Use these
calculator tricks to impress and astound your friends!

**Is That Your Final Answer?**

- Have someone pick a number between 1 and 9.
- Now have him use a calculator to first multiply
it by 9, and then multiply it by 12,345,679 (notice there is no 8 in that
number!).
- Have the person show you the result so you can
tell him the original number he selected! How? Easy. If he selected 5, the
final answer is 555,555,555. If he selected 3, the final answer is
333,333,333. The reason: 9 x 12345679 = 111111111. You multiplied your digit
by 111111111.
*(By the way, that 8-digit number (12,345,679) is easily memorized: only the 8 is missing from the sequence.)*

**The 421 Loop**

- Pick a whole number and enter it into your
calculator.
- If it is even, divide by 2. If it is odd,
multiply by 3 and add 1.
- Repeat the process with the new number over and
over. What happens?
- The sequence
*always*ends in the "loop": 4.....2.....1.....4.....2.....1...

Example: Start with
13.

13
is odd, so we multiply by 3 and add 1. We get 40. (13 x 3 = 39 + 1= 40)

40
is even, so we divide by 2. We get 20. (40 / 2 = 20)

20
is even, so we divide by 2 and get 10.

10
is also even so we divide by 2 again and get 5.

5
is odd so we multiply by 3 and add 1. We get 16.

16
is even, so we divide by 2 and get 8.

8
is also even so we divide by 2 again and get 4.

4
is even so we divide by 2. We get 2.

2
is even, so we divide by 1 and get 1.

1
is odd, so we multiply by 3 and add 1. We get 4.

4
is even so we divide by 2. We get 2. And so we begin the loop
4.....2.....1.....4.....2.....1...

**Good Luck or Bad
Luck?**

- Have someone secretly select a three-digit number
and enter it twice into her calculator. (For example: 123123) Have her
concentrate on the display. You will try to discern her thoughts!
- From across the room (or over the phone),
announce that the number is divisible by 11. Have her verify it by dividing
by 11.
- Announce that the result is also divisible by 13.
Have her verify it.
- Have him divide by his original three-digit
number.
- Announce that the final answer is 7.

You can use this to
predict Good Luck for him. If you wish to predict Bad Luck, have him divide by 7
in step 3; the final answer will be 13.

Why does this work? Entering a three-digit number twice (123123) is equivalent
to multiplying it by 1001. (123 x 1001 = 123,123). Since 1001 = 7 x 11 x 13, the
six-digit number will be divisible by 7, 11, 13, and the original three-digit
number.

**The Secret of 73**

- For this trick, secretly write 73 on a piece of
paper, fold it up, and give to an unsuspecting friend.
- Now have your friend select a four-digit number
and enter it twice into a calculator. (For example: 12341234)
- Announce that the number is divisible by 137 and
have him verify it on his calculator.
- Next, announce that he can now divide by his
original four-digit number. After he has done so, dramatically command him
to look at your prediction on the paper. It will match his calculator
display: 73!

Why does this work?
Entering a four-digit number twice (12341234) is equivalent to multiplying it by
10001. (1234 x 10001 = 12341234). Since 10001 = 73 x 137, the eight-digit number
will be divisible by 73, 137, and the original four-digit number.

**The 6174 loop**

- Select a four-digit number. (Do not use 1111,
2222, etc.)
- Arrange the digits in increasing order.
- Arrange the digits in decreasing order.
- Subtract the smaller number from the larger
number.
- Repeat steps 2, 3, and 4 with the result, and so
on. What happens?

Let's try 7173

Arrange
the digits in increasing order. 1377

Arrange
the digits in decreasing order. 7731

Subtract
the smaller number from the larger number. 7731 - 1377 = 6354

Repeat
the process with 6354

6543
- 3456 = 3087

8730
- 0378 = 8352

8532
- 2358 = 6174

7641
- 1467 = 6174

7641
- 1467 = 6174

7641
- 1467 = 6174 (we're in a loop!)

Amazingly, all
four-digit numbers (not multiples of 1111) end up in the 6174-loop. No reason
has been found for this phenomenon.

**The Golden Prediction**

This trick takes considerable time, but the effect is spectacular.

Give someone a sheet of paper and a pencil and tell him to:

- Number the first 25 lines (1, 2, 3,...).
- Write any two whole numbers on the first two
lines.
- Add the two numbers and write the sum on the
third line.
- Add the last two numbers and write the sum on the
next line.
- Continue this process (add the last two, write
the sum) until he has 25 numbers on his list.
- Select any number among the last five on his list, and divide by the
previous number (the number above it). Now for the trick!

Remind him that you do not know his original two numbers or any of the 25 numbers, that you do not know which of the 25 numbers he selected right now, and therefore you cannot possibly know the number on the display.

With great concentration and much difficulty, you divine the number presently on his calculator: "I'm getting a One... then something funny - oh! a decimal point! Then... a Six.. another One.. and an Eight, I think.. Now I'm getting a blank.. nothing... Oh! It's a Zero!.. then a Three... and... another Three?... then a Nine... had enough?"

That's right! If your subject selects any number between the last five (#21 through #25) and divides it by the number above it,**he'll always get 1.618033989...**, which just happens to be the Golden Mean!*(provided, of course, he did all the addition correctly in steps 3-5 above)*

Why does this work? It's an incredible bit of mathematical trivia. Begin with any two whole numbers, make a Fibonacci-type addition list, take the ratio of two consecutive entries, and the ratio approaches the Golden Mean! The further out we go, the more accurate it becomes. That's why we need 25 numbers: to obtain sufficient accuracy. The proof requires familiarity with the Fibonacci Sequence, pages of algebra, and a knowledge of Limits, all of which go far beyond the scope of this site.

Interesting fact: if you divide one of your last 5 numbers by the*next*number (instead of the previous number), the result is the same decimal without the leading 1. (0.618033989)

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