Ponder This Challenge - February 2011 - Flippable number

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!

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Solution

• Click here to view the solution

  You can solve this challenge in several ways. By exhaustive search (checking all the possibilities), you can obtain the smallest answers: 5000261920005 for conditions A,B,and C, and 10962025901110652029601 for conditions A,B,and C'.

  A simpler solution is to examine numbers of the form 10^n+1 (100...001), which fulfill conditions A and B, and choose n such that condition C is fulfilled too. The first such solution is 10^335+1.

  10^n+1 will never fulfill condition C', so other patterns must be found. A possible solution is 5005*(10^303+1).

Solvers

• *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 (02/25/2011 04:15 PM EDT)
• 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)