## KingGeorge 2 years ago [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? \[8741, 7632, 6552, 9963, 6642, \_\_\_\_, \_\_\_\_\]

1. shubhamsrg

2. shubhamsrg

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

3. sauravshakya

@shubhamsrg I would like to know the reason

4. shubhamsrg

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

5. sauravshakya

Looks like u r right @shubhamsrg

6. shubhamsrg

hmm.. :)

7. KingGeorge

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

8. shubhamsrg

thank you :)

9. KingGeorge

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)

10. ParthKohli

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

11. KingGeorge

@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.

12. ParthKohli

Proved* Thanks :-)