Wednesday, February 07, 2007

A little math magic

Today I'm going to perform a little magic for you. All you have to do is pick any four digit number (2005, 5212, 3850, etc...) and perform the following. Once you've done it, go ahead and look at the answer section to find your final number.

First choose a four digit number where the digits are not all the same (that is not 1111, 2222,…). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

For example, start with the number 2005. The maximum number you can make is 5200 and the minimum number is 0025. Take 2500 - 0025 and you get 5175. Repeat this for 5175 and you take the max: 7551 and subtract the minimum and you get 5994. Repeat until you get the same number.

Example 2: Number: 5748
8754 - 4578 = 1174
7411 - 1147 = 6264
... Keep repeating ...

Get it? OK. So, go ahead and pick your four digit number and see what you end up with.


  1. Your final number is 6174!

    If you want to know why, take a look at file22. It explains Kaprekar’s operation. I found it yesterday (using stumbleupon) just after finding egg all over my face. ;-)

  2. I would imagine it is simply because 6174 is the only 4-digit number which, if you take the largest and smallest digit combinations as shown and subtract, yields itself. The operation is sort of a randomized thing, moving all over the map with random numbers, and 6174 just happens to be the only "trap". I would be interested to find out if this indeed is the case. It would be pretty easy to write a program to look at every number less than 10,000 and check this.

  3. I agree Abe. If you take a random walk, eventually you'll fall into a hole. But the tricky/strange part in this is 1) there are no other holes to fall into and/or 2) there are no loops to fall into.

  4. yeah, that is amazing. the loop part didn't occur to me, that is pretty incredible.

  5. may i know the name for the trick,

    Logical one - theory name please

    kindly send me


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