY ARE THE SAME NUMBER!
    therefore, the answer cant be 2=1

  14. Samantha says:

    Don’t blame me for not getting this i’m still in primary school…(age 11) tho some of my classmates have that a – b = ? some sort of things…

  15. A Math Major says:

    Sigh… the answer, which very few people have correct, is that you cannot divide by 0. ALL of the math here is sound, EXCEPT that one of the steps is not reversible (divide by 0). That is in going from line 4 to 5. If you notice, lines 1-4 are all true as long as a = b, which was the premise. Starting at line 5, after the division by 0, everything is only correct if a = b = 0, which was not a stated condition.

  16. ben says:

    (a+b)(a-b)=b(a-b) ….. isnt tht bit rong?

  17. Ms.Observant says:

    them dudes try devide by zero. Tards. I IS IN 8TH GRADE AND ME FIND ANTSA! NO ZERO DIVISION PPL!

  18. anonymous says:

    It is because they divided by a-b in the 4th step and because a=b that means they divided by zero, which gets UNDEFINED not any real answer. Duh!

  19. Balli says:

    It is not given that a=b=1. That is the only thing that is wrong. And then there is the problem that the only solution is that a=b=0 so you are dividing with 0 which is a problem as the answer infinite.

  20. dido1983 says:

    Besides, 2a=a equals to 2a-a=0 a=0, not to 2=1.

    If two dollars have the same value as one dollar, then those dollars are FAKE!

  21. serenity says:

    ok i’m in 7th grade and i found this easy.
    the big mistake is that(a+b)(a-b) will never equal the statement b(a-b)
    always (a+b)(a-b)=a2+b2

    it’s a simple formula really :)

  22. steve says:

    what are you talking about?
    (a+b)(a-b)= a^2+ab-ab-b^2=a^2-b^2 so

    (a+b)(a-b)=b(a-b) is true

    because a^2-b^2=ab-b^2.

    The part that’s not true is (a+b)=b because if
    a=b, then the above cannot be true.

  23. MiSt says:

    a=b |*a
    a^2=a*b |-b^2 //correct 0=0
    a^2-b^2=a*b-b^2 |faktorize //correct 0=0
    (a+b)(a-b)=b(a-b)|/(a-b) //WRONG: ADDITION 2=1

  24. mad one says:

    qqqqqq is right!!!!!!!!! If a=b how can it be anything else. the mistake is in the second line twin on right should be copying left the whole way down visa versa.

    a=b
    1=1
    2=2
    3=3
    a=b

    get it your all fools. Trick question. all you accadi*#heads. pull your head out of that thing called a bum. Twins??? meant to be the same????? 1=1 2=2 3=3 and so on. copy is the key here ahhhhhh mirror, 1=1 2=2 3=3 a=b d=f s=r trick question. I is in mine 25 year from life and i did fail maths. hang on i is really from da eight grade!!!!

  25. mad one says:

    Sorry, love your site. some of these people claiming they are in the 8th grade are full of it!!!!!!!!! very annoying.

  26. Juhani says:

    Everything is correct to that point where (a+b)=b. Then you see that => a = b-b = 0.

  27. Zerro says:

    I think the mistake is..it’s supposed to be 2=a lol where did he get 1?

  28. Martin says:

    Okay people, lets get something straight. You can divide both sides by (a-b) as they both have it on their sides. THERE IS NO DIVISION BY 0!!! If you divide 2y=2 by 2, then y=1. That is basic algebra. Therefore (a+b)(a-b)/(a-b)=a(a-b)/(a-b) becomes 1(a+b)=1a which is (a+b)=a

    This is what is called formula manipulation, and (a-b) without definition cannot equal 0 in the first place.

    Since a and b were not assigned values, the mistake is assuming they both equal 1.

  29. Tim says:

    Really guys, everyone saying that a and b equal 1…
    2a=a, divide by “a” on both sides and you get 2=1… “a” could be 1,000,000,000 or 27, and you still get 2=1
    the error is when you try to divide (a-b) from both sides, because if “a” and “b” are the same (a-b)=0

  30. hanssi says:

    yea, this is what happens when you divide by zero. idiots

  31. Kei says:

    Considering:

    1 = 1
    1^2 = 1*1
    1^2-1^2 = 1*1-1^2
    (1+1)(1-1) = 1(1-1) -> This is an Error.
    (1+1) = 1 -> Here starts the Wrong Equation.
    (1+1) = 1
    2(1) = 1
    2 = 1

    The error is in fact, 1 Cannot be divided by 0.
    (1+1) != 1 on (a+b) != a and (a+b) != b. So are 2a != b.

  32. Kei says:

    THere’s no error LOL XD I made a mistake.
    Actually the error was on (1+1) != 1 on (a+b) != a and (a+b) != b. So are 2a != b, that’s wrong.

  33. ZEKO says:

    Lol.very simple.its like this:

    a=b (no problem)
    a^2=ab (no problem)
    a^2-b^2=ab-b^2 (no problem)
    but! a^2-b^2=0
    and ab-b^2=0

  34. nathanale says:

    sneezes look like worms

  35. felixnovus says:

    seeing from comments, people looks happy :) more easy illusions please

  36. Rich says:

    http://en.wikipedia.org/wiki/Mathematical_fallacy#All_numbers_equal_all_other_numbers

    It all comes down to the division by 0 in the form of (a-b). Since (a-b)=(a-a)=(b-b) => (a-b)=0=0. No matter what, it’s dividing by 0, leading to an undefined number. Although, I do love seeing everybody else’s attempts to sound smart.

  37. Rafael says:

    Im 20 now and could have answer this in middle school, its cute seeing grown folk think there smart with wrong answers

    if im wrong, email me. RafCintron@Yahoo.com

    1.a=b (ok, easy)
    2.a^2=ab (multiply a to both sides, still equal)
    3.a^2-b^2=ab-b^2 (subract b^2 from both side, fine)
    heres where the problem starts
    4.(a+b)(a-b)=b(a-b) IS A WHOLE DIFFERENT EQUATION

    a=b so (a-b)=0 so anything time 0 equals zero
    but subtract (a-b) from both sides… (a+b) does not equal b.
    1+1 isnt 1, 2+2 isnt 2, and 5+5 will never be 5

    hopefully my explaination was a lil easier than Rich’s up there :P lol

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