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# Fatal Flaw Revealed

Issue 10 and Volume 108.

The August edition of the efun page featured a brain-teaser instead of the usual joke. Hundreds of Power Engineering readers exercised their brain matter on this one and sent us e-mails identifying the fatal flaw. The proof is reprinted again below, along with several of the more amusing replies we received.

1. A=B
2. A2=AB
3. A2 – B2 = AB – B2
4. (A-B)(A+B) = (A-B)B
5. A+B = B

“The problem lies in step 4. To get rid of the (A-B) multiplier in each side of the equation, you have to divide each side by (A-B) and set the resultant quotient equal to one. However, since (A-B) is zero, it is illegal to make that division. Another way of looking at this is that if George Bush’s policies were weight-averaged at “zero” and John Kerry’s policies were weight-averaged at “zero,” it would not necessarily hold that George Bush = John Kerry!”
Submitted by Power Engineering reader Roger Anderson.

“To get from steps 1 to 2, 2 to 3, and 3 to 4, everything is OK and no laws of math are violated. However, to get from step 4 to 5 one would have to divide both sides of the equation by the quantity (A-B). However, A-B is equal to zero, and by the laws of math, dividing by zero is not allowed. Why is dividing by zero not allowed? I was always told that the reason was ‘It would cause situations such as this.’ Probably not an in-depth explanation, but that’s the best I’ve heard.”
– Submitted by Power Engineering reader Dave Workman. Click here to enlarge image

“The August 2004 brain teaser violates the first of Wofford’s laws (Dr. J.B. Wofford, Professor at Carnegie Tech, 1955-1963): ‘You can’t divide by zero.’ Some college professors can, but you can’t. His second law was ‘Give college students a test with three unknowns and two equations and they will madly work equations until they make a mistake, giving them three independent equations and allowing them to solve the problem incorrectly.’ His third law was ‘Check the units of a new equation. If the units do not agree, the equation is wrong.’ This was used by early mathematicians to tell if density or pressure affected chemical reactions. I used this in my doctor’s exam when, given an equation for the propagation area of low-frequency radio stations with three antennas, I finally discovered that the units did not match. I got an A, the next highest grade, with people much smarter than me, was a C.”
– Submitted by Power Engineering reader Thomas Agnew.