IBM Research | Ponder This | February 2011 challenges

# Ponder This

## February 2011

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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 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: 01/31/2011 @ 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)
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)
*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)
*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)
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)

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