### NUMBER MAGIC

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

• 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 not a zero, if there is one, because it's already a circle) - make sure you can't see the circled number.

• Next have them tell you the numbers they didn't circle.

• Using the DigitSum techniques, read your friend's mind and tell them the number they circled.

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. Using 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.