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Colm Mulcahy's Fibonacci-Inspired Trick

September 20, 2010

In the September 2010 episode of "Discoveries and Breakthroughs in Science," Colm Mulcahy (Spelman College) uses a deck of cards to demonstrate the magical aspect of the Fibonacci sequence.

Knowing a few key cards—the ace (or one), two, three, five, eight, and king (or 13)—is all it takes to pull off the "Ice Cream Trick": Identifying the two cards a person is holding just by knowing their sum.
Mulcahy does it by keeping track of the location of a key card that starts on the bottom of his deck, despite the fact that he shuffles the deck.
"What's magic about them is if you add any two of them and tell somebody what the total is, they know what the two numbers must have been," Mulcahy said.
"People think sometimes that math merely has applications to engineering or rocket science or whatever, but it also has entertainment value," he continued.
"Yeah, it's definitely amazing," said student Janiene Thiong.
"Yes, this is living proof that math is literally everywhere," said student Cheyanne Goings.. 

Knowing a few key cardsthe ace (or one), two, three, five, eight, and king (or 13)is all it takes to pull off the trick in question. Mulcahy does it by keeping those six cards on top, despite the fact that he shuffles the deck. The six are mixed further and two selected at random. He's then able to identify both cards knowing their sum.

"What's magic about Fibonacci numbers is if you add any two of them and tell somebody what the total is, they know what the two numbers must have been," Mulcahy said.

For a second effect, called the Ice Cream Trick, Mulcahy keeps track of the location of a single key card that starts on the bottom of the deck. Again, despite several shuffles, and three "ice cream scoop" deals and drops which are determined by a flavor of icecream called out at random, the key card always magically appears at the top of the deck.

"People think sometimes that math merely has applications to engineering or rocket science or whatever, but it also has entertainment value," he continued. 

"Yeah, it's definitely amazing," said student Janiene Thiong.

"Yes, this is living proof that math is literally everywhere," said student Cheyanne Goings.

For more from Mulcahy, read his bimonthly MAA column "Card Colm". 

Source: Discoveries and Breakthroughs in Science

Id: 
960
Start Date: 
Monday, September 20, 2010

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