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## 1 = 2

Math brain teasers require computations to solve.

 Puzzle ID: #21464 Fun: (2.27) Difficulty: (2.36) Category: Math Submitted By: munchtipq Corrected By: Nytwynd

Bob and Sue were having a discussion one day about 1 and 2. Sue reckoned she had seen a way that you could make 1 = 2 but Bob who wasn't called 'logical Bob' for nothing was obviously adamant that this just wasn't possible. Sue said "Ok smarty pants here's the equation to prove you wrong"...

Assumptions: There are two numbers, a and b, and they are equal.

Proof:

a = b

Multiply the equation by b

ab = b^2

Subtract a^2 from the equation

ab - a^2 = b^2 - a^2

Factor difference of squares

ab - a^2 = (b - a)(b + a)

Factor a on the left-hand side

a(b - a) = (b - a)(b + a)

Divide by common factor

a = (b + a)

Substitute a for b

a = (a + a)

Simplify

a = 2a

Divide by common factor

1 = 2

Question:

Bob didn't take long and found the line where there is a crucial mistake in the working though was understanding of Sue's issue as it is well hidden... can you see it?

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 katiebeth123 Mar 10, 2005 BLAH BLHA BLAH BORING cdizzlefoshizzl Mar 10, 2005 i liked it... maybe im just a nerd sosweet487 Mar 11, 2005 I did this in my math class a couple years ago. It duped me then and I didn't get it now until I saw the hint. The hint gave it away... but still a good one! castanz Mar 11, 2005 BTW People here say things are nerdy or geeky. Well, Duh, look at the name of the site. Yea, I is a nerd to and proud of it. castanz Mar 11, 2005 Yes, I know. The rest of the nerds are saying "to" is supposed to be "too" in my last comment. And the really nerdy ones are saying it should be "I am a nerd". I like math and chess btw. (user deleted) Mar 11, 2005 You can prove 0.999... = 1. Say y = .999..., then 10y = 9.999..., So, 10y - y = (9.999...) - (0.999...) = 9y. Then, 9y = 9, that implies y = 1. Therefore, 0.999... = 1. poopie Mar 12, 2005 this was soooooooooooooooo boring i hated it i rated it as BORING and o didnt vote on diffuculty runscapekiller Mar 12, 2005 ok i dont get it.im in the third grade here. melilyn Mar 12, 2005 I've always wanted to prove this one wrong!! koolkat57 Mar 16, 2005 Eh, didn't get it. ` Sane Mar 20, 2005 Thankyou for duplicate searching...I can't believe this slipped by even when one of the editors was the one who submitted the original one. http://www.braingle.com/2013.html munchtipq Mar 21, 2005 Whoops, I did try to search, but I (stupidly) was searching on 1=2, not 2=1, so I missed the title of the other one. My bad. Sane Mar 21, 2005 lol, ya I don't blame ya. It just surprises me how Mogmatt16, an editor (and creator of the original), let it slip. Just be sure when seaching for a duplicate, don't just enter stuff like 1=2. Because if it even was "1 = 2" the search wouldn't pick it up because of the spaces. I think I searched for "what is wrong" or something along those lines in the answer field. sotnakitt Mar 23, 2005 This is a fairly old problem i believe, lol i mean i knew the answer before i read the problem. My teacher had to ruin a possibly great problem by introducing and immediately solving this one, when i was first learning algebra. robinmckenzie Mar 25, 2005 Nice problem. Didn't find it particularly hard, but still good to work the old grey matter. More like this, please! trumpetduck13 Apr 03, 2005 I'm CONFUZZLED Ms50cent Apr 17, 2005 This wuz sure stupid one.nerdy. brianz Apr 23, 2005 By the way, there's another one that's similar to this. a=b a^2=ab a^2+a^2=ab+a^2 a^2+a^2-2ab=ab+a^2-2ab 2a^2-2ab=a^2-ab 2(a^2-ab)=a^2-ab 2=1 Of course, it doesn't work because when you divide by a^2-ab at the end, you're dividing by 0.