Date:- 04 April 2000. I hope you have already gone through my "Magic Squares" document. On this one, I shall discuss a very peculiar thing which occurs when doing a trivial operation, such as subtraction, on a four digit number. I shall like to point out that the four digits should not all be the same. For example, what I am going to show in this page will never work for numbers like 2222, 7777, 9999, etc.. The reason for such a "property" will become obvious as you go along the article below. Similar to the notes I wrote about "Magic Squares" this one, too, was first introduced to me during my BSc days. Step 1: Take any 4 digits number, with properties defined as above.! Step 2: Write the digits in ascending order. E.g If I take 7526, the ascending order form is taking the smallest digit first, to the biggest diggit last. In this case, its 2567. Step 3: Write the digits in descending order. E.g If I take 7526, the descending order form is taking the biggest digit first, to the smallest diggit last. In this case, its 7652. Step 4: Find the difference between the two resulting numbers. In the example in steps 2 and 3, we are doing the following operation:- 7652-2567 Step 5: Repeat Steps 2,3 and 4 for the resulting difference we get in step 4. CLAIM: It is observed that the number 6174 will finally be obtained if any 4-digits number [with the above properties] is taken. It can also be claimed that, the number will definitely appear within 7 iterations. [i.e Repeating Step 5 for a maximum 7 times.] Check for yourself:- Let us consider a 4-digits number, 8262 Ascending Order= 2268 Descending Order= 8622 Difference [Iteration (1)]= 8622-2268= 6354 Ascending Order= 3456 Descending Order= 6543 Difference [Iteration (2)]= 6543-3456= 3087 Ascending Order= 0378= 378 Descending Order= 8730 Difference [Iteration (3)]= 8730-378= 8352 Ascending Order= 2358 Descending Order= 8532 Difference [Iteration (4)]= 8532-2358= 6174 {--!!Bingo!!--} In the example we just solved, we notice that we get 6174 in the 4th Iteration. Even if we continue to iterate with 6174, we will still end up with itself [6174]. This is shown here, Ascending Order= 1467 Descending Order= 7641 Difference= 7641-1467= 6174 !!!!!!!!!!!!!!!!!!!! Questions you have to ask yourself: 1. What is so special about 6174. 2. Why is it that we get 6174 in maximum 7 iterations. [why not more than 7]. Send me an email if you have an idea about 6174.