NUMBER MAGIC

ABACUS: MYSTERY OF THE BEAD

The Bead Unbaffled - An Abacus ManualHere's a good trick that's easily performed while using a soroban. It uses

DigitSumtechniques to quickly find the answer.

T H E T R I C K

- Tell a friend you can read their mind.

- To prove this, ask them to write down any three or four digit number.

- Get them to jumble all the digits in their number to make a second new number.

- Take the two numbers and subtract the smaller number from the larger one.

- Now have them jumble all the numbers in the answer.

T H E M A G I C

- Get them to circle one of the numbers in the answer (but
, if there is one, because it's already a circle) -not a zeromake sure you can't see the circled number.

- Next have them tell you the numbers they
didn'tcircle.

- Using the DigitSum techniques, read your friend's mind and tell them the number they circled.
This is best explained by example.

H O W T H E T R I C K W O R K SExample 1: Your friend chooses 752

The Secret to the Trick752 is the chosen number

-275jumble the numbers and subtract the smaller from the larger

477 <=== Here's the secret. UsingDigitSumtechniques you'll notice that the subtracted answer will always be 9 or will reduce to 9. In this case (4 + 7 + 7 = 18 which reduces to 9.)Now that you know the secret continue with the trick. Have your friend circle one of the numbers in the answer. (Remember: tell them

because it's already a circle.) In this case they'll circle either 4 or 7.not a zeroNow ask your friend to give you the names of all the numbers

notcircled. In a moment you'll be able to read your friend's mind and name the circled number.If your friend circles 4 you'll be given 77

7 + 7 = 14 ===> cast out 9's leaving 5

9 - 5 = 4, which is the circled number.If your friend circles 7 you'll be given 47

4 + 7 = 11 ===> cast out 9's leaving 2

9 - 2 = 7, which is the circled number.

Example 2: Your friend chooses 6897

The Secret to the Trick9786 jumble the numbers and

-6897subtract the smaller from the larger

2889 <=== Once again this is the advantage. UsingDigitSumtechniques the subtracted answer will always be 9 or will reduce to 9. In this case (2 + 8 + 8 + 9 = 27 which reduces to 9.)Have your friend circle one of the numbers in the answer. (Remember: tell them

because it's already a circle.) In this case they'll circle 2, 8, or 9.not a zeroNow ask your friend to give you the all names of the numbers

notcircled. In a moment you'll be able to read your friend's mind and name the circled number.If your friend circles 2 you'll be given 889

8 + 8 + 9 = 25 ===> cast out 9's leaving 7

9 - 7 = 2, which is the circled number.If your friend circles 8 you'll be given 289

2 + 8 + 9 = 19 ===> cast out 9's leaving 1

9 - 1 = 8, which is the circled number.If your friend circles 9 you'll be given 288

2 + 8 + 8 = 18 ===> cast out 9's leaving 0

9 - 0 = 9, which is the circled number.

Save Yourself a StepNow that you see how the magic works you can save yourself a step. You don't have to calculate the DigitSum of the subtracted jumbled numbers in the answer. It's enough to know that they will always reduce to 9. Simply subtract the numbers that you're given from 9. This will always yield the number that your friend circled.

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Abacus: Mystery of the Bead

▪Advanced Abacus Techniques© Septemberr, 2007

Totton Heffelfinger Toronto Ontario Canada

totton[at]idirect[dot]com