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.
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.
“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.