In the highlighted grid on the calendar ( Diagram C), circle four dates so there is one circled in each row and each column. Adding 1 + 8 or adding 2 + 7 (as specified in the problem) again gives 9.Ħ. For example, the number 4,968 is a multiple of 9 (552 × 9), and its digits add up to 27 (3 × 9).īecause of how the problem is stated, with four-digit numbers, the sum of the digits will always be 9 or 18 or 27. Second, every multiple of 9 (9, 18, 27, 36, etc.) has the property that its digits will always add up to a multiple of 9. Hence, when subtracting the smaller number from the larger one, the identical remainders will cancel each other out, and the result is - poof! - a multiple of 9.Īlgebraically, what you have is (9 x + r) - (9 y + r) = 9( x - y). Swapping the digits, for 82, and dividing by 9 gives 9, and again the remainder is 1. It's based on "casting out nines.") For example, 28 divided by 9 is 3 with a remainder of 1. This happens because, when you divide any number and any scrambled variation of it by 9, the remainder - what’s left over after dividing - is always the same. How do I do it? Here’s a two-part explanation for how this trick works, thanks to the amazing properties of 9.įirst, when you subtract the smaller number from the larger one, the result is always a multiple of 9. If your sum is a two-digit number, then add the two digits together. (For instance, if your first number is 2,357, your second number might be 7,325.) Subtract the smaller number from the larger, and add together the digits of the resulting number. Scramble the digits to create a new number. Choose a four-digit number, with each digit different. 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 credit and 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. After subtracting the original number x, you have 5.Ĭredit. How do I do it? After doubling x, you have 2 x add 10 and it becomes 2 x + 10. (Based on what you learned with Problem 2, you should be able to predict this number along with me.) Double it, add 10, divide by 2, and then subtract the number you started with. 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, for 2 x add 5, for 2 x + 5 then multiply by 50, for 100 x + 250. ![]() How do I do it? As with most of this mathematical magic, the secret is elementary algebra. Your answer begins with your favorite number, followed by your age. If you have had your birthday already in 2010: happy birthday and add 1 to the total. Choose your favorite number from 1 to 100. Think of these numbers as in a circle ( Diagram A), and going around that circle forever. How do I do it? The six fractions 1/7 to 6/7 have the same repeating sequence of six numbers after the decimal 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. (I’ll be nice and let you use a calculator, but you’ll 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. ![]() 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 move expeditiously 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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