IBM Research | Ponder This | February 2011 challenges

# Ponder This

## February 2011

<<January February March>>

Ponder This Challenge:

We define flip(n) as writing the integer n in seven-segment font and flipping it (rotating it 180 degrees). For example, flip(168)=891. The flip operation is only defined for digits that have a numerical meaning when flipped. For example, the digit "4" becomes the letter "h", which is not a digit, so the flip operation is not defined for numbers like 4 or 141.
If flip(n) is well-defined, we call n a flippable number.
Find an integer n > 0 for which all of the following three conditions hold:
A. n is flippable and flip(n) = n.
B. n*n is flippable.
C. n is divisible by 2011.

For example,

(192555261) satisfies conditions A and C but not B, since n*n starts with the unflippable digit 3.

For extra credit, send us another integer that satisfies conditions A, B, and the new condition C': n divided by 2011 leaves a remainder of 100.
Correct solutions to the extra credit challenge will earn solvers a star next to their names.

Update: February 4th: Note that flipping "2" gets a "2", not "5".

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 webmaster.

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

Challenge: 01/31/2011 @ 05:00 PM EST
Solution: 02/28/2011 @ 05:00 PM EST
List Updated: 01/31/2011 @ 05:00 PM EST

*Albert Stadler (02/01/2011 02:47 PM EDT)
Kipp Johnson
(02/01/2011 03:18 PM EDT)
*Michael Brand
(02/01/2011 03:30 PM EDT)
*Joseph DeVincentis (02/01/2011 03:55 PM EDT)
*Daniel Bitin (02/01/2011 04:04 PM EDT)
*Dan Dima (02/01/2011 04:50 PM EDT)
*Harald van Dijk (02/01/2011 05:24 PM EDT)
*Nick McGrath (02/01/2011 05:53 PM EDT)
*Mark Mammel (02/01/2011 07:08 PM EDT)
*Vladimir Sedach (02/01/2011 07:24 PM EDT)
Robert DiMarco (02/01/2011 10:11 PM EDT)
Dan Wood (02/01/2011 10:46 PM EDT)
*Mark Mixer (02/01/2011 11:02 PM EDT)
*John T. Robinson (02/02/2011 02:19 AM EDT)
Danny Lynch (02/02/2011 07:51 AM EDT)
*Aviv Nisgav (02/02/2011 08:00 AM EDT)
*Pataki Gergely (02/02/2011 12:10 PM EDT)
*Danny Scheinerman (02/02/2011 12:37 PM EDT)
*Piet Orye (02/02/2011 03:47 PM EDT)
*Thijmen Krebs (02/02/2011 08:18 PM EDT)
*Arovit Narula (02/03/2011 10:22 AM EDT)
*Viacheslav Chernoy
(02/03/2011 10:22 AM EDT)
Philippe Fondanaiche
(02/03/2011 10:31 AM EDT)
David Setiawan Putra Robianto
(02/03/2011 12:51 AM EDT)
*Benjamin Bachmann (02/03/2011 02:09 PM EDT)
*Álvaro Begué (02/03/2011 02:31 PM EDT)
*Michael Wegener (02/03/2011 02:42 PM EDT)
*Adam Daire (02/03/2011 03:04 PM EDT)
*Victor Chang (02/03/2011 03:40 PM EDT)
Eli Biham (02/03/2011 03:53 PM EDT)
Hubert Kahlert (02/03/2011 03:57 PM EDT)
*John Tromp (02/03/2011 09:06 PM EDT)
*Alan Curry (02/04/2011 03:48 AM EDT)
Richard Frank (02/04/2011 11:05 AM EDT)
*Viacheslav Chernoy (02/04/2011 12:41 PM EDT)
Jim Altieri (02/04/2011 01:27 PM EDT)
*Christian Blatter (02/04/2011 02:39 PM EDT)
*Herbert Groscot (02/04/2011 05:56 PM EDT)
Eric Harley (02/04/2011 06:12 PM EDT)
*Tom Sirgedas (02/04/2011 08:36 PM EDT)
Emile Joubert (02/05/2011 07:57 AM EDT)
*Hakan Summakoğlu (02/05/2011 01:29 PM EDT)
Kiyoto Tamura (02/05/2011 06:31 PM EDT)
*Sylvain Becker (02/05/2011 07:18 PM EDT)
*Amos Guler (02/06/2011 06:56 AM EDT)
*Daniel Chong Jyh Tar (02/06/2011 12:06 PM EDT)
*Jan van Delden (02/06/2011 08:49 PM EDT)
Fred Schalekamp (02/07/2011 06:46 AM EDT)
*Lukasz Bolikowski (02/07/2011 07:41 AM EDT)
*David Vino (02/07/2011 10:44 AM EDT)
Michael Liepelt (02/07/2011 10:45 AM EDT)
Kiyoto Tamura (02/07/2011 11:41 AM EDT)
*Or Zuk (02/07/2011 06:22 PM EDT)
Adrian Hartline (02/07/2011 09:05 PM EDT)
*Jason Crease (02/07/2011 10:25 PM EDT)
Firman Wijaya (02/08/2011 01:05 AM EDT)
Adrian Toncean (02/08/2011 09:28 AM EDT)
*Dmitry Litvinenko (02/08/2011 10:04 AM EDT)
*Ian Barnard (02/08/2011 02:43 PM EDT)
Ashutosh Mahajan (02/09/2011 12:00 AM EDT)
Ubaid Mohammed (02/09/2011 06:21 AM EDT)
Guillaume (02/09/2011 06:41 AM EDT)
Harish Haridas (02/09/2011 06:52 AM EDT)
*Greg Janée (02/09/2011 02:02 PM EDT)
Dejan Stakic (02/09/2011 02:10 PM EDT)
Victor Balacescu (02/09/2011 04:27 PM EDT)
*Donald T Dodson (02/09/2011 05:01 PM EDT)
*Chuck Carroll (02/09/2011 06:05 PM EDT)
Ante Kovacic (02/09/2011 06:13 PM EDT)
Amrith Raghavan (02/09/2011 06:31 PM EDT)
Hengfeng Tian (02/09/2011 09:33 PM EDT)
Robert Rafaeil Hannah (02/10/2011 09:22 AM EDT)
Chidambaram Annamalai (02/10/2011 10:21 AM EDT)
*Haik Alexanyan (02/10/2011 06:52 PM EDT)
*Tom Harley (02/11/2011 12:58 AM EDT)
Prithu Tiwari (02/11/2011 02:40 AM EDT)
*David Friedman (02/11/2011 02:49 AM EDT)
Priya R Sahoo (02/11/2011 09:22 AM EDT)
Robin Ryder (02/11/2011 12:12 PM EDT)
Dionysus Blazakis (02/11/2011 09:14 PM EDT)
Clive Tong (02/12/2011 05:34 PM EDT)
Sandeep Rathour (02/12/2011 06:05 PM EDT)
*Ante Kovacic (02/13/2011 07:07 AM EDT)
*Rani Hod (02/13/2011 11:19 AM EDT)
Stanislav Grudnitskiy (02/14/2011 03:06 AM EDT)
Nirvay Kumar (02/14/2011 06:36 AM EDT)
Allen WAN (02/14/2011 07:46 AM EDT)
*Mathias Schenker (02/14/2011 07:46 AM EDT)
*Stanislav Grudnitskiy (02/14/2011 03:14 PM EDT)
William Easton (02/14/2011 05:08 PM EDT)
Assaf Natanzon (02/15/2011 06:28 AM EDT)
Valdes Woo (02/15/2011 10:19 AM EDT)
*Ante Turudic (02/15/2011 05:31 PM EDT)
Christopher Meyer (02/16/2011 12:26 PM EDT)
*Radek Marciňa (02/16/2011 12:45 PM EDT)
Matthew R Wood (02/16/2011 01:25 PM EDT)
*Kurt Hectic (02/16/2011 02:35 PM EDT)
*Mutaamba Maasha (02/18/2011 01:54 AM EDT)
Mike Kennedy (02/18/2011 02:12 PM EDT)
Justin McDonough (02/18/2011 02:17 PM EDT)
*Jamorn Horathai (02/18/2011 04:05 PM EDT)
Dustin Shively (02/18/2011 08:52 PM EDT)
*Paul Vishayanuroj (02/18/2011 10:43 PM EDT)
Sandipan Dey (02/19/2011 01:36 AM EDT)
Kalyana Chakravarthy (02/19/2011 02:06 AM EDT)
Fabian Eriksson (02/20/2011 05:46 PM EDT)
*Phil Benamy (02/21/2011 01:48 AM EDT)
Matthieu Jeanson (02/21/2011 04:37 PM EDT)
Robin Chandra (02/22/2011 09:01 AM EDT)
Ananda Raidu (02/22/2011 11:07 AM EDT)
Razvan Gheorghita (02/23/2011 01:42 AM EDT)
Kaverappa O T (02/23/2011 04:00 AM EDT)
*Bojan Basic (02/23/2011 11:44 AM EDT)
Dustin Lee (02/23/2011 02:58 PM EDT)
*Stephen Herbert (02/23/2011 07:30 PM EDT)
Niketh Nair (02/23/2011 10:40 PM EDT)
*Kiankok K (02/24/2011 12:47 PM EDT)
Jean Marcel Duvoisin Shmidt (02/24/2011 02:08 PM EDT)
Eugene Jorov (02/24/2011 04:37 PM EDT)
*Allen Wan (02/25/2011 06:10 AM EDT)
*Oliver Florian and Ludwig Maronna (02/25/2011 04:15 PM EDT)
*Mauro Bampo (02/26/2011 01:36 AM EDT)
*Tudor Coserea (02/26/2011 04:02 AM EDT)
Mindaugas Zaleckis (02/26/2011 11:39 AM EDT)
Gale Greenlee (02/27/2011 03:13 PM EDT)
Kenneth Kwok (02/28/2011 03:23 AM EDT)
Wolfgang Kais (02/28/2011 10:45 AM EDT)
Taher Jamshidi (02/28/2011 04:52 PM EDT)
Thomas Rohr (02/28/2011 05:18 PM EDT)
*Antonio García Astudillo (02/28/2011 06:16 PM EDT)
Gert Geringer (03/01/2011 02:20 AM EDT)
Oriol Vilanova (03/01/2011 06:13 AM EDT)

Attention: If your name is posted here and you wish it removed please send email to the webmaster.