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## In this mathematics seminar, the magician reveals his secrets

In Math, Magic, Games & Puzzles, longtime Northeast math teacher Stanley Eigen discovers the numerical principles behind popular card tricks and helps his specialty students teach them to children.

Going to an honors-level math seminar on Northeastern University’s Boston campus in early September, you might expect to see graphing calculators, thick textbooks, algebraic equations and parabolas scratched out on a marker board – trappings of the serious work that top STEM-focused students at a world-class research university are undertaking.

Instead, in Stanley Eigen’s classroom, you’ll see a flurry of shuffled playing cards; hear a faint cacophony of impressed chatter. You’ll watch a grainy YouTube video of the famous 90s magician David Copperfieldwhich, between corny jokes and a terrible moonwalk, correctly identifies the seemingly random card you, the amateur spectator, drew from your deck.

This course is HONR 1310: Mathematics, Magic, Games and Puzzles, for first-year students in Northeastern’s Honors program. It covers the mathematical concepts behind well-known card tricks and puzzles, but the most important takeaway is how to communicate them effectively. This is a service-learning course, and students must perfect the tricks in order to teach them to elementary and middle school-age children in Boston-area partner programs.

Today’s lesson, the second of the semester, focuses on card tricks that use “orbits” – the predictable paths of a number system. Eigen starts with the “Nine Card Liar” trick. (You, readers, can now pick up a deck of cards and play the game).

“Everyone, get yourselves nine cards,” Eigen said. “Mix them or not, it doesn’t matter. Now distribute them into three piles, one at a time, from left to right. The students, who have all been on campus for about a week, arrange the cards on the small desks, creating square grids.

“Pick up the middle pile,” he orders. “Look at the bottom card and remember it.” I select the 10 of Diamonds. “Drop it on one of the piles, pick it all up and put it on the third pile. Everyone is well ?

This is a “spelling round” in which cards are shuffled based on seemingly random words – the letters of a name, or the suit and value of a given card. Eigen continues: “Now think about your map, but *lie* and spell out a completely different card. He makes the Four of Clubs, each placing a card for the letters of FOUROFCLUBS.

“Everyone spelled something different,” he said. “You lied, but the truth will solve everything. So take the top card, place it on the table: TRUT – and if you look at the H, that should be your card. Sure enough, the 10 of diamonds appears. The students, all recognizing their own card, gasp and laugh.

Eigen explains that the trick works by locking the trajectory – the orbit – of the map from the start. “It doesn’t matter what you spell,” he said. “Due to the length of the words, the card will always be third from the top, third from the bottom, fifth from the middle.”

The variants work the same way. Some magicians use the letters in people’s names, their suits or random numbers called out by the audience – keeping track of the card in the lineup is all that matters. “If you can add basic sums, you can do this trick,” says Eigen.

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