A Dublin student has taken some of the magic out of the magic square, the familiar number puzzle that even in its simplest form can defeat most people. She has developed a method that will solve any square, no matter how large.
Isabel Zhang (16) is a third-year student at St Louis High School, Rathmines, Dublin. Originally from Chong qing in south-west China, she has lived in Dublin for the past three years. She is a first-time exhibitor at the annual Esat BT Young Scientist and Technology Exhibition under way at the RDS in Dublin.
The top prizes in the event will be announced this evening.
"The magic square is an ancient puzzle existing for thousands of years," explained Isabel.
Its traditional form is a square divided into nine smaller squares, each containing a number. The trick is to place numbers in the smaller squares so that every row, column or diagonal adds up to the same total.
This is simple enough with the three by three magic square but becomes more of a challenge as the square enlarges to five by five or eight by eight. The rules remain the same, each smaller square must be filled with a number and each row, column or diagonal must add up to the same total for the magic square to be considered solved.
She developed an apparently new method for solving the puzzle no matter how large the magic square. "I produced a pattern to solve all the squares," she explained.
The largest square tested with her method so far is a 100 by 100 square but it should work for any sized magic square provided it has three or more elements per side.
She began by looking for repeating patterns in squares of different sizes. "What I did was look at the squares using trial and error. It was very hard at the start I have to say."
After a time she noticed that patterns began to emerge. These repeated in a way that allowed her to solve progressively more difficult magic squares using this technique.
She worked on the problem for three months and wrote to maths professors at UCD, NUI Galway and UCC looking for more information about solutions to the magic square. "I can't say it is absolutely unique, but I haven't found a solution such as my own," Isabel said. "I looked on the web and didn't find a solution the same as mine."
Andrew Shortt (14) and Niall Spillane (13), both second years at Castletroy College, Limerick, tackled a problem of a different sort - finding the optimal inflation pressure for a basketball. "We tried to find the best pressure to make the basketball bounce highest," explained Andrew.
They used a laser device to measure rebound height after dropping the ball from 180 cm. They repeated the experiment over and over to confirm measurements and at varying pressures from six to 11 lb per square inch. They found that the bounce improved but then stopped as pressure rose.
"Once it gets to 10 lb it doesn't go higher, it levels off," Andrew said.
Both were newcomers to the exhibition but would like to return next year. "If we continue it, we would study the difference between outdoor and indoor basketballs and men's and women's basketballs," Niall said.
The Esat BT Young Scientist and Technology Exhibition is open at the RDS in Ballsbridge to the public today until 5.30 p.m. and from 10.30 a.m.-5.30 p.m. tomorrow, when it will close.
