This mathematical trick was not part of my Pi Day magic show but probably should have been… I’ve performed this for my Precalculus classes in the past but flat forgot about it when organizing my Pi Day show. The next time I perform a magic show, I’ll do this one right after the 1089 trick. (I think I learned this trick from a Martin Gardner book when I was young, but I’m not sure about that.)
Here’s a description of the trick. I give my audience a deck of cards and ask them to select six cards between ace and nine (in other words, no tens, jacks, queens, or kings). The card are placed face up, side by side.
After about 5-10 seconds, I secretly write a pull out a card from the deck and place it face down above the others.
I then announce that we’re going to some addition together… with the understanding that I’ll never write down a number larger than 9. For example, the 4 and 6 of spades are next to each other. Obviously, , but my rule is that I’m going to write down a number larger than 9. So I’ll subtract 9 whenever necessary: . Since 1 corresponds to ace, I place an ace about the 4 and 6 of spades.
Next, I consider the 6 of spades and 2 of diamonds. Adding, I get 8. That’s less than 9, so I pull an 8 out of the deck.
Next, , so I pull out a 5 from the deck.
Next, , and . So I pull out a 7.
(To keep this from getting dry, I have the audience perform the arithmetic with me.)
On the the next row. The next cards are , , , and .
On the the next row. The next cards are , $latex $4+7-9 = 2$, and .
Almost there: and .
Finally, , and I dramatically turn over the last card to reveal a 6.
Naturally, everyone wonders how I knew what the last card would be without first getting all of the cards in the middle. I’ll discuss this in tomorrow’s post.