Ponder This Challenge - May 2009 - Palindrome time

Ponder This Challenge:

Find all times that when viewed as

1. an analog watch, the second hand is a bisector of the angle between the minute hand and the hour hand.
2. a digital watch, the time is palindrome.

Update (05/01): To clarify: the time should satisfy both conditions when the analog clock moves continuously, while the digital one is rounded to the nearest second and shows the time in hh:mm:ss format.

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Solution

• Click here to view the solution

  Apart from the trivial 00:00:00, there are 00:55:00, 04:00:40, 04:55:40 and 10:11:01.
  using a 24 hours clock we have also 14:11:41, 20:22:02 and also 24:22:42 can be viewed as an answer. Allowing for h:mm:ss formats gives many more solutions.

Solvers

• Brian Hackney (04/30/2009 01:12 PM EDT)
• Dan Dima (04/30/2009 01:33 PM EDT)
• Dan Colestock (04/302009 07:25 PM EDT)
• JI Senshan (05/01/2009 10:57 AM EDT)
• Shail Bains (05/01/2009 11:20 AM EDT)
• Dmitry Litvinenko (05/01/2009 05:17 PM EDT)
• John T. Robinson (05/01/2009 01:17 PM EDT)
• Alan O'Donnell (05/01/2009 01:38 PM EDT)
• Bojan Basic (05/01/2009 07:04 PM EDT)
• Mallik Bulusu (05/02/2009 01:38 AM EDT)
• Hui Wang (05/02/2009 03:11 AM EDT)
• Are Hjørungnes (05/02/2009 03:40 AM EDT)
• Subhobrata Dey (05/02/2009 04:58 AM EDT)
• Eli Biham (05/02/2009 05:31 AM EDT)
• Zack Thomas (05/02/2009 11:19 AM EDT)
• Gale Greenlee (05/02/2009 12:26 PM EDT)
• Kalyana Chakravarthy (05/02/2009 02:53 PM EDT)
• Nick Miller (05/02/2009 03:46 PM EDT)
• Joseph DeVincentis (05/02/2009 10:23 PM EDT)
• Mingque Wu (05/03/2009 12:25 AM EDT)
• Tiago Brito (05/03/2009 04:02 AM EDT)
• Chris French (05/03/2009 12:08 PM EDT)
• Satish Kumar K N (05/2009 12:24 PM EDT)
• Markus Nauroth (05/03/2009 01:25 PM EDT)
• Gary M Gerken (05/03/2009 04:36 PM EDT)
• Bill Magaletta (05/03/2009 07:55 PM EDT)
• Sridivakar Inakonda (05/042009 01:26 AM EDT)
• John G Fletcher (05/04/2009 03:32 AM EDT)
• Daniel Chong Jyh Tar (05/04/2009 03:16 AM EDT)
• Ankur Gupta (05/04/2009 09:49 AM EDT)
• Jonathan Campbell (05/04/2009 11:20 AM EDT)
• Paul Fodor (05/04/2009 12:54 PM EDT)
• Steffen Wolf (05/04/2009 01:10 PM EDT)
• Joe Fendel (05/04/2009 06:24 PM EDT)
• Giorgio Antonelli (05/04/2009 06:44 PM EDT)
• Wolf Mosle (05/04/2009 09:43 PM EDT)
• Ioan Marius Popdan (05/05/2009 10:09 AM EDT)
• Abhisek Ukil (05/05/2009 10:24 AM EDT)
• Albert Stadler (05/05/2009 12:55 PM EDT)
• Michael Schaaf (05/05/2009 01:31 PM EDT)
• Kai Guttmann (05/05/2009 01:11 PM EDT)
• Robert DiMarco (05/05/2009 01:48 PM EDT)
• Andreea Fodor (05/05/2009 02:28 PM EDT)
• Francois Galilee (05/05/2009 03:17 PM EDT)
• Michael Liepelt (05/05/2009 04:22 PM EDT)
• David Friedman (05/05/2009 08:06 PM EDT)
• Karthik Thyagaraja (05/05/2009 10:17 PM EDT)
• Bobby Brennan (05/06/2009 03:23 AM EDT)
• Fred Schalekamp (05/06/2009 03:56 AM EDT)
• James Carter (05/06/2009 04:14 AM EDT)
• Corey Cerovsek (05/06/2009 06:43 AM EDT)
• Parashar Dave (05/06/2009 09:27 AM EDT)
• Pataki Gergely (05/06/2009 03:36 PM EDT)
• Matt Hickford & James Brister (05/06/2009 04:53 PM EDT)
• Jeff Blohm (05/06/2009 08:28 PM EDT)
• Don Dodson & David Dodson (05/06/2009 12:59 PM EDT)
• Byron Rakitzis (05/07/2009 04:12 AM EDT)
• Latchezar Christov (05/07/2009 06:34 AM EDT)
• Adrian Eddy (05/07/2009 07:36 AM EDT)
• Michael Swart (05/07/2009 04:52 PM EDT)
• S (05/07/2009 06:03 PM EDT)
• achin Tendulkar (05/07/2009 06:03 PM EDT)
• Amos Guler (05/07/2009 06:54 PM EDT)
• Gaurav Raizada (05/08/2009 02:02 AM EDT)
• Shmuel Menachem Spiegel (05/08/2009 03:30 AM EDT)
• Nicusor Timneanu (05/08/2009 04:29 AM EDT)
• Britt Fugitt (05/08/2009 06:55 PM EDT)
• Anant Mudambi (05/09/2009 01:53 PM EDT)
• Graham McHardy (05/09/2009 09:57 PM EDT)
• Guy Tannenbaum (05/10/2009 04:23 AM EDT)
• Vivek Nema (05/11/2009 03:41 AM EDT)
• Jeff Steele (05/11/2009 11:02 PM EDT)
• Yu Yat Hong (05/12/2009 12:48 AM EDT)
• Jens Voss (05/12/2009 11:01 AM EDT)
• Balakrishnan V (05/12/2009 03:44 PM EDT)
• Leandro Bugnon (05/13/2009 03:10 AM EDT)
• Pritpal Ahuja (05/13/2009 07:42 PM EDT)
• Matthew Paterson (05/13/2009 09:36 PM EDT)
• Cristina Popdan (05/14/2009 06:27 AM EDT)
• Nyles Heise (05/14/2009 11:17 PM EDT)
• Jack Rouse (05/15/2009 10:28 AM EDT)
• Karl D'Souza (05/15/2009 11:50 AM EDT)
• Kin-Keung Ma (05/15/2009 08:57 PM EDT)
• Mauro Bampo (05/16/2009 01:50 AM EDT)
• Sun Hongkai (05/17/2009 09:21 AM EDT)
• Fabio Filatrella (05/17/2009 10:22 AM EDT)
• Tadinada Karthik (05/18/2009 07:15 AM EDT)
• Tadej Svetek (05/18/2009 09:56 AM EDT)
• Amol Lahane (05/18/2009 10:38 AM EDT)
• Ganesh Pagade (05/18/2009 10:40 AM EDT)
• Thomas Rohr (05/18/2009 10:43 AM EDT)
• Milan Jovanov (05/19/2009 10:48 AM EDT)
• Jochen Hoenicke (05/19/2009 01:28 PM EDT)
• Ionel Santa (05/20/2009 06:16 AM EDT)
• Andrea Andenna (05/20/2009 06:43 AM EDT)
• Sevag Papazian (05/20/2009 07:46 AM EDT)
• Brandon Fitz (05/20/2009 04:18 PM EDT)
• Mihai Cioc (05/21/2009 03:08 PM EDT)
• Joseph Bonneau (05/21/2009 09:51 PM EDT)
• Vladi Tsipenyuk (05/22/2009 04:17 AM EDT)
• Harish Haridas (05/22/2009 06:04 AM EDT)
• Arunkumar Sundararajan (05/22/2009 09:20 AM EDT)
• Beat Gfeller (05/23/2009 12:00 AM EDT)
• Martin Walochnik (05/24/2009 09:21 PM EDT)
• Jessica Callaghan (05/24/2009 11:00 PM EDT)
• Dan Peleg (05/25/2009 04:26 PM EDT)
• Steven Langerwerf (05/26/2009 06:51 AM EDT)
• Siva Dirisala (05/27/2009 01:51 AM EDT)
• Alexandru Nicau (05/27/2009 10:38 AM EDT)
• Mario Patino (05/28/2009 06:25 AM EDT)
• Adriana Clerici (05/28/2009 12:16 PM EDT)
• Chris Shannon (05/29/2009 06:46 PM EDT)
• Philipp Beau (05/29/2009 05:59 AM EDT)
• Gurunandan Pai and Ranjit Eswaran (05/29/2009 09:48 AM EDT)
• A (05/30/2009 09:37 PM EDT)
• marpal Singh (05/30/2009 09:37 PM EDT)
• Lilesh Ghadi (05/31/2009 03:35 AM EDT)
• Boris Nikolaus (05/31/2009 08:59 AM EDT)
• Uri Yanover (05/31/2009 04:25 PM EDT)
• Edgardo Deza (05/31/2009 07:35 PM EDT)
• Samuel Schwager (05/31/2009 10:50 PM EDT)
• Ivan Tsoi (06/01/2009 00:41 AM EDT)