Puzzle time: Mathematician shares some of his favorites
BY WAYNE GREENE World Senior Writer
Tuesday, December 25, 2012
12/25/12 at 7:44 AM
Try three additional puzzles —
including one for which Constanda
says there is no known answer yet.
Christian Constanda can remember the exact incident that sparked his passion for mathematics.
He was a 7-year-old growing up in Romania and an older playmate showed him the solution to a geometry challenge from school: How to construct a triangle with sides of three specific lengths, using nothing but a ruler and a compass.
"I was fascinated," said Constanda, the University of Tulsa's Charles W. Oliphant Endowed Chair in Mathematical Sciences.
He thought about the puzzle and then posed one of his own: How do you construct a triangle if you know only the lengths of two sides and their included angle?
His playmate shrugged. The teacher hadn't demonstrated that yet.
"So I thought about it, and I came up with the answer right away," Constanda said.
Constanda has a mind made for math, and a natural love of puzzles.
"Mathematics is all pervasive," Constanda said. "In all walks of life you will come across it sooner or later."
When people ask him to define his field of research in simple words, he has a sure answer.
"Mathematics is numbers, logic and the power of abstraction," he said. "That's all. Everything else ... is man-made."
And that's the stuff of a good puzzle.
When he was in middle school and high school in Romania, Constanda worked on a vast number of problems published in a mathematical journal for students. The journal offered prizes to readers who could solve its challenges.
As an adult, he and his wife approached the problem of how to escape from behind the Iron Curtain as a sort of a puzzle with very high stakes.
"If you want to beat the system you have to study it carefully, understand it and discover its weakest link," he said. "My wife and I took our time, we did our homework and in the end ... we won."
The details of the escape he waves away. That's a "three-bottle-of-wine" story, he said, but the important point is that the puzzle had been solved. They were free.
Puzzles, math jokes and outrageous examples of students' bad math gone bizarrely wrong are the foundation for his book, "Dude, Can You Count?" which takes a serious look at the difficulties modern society has with math.
In it, he proves (using math errors taken from students' work) that the earth is flat, that the universe doesn't exist and that 1=0. Constanda said those errors highlight the kind of nonsense he sees in contemporary society - in the criminal justice system, advertising, modern art and even, occasionally, in newspapers.
Puzzles and humor are important elements of Constanda's popular senior-level applied analysis course - a means of spicing up the high-end math instruction and getting his students to think like problem-solvers, he said.
They're even a means of lulling himself to sleep after a hard day's travel along the byways of applied analysis.
Puzzles, he believes, are a key to a healthy mental state.
"They keep the mind agile," he said. "The mind stays supple. The brain works. The synapses fire up and function."
That's important for Constanda, who can't imagine the prospect of retirement.
"If I did that, in three years, I'd be solving equations in the Elysian fields," he said.
Take the quiz
Here are four puzzles chosen by University of Tulsa professor Christian Constanda. He has ranked each on an incremental scale of difficulty with 1 as the easiest puzzle.
PUZZLE NO. 1: The Weight of Time
Difficulty level: 1
Imagine Big Ben, the giant clock that dominates the London skyline. Suppose that the hour hand weighs 300 kilograms and the minute hand weighs 500 kilograms. What is the total weight of the hands on Big Ben?
PUZZLE NO. 2: The Biggest Chess Tournament Ever
Difficulty level: 2
A gigantic single-elimination chess tournament is organized with 274,877,906,944 entrants from throughout the universe. Every game has a winner and a loser. There are no draws. How many games would be needed to determine the champion? Can you find the answer through slick logical reasoning rather than through brute-force computation?
PUZZLE NO. 3: A Bridge Too Dark
Difficulty level: 2
Four travelers come to a rickety bridge at night. They have only one flashlight, which is essential to crossing the bridge. They determine that only two of them can safely be on the bridge at any time. Suppose that one of the four can cross the bridge in one minute, a second requires two minutes, the third member of the party needs five minutes and the final traveler must have 10 minutes to cross. A pair can only cross at the speed of the slower person. What is the fewest number of minutes it will take to get all four people across the bridge? The flashlight can't be thrown back across the bridge, nor is anyone allowed to be carried piggyback.
PUZZLE NO. 4: The House with Three Daughters
Difficulty level: 4
A mathematician encounters an old friend whom he hasn't seen in many years. After exchanging pleasantries, the friend tells the mathematician that he now has three daughters.
"How old are they?" the mathematician asks, and his friend suggests the answer in a puzzle: "The sum of my daughters' age is 13, and if you multiply all their ages, the result is the number on that house across the street."
The mathematician looks at the house and thinks about that information for a few seconds, then says that he needs more information.
"The oldest girl has a dog," the man says, and the mathematician immediately tells him the correct ages of the three girls. How old are the friend's daughters?
Click here to see answers.
More of Constanda's puzzles can be found in his book, "Dude, Can You Count," which is available at the University of Tulsa book store, Barnes & Noble and through Amazon.com.
Original Print Headline: He knows all the angles
Wayne Greene 918-581-8308
TIM CHAMBERLIN and TOM GILBERT / Tulsa World photo illustration
Christian Constanda is the University of Tulsa's Charles W. Oliphant Endowed Chair in Mathematical Sciences. MIKE SIMONS / Tulsa World