### Problem 238: Math quiz

Mr. Poushover, a substitute teacher known to let school kids run reckless under his watch, decided he was going to take control – no more “kick me” signs, paper airplanes, or spit wads.

He’d been assigned Ms. Hookie’s eighth grade algebra class, and, aside from a minor whoopee cushion incident, things started out well.

“Now class, what you do to one side of the equation, you must always do to the other side of the equation. That’s one of many rules in algebra.” He copied an example from Ms. Hookie’s nearly illegible lesson plans onto the blackboard, relying on his own sketchy knowledge to fill in where the chicken scratch was unreadable. But when he plugged in some numbers, he ran into problems.

1. Statement | X=Y |

2. Multiply both sides by X | X^{2}=YX |

3. Subtract Y^{2} from each side | X^{2}-Y^{2}=YX-Y^{2} |

4. Factor | (X+Y)(X-Y)=Y(X-Y) |

5. Simplify, divide out (X-Y) | (X+Y) = Y |

6. Substitute X=Y=1 | 1+1=1 |

Mr. Poushover scratched his head and paced in front of the blackboard, his blood pressure rising.

“This cannot be. I did everything to both sides of the equation. One plus one cannot equal one, but here it does!” The problem was just enough to push him over the edge. Mr. Poushover ran out of the school pulling his hair and howling.

Truth be told, 1+1 does not equal 1. Where did Mr. Poushover go wrong?

### Solution to the July problem, 237: Fish bait

### Winners Circle

**Fun problem 236:** Tropical Teaser June, 2000**Total entries:** 197**Number correct:** 114 (58%)**Winner:** Robert Eddy, South Bend, Ind. Robert’s prize: Maple 6, a fully integrated analytical computation system.

Maple 6 combines the intelligence of Waterloo Maple’s symbolic computation algorithms with the reliability, accuracy, and power of the NAG numerical solver. Its math engine lets you define, solve, modify, optimize, and explore the mathematics or data in technical projects. This includes modeling and simulation, theoretical analysis, engineering design, and scientific application development.

### Puzzle us

Get your creative juices flowing and send us your *original* problems and solutions. If we publish yours, you’ll win a prize. Rudi Krenz, Albuquerque, N.M., wins a WD-40 prize pack for contributing this month’s problem.