Question

[SOLVED] While I'm not terribly busy, have this as a challenge problem.

What are the next two numbers in this sequence of four digit positive integers? \[8741, 7632, 6552, 9963, 6642, \_\_\_\_, \_\_\_\_\]

Answer 1

i have heard about this before
ans is 7641,7641
please confirm

Answer 2

i also know the deep theory behind it,though roughly only..

Answer 3

@shubhamsrg I would like to know the reason

Answer 4

i'd want to confirm @KingGeorge to confirm the ans first..
otherwise am 99% convinced am correct..
i'll message you the reason..

Answer 5

Looks like u r right @shubhamsrg

Answer 6

hmm.. :)

Answer 7

We have a winner! Excellent work. I was wondering how long it would be until someone noticed the pattern :P

Answer 8

thank you :)

Answer 9

For those wondering what the pattern is, you take the starting number, order the digits in increasing order to create one new number, and order the digits in decreasing order to create a second number. Then, you subtract the smaller number from the larger number, and repeat the process with your new number.

As I did above,
8741-1478=7263
7632-2367=5265
6552-2556=3996
9963-3699=6264
6642-2466=4176
7641-1467=6174

Curiously enough, if you do this pattern for any positive 4-digit number, you always get 6174 after 7 steps or less. See here for more info. http://en.wikipedia.org/wiki/6174_(number)

Answer 10

Wow, that's a nice conjecture! :)
Can it be prove? @KingGeorge

Answer 11

@ParthKohli I do not have the required knowledge to prove it other than through brute force. However, it can be proven with brute force.

I should also qualify that there are some numbers (1111, 1211, 4443, 4444, etc) that do not reach 6174, and instead reach 0.

Answer 12

Proved*
Thanks :-)