NUMBER MAGIC

ABACUS: MYSTERY OF THE BEAD
The Bead Unbaffled - An Abacus Manual

Here's a good trick that's easily performed while using a soroban.  It uses DigitSum techniques to quickly find the answer.

T H E   T R I C K

T H E   M A G I C


H O W   T H E   T R I C K   W O R K S

This is best explained by example.

Example 1: Your friend chooses 752

The Secret to the Trick  

 752  is the chosen number
-275  jumble the numbers and subtract the smaller from the larger
 477  <=== Here's the secret.
U
sing DigitSum techniques 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 not a zero because it's already a circle.) In this case they'll circle either 4 or 7.

Now ask your friend to give you the names of all the numbers not circled. 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 Trick 

 9786  jumble the numbers and
-6897  subtract the smaller from the larger
 2889  <=== Once again this is the advantage. Using DigitSum techniques 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 not a zero because it's already a circle.) In this case they'll circle 2, 8, or 9.

Now ask your friend to give you the all names of the numbers not circled. 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 Step 

Now 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.

 

 

Abacus: Mystery of the Bead
Advanced Abacus Techniques

© Septemberr, 2007
Totton Heffelfinger   Toronto Ontario  Canada
Email
totton[at]idirect[dot]com