There is an easy "magic" trick that can be performed by anyone who can add a few single digits together.
Set-up of the trick:
Give your friend a calculator or have them use the calculator function on their phone.
Without showing you, ask them to
enter a private 4-digit pin or any number other than 0000.
Ask your friend to multiple their
private number by 153; your friend should not tell or show you the result.
Ask your friend to pick one of
the digits of their result as the “secret number” but not zero if there was a
zero in the result.
Now
ask for all the other digits in the result.
You then tell your friend the digit that was not revealed.
How you do it?
As your friend tells you the digits in their number (other than the secret digit), you add them up. Usually, you will have 5 or 6 single digits to add. When you get to the total, subtract that total from the next higher multiple of 9. The answer will be your friend's secret number. For example, suppose they tell you the other digits are: 1, 0, 3, 3, and 4. Adding these numbers, 1 + 0 + 3 + 3 + 4 = 11. The next multiple of 9 is 18, so 18 - 11 = 7. The secret digit is 7. Another example: suppose you are told the other digits are: 5, 3, 4, 1, and 8. The sum of these numbers is 21. The next multiple of 9 greater than 21 is 27. 27 - 21 = 6, so their secret number is 6.
How does the trick work?
The basis of the trick is an interesting property of all numbers that are multiples of 9. The sum of the digits of every
number that is a multiple of 9 will equal 9 (or a multiple of 9). Examples:
2 x 9 = 18 1 + 8 = 9
3 x 9 = 27 2 + 7 = 9
21 x 9 = 189 1 + 8 + 9 = 18
(multiple of 9) or one can continue with the digits of 18 to get 1+8 =9
The trick starts with your friend
choosing any number. You don’t know if the starting number is a multiple of 9
or not but 153 is a multiple of 9 (1 + 5 + 3 = 9). Therefore, any starting
number multiplied by 153 will result in a multiple of 9. So now you know all
the digits in the final result will add up to 9 or a multiple of 9. There is
nothing extra special about 153 other than it is a multiple of 9. If you repeat
the trick you might want to use a different multiple of 9 each time. Another
good one to use is 117.
Some extra tips:
With practice, one can get good at quickly adding up the digits given to you. As you add up the digits, here are three tips to speed up the process.
1. Ignore any 9's. Dropping any 9 from your addition will not change the final result. For example if you are given the numbers: 3 + 1 + 0 + 9 +9, their sum is 22. The next multiple of 9 is 27; 27 - 22 = 5. Ignoring the two nines, gives you a total of 4 and, again, you need a difference of 5 to get to the next multiple of 9 so you still end up with the same result.
2. Ignore any pair of numbers that equal 9. In the second example above, the numbers given were: 5, 3, 4, 1, and 8. Ignore the 5 and 4 (their sum = 9) and ignore the 1 and 8. Now you are left with 3. 9-3 = 6 which is the same answer from the example.
3. If your final sum has more than 1 digit, add the digits of the sum together to get a single digit number. Now, the secret number will be 9 minus this new total. In the first example above, you had the numbers 1, 0, 3, 3, and 4. Their total is 11. Adding 1 + 1 = 2 and 9 - 2 = 7. Again you get the same answer.
Special notes:
1. During the set-up of the trick, remember to ask your friend if any of the digits of their multiplication result is zero. You don't want them to use zero as the secret digit. The reason why is if zero was the secret digit the sum of the remaining digits will be 9 and then you would not know if the secret digit was zero or 9.
2. Sometimes their multiplication will result in a number with repeating digits. The first example had the digits 1, 0, 3, 3, 4 and 7. If your friend picked one of the 3's as the secret digit, they still need to tell you all the other digits in the number including the other 3. You may need to reinforce this by saying "now tell me all the other digits in the result, even if one them is the same as your secret digit. You don't need to tell me if there are any repeats with your secret digit."
Google sheets to complete this trick:
I just updated with a link to Google Sheets with spreadsheet that completes this trick using the MOD (modulo) function.
ReplyDeleteThank you for taking the time to publish this information very useful! spells that work
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