FunTrivia Homepage New Questions Unanswered Post a Question Goto Qn # Archives

# What 4-digit number equals the difference between its re-arranged greatest possible 4-digit value and its re-arranged smallest possible 4-digit value?

Question #96305. Asked by surflexor. (Jun 03 08 9:37 AM)

neelie_447

6174.

"Most black holes, nonetheless, involve numbers. Take any four-digit number except an integral multiple of 1111. (I.e., don't take one of the nine numbers with four identical digits.) Rearrange the digits of your number to form the largest and smallest strings possible. That is, write down the largest permutation of the number, the smallest permutation (padding initial zeros as digits, if needed, to create a four-digit number), and subtract. Apply this same process to the difference just obtained. Within a total of seven steps, you always reach 6174. At that point, further iteration with 6174 is pointless: 7641 – 1467 = 6174."

This means that, for the end result to equal the start number, the start number must be 6174.

6174 can be rearranged into 7641 and 1467.
7641-1467=6174.

http://members.aol.com/DrMWEcker/mathhole.html

 Jun 03 08, 12:36 PM