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This is the Luhn system used for credit and A. The steps you just took are what happens automatically when you use your card. See for yourself.

Do the math and your last digit will be 0. Choose a four-digit number, with each digit different. Scramble the digits to create a new number. For instance, if your first number is 2,, your second number might be 7, Subtract the smaller number from the larger, and add together the digits of the resulting number. If your sum is one digit, go no further.

If your sum is a two-digit number, then add the two digits together.


Your number is 9. First, when you subtract the smaller number from the larger one, the result is always a multiple of 9. You'll have to trust us on why. It's based on "casting out nines. Swapping the digits, for 82, and dividing by 9 gives 9, and again the remainder is 1. Hence, when subtracting the smaller number from the larger one, the identical remainders will cancel each other out, and the result is — poof!

Second, every multiple of 9 9, 18, 27, 36, etc. Because of how the problem is stated, with four-digit numbers, the sum of the digits will always be 9 or 18 or In the highlighted grid on the calendar Diagram C , circle four dates so there is one circled in each row and each column. Add the four circled numbers.

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Your total is Look at the Sunday dates, to the left of the grid Diagram E. Now think of the numbers for Monday through Thursday as simply those Sunday numbers plus 1, 2, 3 or 4. In a table like the one shown in Diagram D , write any number in Rows 1 and 2. Add those numbers, and put the total in Row 3. Add the numbers in Rows 2 and 3, and put the answer in Row 4. Continue this process until you have numbers in all 10 rows.

Now add up the 10 numbers and divide by the number in Row 7. Suppose you start with the number x in Row 1 and number y in Row 2. Diagram F shows what the final table looks like.

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Tip: To look like a human calculator, ask somebody to write numbers in the table, as before. Just multiply Row 7 by The skill of math is not in juggling a multitude of numbers. The skill is in recognizing a pattern that greatly simplifies the calculation. The following problems can be easily done in your head if you know the tricks. The great German mathematician Carl Friedrich Gauss supposedly solved this problem in his head as a boy, an early indication of his genius.

Use what you just learned. You have 25 pairs, giving 2, Without a calculator, determine 2, divided by Compute to two decimal places. Here, we multiply 2, by 4 getting 9, , then divide by to get An answer to a math problem in the Pop Quiz last Sunday misidentified the system commonly used by credit and A.

It is not the Codabar. It is the Luhn. Tell us what you think.


Please upgrade your browser. There are many posts in the archives that might get you going. Ask yourself what makes you come alive and then go do that. Because what the world needs is people who have come alive.

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