# Mathemagic

Discussion in 'Math' started by Mark44, Mar 27, 2008.

1. ### Mark44 Thread Starter Well-Known Member

Nov 26, 2007
626
1
Here's a nifty piece of mathematics magic you can show your friends, family, and coworkers. Most everyone I've tried this with was pretty amazed by it.

1. Ask the person to think of a four-digit number, and write it down so that you can't see it.
2. Now ask him/her to rearrange the digits and write down the new number.
3. Ask him/her to subtract the smaller of the two numbers from the larger number.
4. Ask him/her to tell you all but one of the digits of the result of the subtraction. The only restriction is that the digit you are NOT told can't be zero.
5. Mentally add the digits you were told. If you get a two digit number, add those two digits to get a single digit (call it n).
6. Tell the
person the number he or she didn't tell you is 9 - n.

Here's an example of how this might work.
Your friend thinks of a number, say 4281. (You don't see this number.)
Your friend rearranges this to 2481. (You don't see this either.)
Your friend subtracts 2481 from 4281, getting 1881. (You don't see this.)
Your friend tells you three of the digits: 8 1 8 (Thinking he's being tricky, he tells them to you out of order.)
You add 8, 1, and 8 to get 17, and then add these two digits to get 8.
You subtract 8 from 9 to get 1, and tell your friend that the digit you weren't told is 1.

There is actually some mathematics behind this trick, namely number theory. As stated, we were working with four-digit numbers, but it can be done with numbers with two or three digits, or with numbers with more than four digits.

Starting with any whole number with two or more digits, and any permutation (same digits in different order) of the digits of the starting number, it can be shown fairly easily that the difference will always be divisible by 9. Furthermore, for any number that is divisible by 9, it's digits always add up to 9 or a multiple of 9 (such as 18, 27, and so on).

When your friend thought of a number, and then a permutation of it, and then subtracted one from the other, the result he/she obtained was divisible by 9. When he/she told you all but one of the digits, including any 0 digits, all you had to do was add the digits you were told, and figure out what digit was needed to make 9.

Mark

2. ### Dave Retired Moderator

Nov 17, 2003
6,960
170
Hehe, seen this one before.

I am the only one who fails to impress people with Mathematics? (Not that there is anything impressive of course!) The problem I find with these questions where you say, "right calculate something in your head, and I'll tell you something about what you have calculated", is that people 9 times out of 10 get the calculations wrong! Then the whole trick becomes me trying to explain to them the rudiments of addition, multiplication and subtraction!

The trick is good. People are not!

Dave

3. ### Mark44 Thread Starter Well-Known Member

Nov 26, 2007
626
1
If this one doesn't work for you, I have another one where they use a calculator.

Coming soon...

4. ### Dave Retired Moderator

Nov 17, 2003
6,960
170
Sounds good. Just got to remember to take a calculator with me to parties!

On a side, we have had some good mathematical ditties on this forum over the years; perhaps we should document them one day.

Dave

5. ### aliashar86 Active Member

Nov 23, 2006
71
0
no dont take it carry ur cell

6. ### Dave Retired Moderator

Nov 17, 2003
6,960
170
Tis true. Everyone carries one these these days.

Dave