I'm a financial analyst for TNTP by day and magician by night (catch me performing around greater Orlando, Florida). Previously I taught math as a 2009 corps member in Marianna, Arkansas, and I’ve always been fascinated by the math-magic connection. This trick, which I'm demonstrating with my wife, Lois Kamandulis (Greater Delta '08), is based on a creation of Ron Edwards from The Pallbearers Review Volume 10. Learning it involves applying basic algebra. Let’s find out how it’s done.

Let's Break It Down

But How Is It Done?

The year on each coin is selected to force the calculation to always equal 2045. So if you follow the steps above with a 2003 penny, 1999 nickel, 1994 dime, and 1979 quarter, it will always result in 2045. Prepare to do this trick by gathering those coins, a calculator and a book. On a piece of paper, write the fifth word from page 204 of the book you’re using for this trick, and then seal this prediction in an envelope marked with an X.

Math-Magic Questions for Students:

1. Assume the spectator chooses the nickel with the year 1999. Write an equation that represents the steps used to solve for the page and word number (i.e., double the value of the coin, add the value of the remaining coins and add the year of the selected coin).

5x2 + 1 + 10 + 25 + 1999 = 2045

2. Now that you know we are forcing the number 2045, write an equation and solve for the year on the…A) Penny, B) Dime, C) Quarter.

a) 1x2 + 5 + 10 + 25 + P = 2045

42 + P = 2045

P = 2003

The year on the penny is 2003.

b) 10x2 + 1 + 5 + 25 + D = 2045

51 + D = 2045

D = 1994

The year on the dime is 1994.

c) 25x2 + 1 + 5 + 10 = 2045

66 + Q = 2045

Q = 1979

The year on the quarter is 1979.

3. Instead of forcing the number 2045, suppose you want to force 2050. What years would the coins need to be for the trick to work?

Penny:

1X2 + 5 + 10 + 25 + P = 2050

42 + P = 2050

P = 2008

The year on the penny is 2008.

Nickel:

5X2 + 1 + 10 + 25 + N = 2050

46 + N = 2050

N = 2004

The year on the nickel is 2004.

Dime:

10X2 + 1 + 5 + 25 + D = 2050

51 + D = 2050

D = 1999

The year on the dime is 1999.

Quarter:

25X2 + 1 + 5 + 10 + Q = 2050

66 + Q = 2050

Q = 1984

The year on the quarter is 1984.

4. If you have a 1992 quarter, what page/word number will you force? What year penny, nickel, and dime do you need to force this same number?

25X2 + 1 + 5 + 10 + 1992 = X

X = 2058

A quarter with the year 1992 would force the number 2058.

Penny:

1X2 + 5 + 10 + 25 + P = 2058

42 + P = 2058

P = 2016

The year on the penny is 2016.

Nickel:

5X2 + 1 + 10 + 25 + N = 2058

46 + N = 2058

N = 2012

The year on the nickel is 2012.

Dime:

10X2 + 1 + 5 + 25 + D = 2058

51 + D = 2058

D = 2007

The year on the dime is 2007.

5. Given the magic trick process (i.e., think of a coin, double the value, add the value of the remaining coins and add the year of the selected coin), can you force the number 2098? Why or why not? What’s the largest number you can force?

1X2 + 5 + 10 + 25 + P = 2098

42 + P = 2098

P = 2056

No, you cannot currently force the number 2098 using this magic trick because that would require a penny with the year 2056.

1X2 + 5 + 10 + 25 + 2018 = X

X = 2060

As of 2018, the largest number you can force with this magic trick is 2060.

Common Core Connection: The above series of questions works on the 6th grade Common Core standard regarding writing and solving equations in the form x + p = q  (where p, q and x are all non-negative rational numbers).