January 2017 - Challenge

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Ponder This Challenge:

There is exactly one integer solution for 0<x<y, xy=yx.

Hertsel Amrani (thanks!) asked me about rational solutions and inspired the idea for this month's challenge, which is to find a rational solution for xy=yx, where the last eight digits of x are different from each other.

Supply your answer as a formula for x and y, and the first and last 10 digits of x and y.


Update (2/1): Bonus '*' for a solution where the last eight digits of x are a permutation of 1,2,3,4,5,6,7,8.

Update (4/1): To clarify: x should have a finite decimal representation to have "last" digits.

Update (17/1): We are looking, of course, for a solution where x does not equal y, but not necessarily x<y.


We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 01/01/2017 @ 12:00 PM EST
Solution: 08/02/2017 @ 12:00 PM EST
List Updated: 16/01/2017 @ 12:00 PM EST

People who answered correctly:

*Robert Gerbicz (01/01/2017 01:21 PM IDT)
Jonathan Hoch (01/01/2017 03:31 PM IDT)
Kang Jin Cho (01/01/2017 04:48 PM IDT)
*Kipp Johnson (01/01/2017 07:10 PM IDT)
*Arthur Vause (01/01/2017 09:38 PM IDT)
*Yan-Wu He (01/01/2017 09:41 PM IDT)
*George W Barnett (01/01/2017 11:42 PM IDT)
*Jesse Rearick (02/01/2017 01:32 AM IDT)
*Tamir Ganor & Shouky Dan (02/01/2017 09:37 AM IDT)
*Raymond Lo (02/01/2017 10:27 AM IDT)
Wilder Boyden (02/01/2017 10:30 AM IDT)
Shirish Chinchalkar (02/01/2017 02:52 PM IDT)
*Serge Batalov (03/01/2017 08:05 AM IDT)
*Zusheng Ji (03/01/2017 08:27 AM IDT)
James Dow Allen (03/01/2017 03:27 PM IDT)
Alex Fleischer (03/01/2017 04:37 PM IDT)
*Yuanjie Pu (04/01/2017 04:26 AM IDT)
*Liubing Yu (04/01/2017 06:03 AM IDT)
John Snyder (04/01/2017 07:11 PM IDT)
*Reiner Martin (05/01/2017 01:51 AM IDT)
*Radu-Alexandru Todor (05/01/2017 01:53 AM IDT)
*Luke Pebody (05/01/2017 06:56 AM IDT)
*Mathias Schenker (05/01/2017 06:52 PM IDT)
Rudy Cortembert (05/01/2017 07:47 PM IDT)
*Philippe Fondanaiche (06/01/2017 04:12 PM IDT)
*Stephen Lesko (06/01/2017 07:14 PM IDT)
*Aviv Nisgav (08/01/2017 05:39 AM IDT)
*Franciraldo Cavalcante (08/01/2017 08:27 PM IDT)
*Yves Miennée (08/01/2017 10:01 PM IDT)
*Peter Gerritson (08/01/2017 10:27 PM IDT)
*Tyler Mullen (09/01/2017 08:47 AM IDT)
*Adrian Neacsu (09/01/2017 11:36 AM IDT)
Martí Bosch and Sebastian Bohm (09/01/2017 01:28 PM IDT)
*JJ Rabeyrin (10/01/2017 12:06 AM IDT)
*Francis Golding (10/01/2017 04:43 PM IDT)
*Oleg Vlasii (11/01/2017 03:32 PM IDT)
*Muralidhar Seshadri (13/01/2017 09:18 AM IDT)
Joaquim Neves Carrapa (13/01/2017 05:04 PM IDT)
Husen Wang (13/01/2017 11:49 PM IDT)
*Motty Porat (15/01/2017 01:20 AM IDT)
David F.H. Dunkley (15/01/2017 12:20 PM IDT)
*Aaradesh (16/01/2017 05:58 PM IDT)
Hyung Sik Hwang (17/01/2017 07:34 AM IDT)
*Robert Lang (17/01/2017 07:02 PM IDT)
*David Greer (17/01/2017 08:39 PM IDT)
*Pål Hermunn Johansen (18/01/2017 12:50 AM IDT)
*Andreas Stiller (18/01/2017 07:21 PM IDT)
*Steven Langerwerf (19/01/2017 03:54 PM IDT)
Dan Dima (20/01/2017 11:44 AM IDT)
Jeff Boyle (23/01/2017 02:34 AM IDT)
Adir HaCohen (23/01/2017 02:56 AM IDT)
The Questionable Squad (23/01/2017 07:03 AM IDT)
*Armin Krauss (25/01/2017 08:39 PM IDT)
*Joehyun Kim (25/01/2017 08:52 PM IDT)
*Sergey Koposov (26/01/2017 09:47 PM IDT)
*Chris Shannon (27/01/2017 03:49 AM IDT)
*Chuck Carroll (27/01/2017 02:22 PM IDT)
*Vladimir M. Milovanović (27/01/2017 03:11 PM IDT)
Hao Zheng (27/01/2017 04:34 PM IDT)
*Sergey Grishaev (27/01/2017 09:34 PM IDT)
Pieter Meijer (27/01/2017 11:14 PM IDT)
*Alessandro Marzo (28/01/2017 07:28 PM IDT)
*Bert Dobbelaere (29/01/2017 08:19 PM IDT)
Jason Lee, Jamie Jorgensen & Peter Farbman (30/01/2017 08:53 PM IDT)
*Teake Nutma (30/01/2017 09:39 PM IDT)
Hao Zheng (30/01/2017 10:07 PM IDT)
*Uoti Urpala (31/01/2017 05:25 PM IDT)
*Martin Sergio H. Fæster (01/02/2017 11:54 PM IDT)