[Matt Connell's solution to MATH 110 (2003-2004 edition) Assignment #3.]

### De Omnibus Rebus, cont'd...

Matt Connell

... under the personal superintendence of the Commander-in-Chief.

"Have you got it yet?" asked the old man as they continued to walk down the road.

"I'm still thinking on it," replied Norman. "lt reminds me of an episode of Xena I once watched. You see, her friend and companion in the Trojan War - Achilles - came upon the idea to race a tortoise."

"Was he lame?" inquired the elder traveller.

"Why, no, it was an exercise in logic," answered Norman. "The tortoise was given a head start, of course. Then, Xena would try to see if Achilles could pass him. Obviously, Achilles is faster than the tortoise, but if it is ahead of him at one point it seems impossible to pass him."

"Sounds like an exercise in illogic to me."

"When Achilles gets to the point where the tortoise was when Achilles started, it will be at another point. When he gets to that point, the tortoise will be ahead again."

"Good start, but how is it finished?" the old man replied.

"That I cannot answer," said Norman, still thinking furiously. Perhaps too much Kgovjnian had tangled his mind. "Square it?" he blurted out blindly.

"Well, young one," the oId knight began pompously, "two and a half minutes from ww, that is, fifteen minutes from when we started, that grurmnibus will be back at the station. In simpler words, in three minutes minus half, it will have travelled as much as we will have had in thrice of five minutes."

Norman did some quick calculations in his head. "So it's travelling five times as fast as us!"

"Precisely," he answered. "Either that omnistipth is very slow or our bipedal velocitable capabilities have increased exponentialy since our escapades in the mountains."

"That's quite the hyperbole," said the clever young one.

"Yes, I suppose it would look like one ofthose," responded the confused old man, noting that he must give his friend some pronunciation lessons later. "Alas, we digress back to the task at hand. The vehicle is some distance behind us now, let's call it 'p'; we walk a certain distance, say 'e', to the point where we are overtaken. Therefore, the entire distance it will have travelled is p + e. Since it travels five times faster than us, its total distance can be defined in terms of ours, or: 5e. Thusly, p + e = 5e."

It looked like the young one was starting to understand.

"So," Norman ignited exuberantly, "if p + e = 5e, then p = 4e, and p/4 = e!"

"Eureka," the elder quoffed sarcastically. "And since it takes it only fifteen minutes to conquer p, it will only take a quarter of that - three minutes and forty-five seconds - to travel ours. Conversely, it will take us that time times five - eighteen minutes and forty-five seconds to meet with another omnigrurmbustipth."

"So it will be six minutes and fifteen seconds since we met the last one?"

"Well, yes," said the old man, "but we've been talking about this for seven minutes and it passed us again."

"Oh, bamboo," said Norman, causing the old man to shiver. "Well, you may have been able to figure that one out, but I bet I know how to solve the pig problem."

"Do tell," he replied expectantly.

"In the first sty one places five pigs, nine in the second, and ten in the third."

"... and what of the fourth?" the elder asked.

"I was thinking of an old riddle while you were spouting that omnibus nonsense: What is greater than God and more evil than the devil?"

"What is it that rich men need but poor men have?"

"Nothing."

"What is closer to ten than ten?"

"Nothing."

"And that's what goes in the last sty," boasted Norman, smirking.

The old man was angered. "That's the most ridiculous thing I've ever heard! No wonder I didn't get it, I studied math! Her Radiance would never accept that answer!"

"You're right," he grovelled. "What was I thinking!"

It's not 7; it's not 9; it's knot 8 from Lewis Caroll's A Tangled Tale!

Copyright 2003 by Matt Connell. Used by permission.

Assignment #3.
Official Solution to Assignment #3.