Change any number on your card and it won’t.ĥ. Do the math and your last digit will be 0. A wrong digit or transposing nearly any two consecutive digits in your 16-digit card number can be detected, without using a database, because the final digit of the total won’t add up to 0. The steps you just took are what happens automatically when you use your card. This is the Luhn system used for creditĪnd A.T.M. Now add the three numbers you wrote down, and look at the last digit of your answer. How many of the digits of the top number are 5 or greater? Write that down. Write that number down.Īdd up the digits of the bottom number. ![]() Photo Illustration by Richard Faverty/Beckett StudiosĪdd up the digits of the top number, then double it. Write the number in a grid of boxes like the one shown in Diagram B, in alternating fashion. After subtracting the original number x, you have 5.Ĥ. (Based on what you learned with Problem 2, you should be able to predict this number along with me.)Īfter doubling x, you have 2x add 10 and it becomes 2x + 10. ![]() Double it, add 10, divide by 2, and then subtract the number you started Note: This trick will fail if you are more than 99 years old.ģ. Subtracting the year you were born (and adding the number 1 if you had your birthday already this year) will produce your favorite number followed by your age. Double it, forĢx add 5, for 2x + 5 then multiply by 50, for 100x + 250. Your answer begins with your favorite number, followed by your age.Īs with most of this mathematical magic, the secret is elementary algebra. If you have had your birthday already in 2010: happy birthday and add 1 to the total. Adding 1, 4, 2, 8, 5 and 7, you always get 27.įavorite number from 1 to 100. Think of these numbers as in a circle ( Diagram A), and going around that circle forever. The six fractions 1/7 to 6/7 have the same repeating sequence of six numbers after theĭecimal point, each fraction starting with a different number in the sequence 142857. Am I right? Now add up the first six digits after the decimal point. Is there a 1 somewhere after the decimal point? I predict that the number after the 1 is 4. Need one that has at least seven decimal places.) If your total is a whole number (that is, no digits after the decimal point) divide the answer by 7 again. (I’ll be nice and let you use a calculator, but you’ll Choose a number from 1 to 70 and then divide it by 7. Benjamin shares some of the concepts from his DVD course “The Joy of Mathematics” and his book “Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks.”įollow the instructions below. dissertation, at Johns Hopkins, titled “Turnpike Structures for Optimal Maneuvers”: the maneuvers were inspired by a way of arranging Chinese checkers to moveĮxpeditiously across the board. ![]() When not amazing audiences around the country - squaring five-digit numbers in his head or guessing your number, any number - the Mathemagician is a professor of math at Harvey Mudd College in Claremont, Calif. Benjamin has two passions: magic and math.
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