Does 3 Equal 11?

by Ron Haynes

It can, if you know how to do a few tricks with algebra. Why point this out? If you aren’t paying attention, you can be tricked into believing all sorts of crazy things, from financial scams like the one that Bernie Madoff pulled to the latest conspiracy theory. In the end however, logic and reason usually prevail. In the meantime, brush up on your high school math skills for a moment and examine the following:

Given that a = b

  1. 3a = 3b and 11a = 11b
  2. Multiply by a on both sides, 3a^2 = 3ab
  3. Multiply by b on both sides, 11ab = 11b^2
  4. Subtract the above equation from the one in step 2, 3a^2 – 11ab = 3ab – 11b^2
  5. Subtract 3ab and add 11ab to both sides, 3a^2 – 3ab = 11ab – 11b^2
  6. Add ab and subtract b^2 from both sides, 3a2 – 3ab + ab – b^2 = 12ab – 12b^2
  7. Factor out common factors, 3a(a-b) + b(a-b) = 12b(a-b)
  8. Divide both sides by a-b, 3a + b = 12b
  9. Subtract b from both sides, 3a = 11b
  10. Substitute a for b, remembering that they are equal, 3b = 11b
  11. Remove common terms and 3 = 11

Did you see that? Three DOES equal eleven? … Ha ha! It really didn’t matter which numbers I used so long as they were different. I could just as easily made $12 equal $300 million. Where does this simple equation go wrong? When we “factor out the common items” in step 7, we’re actually dividing by zero and any one who passed 5th grade math can tell you that dividing by zero is a big mathematical NO-NO.

But it’s easy to get caught up in the moment and overlook that step because the rules violation is hidden. What’s always odd is that sometimes the most important, most common sense rule can get obscured by technical mumbo-jumbo, quickly glossed over, and ignored by someone who should know better.

Such is the case with most scams. They lure us in with an outrageous claim (“make $50,000/yr stuffing envelopes at home!”) just like the 3 = 11 title. Then they convince us that we really can “buy a home with no money down,” or “join this multi-level marketing ‘business’ and become rich in 12 months,” or even “I am a Nigerian prince who needs to hide $700 million in your bank account for a few days.”

But, if you’ll take your time, examine the claims slowly and with a discriminating eye for detail, you will usually find that one fatal flaw. Or you could use the old pessimist’s rule: if it sounds too good to be true, it probably is.

About the author

Ron Haynes has written 1000 articles on The Wisdom Journal.

The founder and editor of The Wisdom Journal in 2007, Ron has worked in banking, distribution, retail, and upper management for companies ranging in size from small startups to multi-billion dollar corporations. He graduated Suma Cum Laude from a top MBA program and currently is a Human Resources and Management consultant, helping companies know how employees will behave in varying situations and what motivates them to action, assisting firms in identifying top talent, and coaching managers and employees on how to better communicate and make the workplace MUCH more enjoyable. If you'd like help in these areas, contact Ron using the contact form at the top of this page or at 870-761-7881.

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I think it’s a crying shame that so many people have few, or no, critical thinking skills. In my opinion, this is truly crippling our ability as a society. One could blame the schools for not teaching it, but honestly, I think most schools aren’t allowed to do much more than “teach to the test.” It would also be easy to blame our current culture, which has severely blurred the line between truth and fiction. But the problem isn’t always with younger, naive people; the elderly often fall prey to scams that it seems “anyone” could see right through. Why is this?

Pa Ed

The internet’s middle name is “scam.” But the beauty of it is that if you can filter out the 98% that is nonsense, the other 2% will be well worth the effort of finding.

The Biz of Life

In government accounting 11 does equal 3 quite often. But we were talking about scams, weren’t we?

Joe Morgan

Not for nothing, but 3 is represented as 11 in binary… ;-)

But seriously, good post. I think we need more examples of how scams use math to fool people, but I fear that most people just glaze over when confronted with facts and figures anyway… which is why scammers (and politicians) use fuzzy math to begin with.


I was wondering if anyone would catch the binary thing — good job!

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