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Ponder This

May 2011

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Ponder This Challenge:

A barcode is composed of a series of variable-width white and black bars.

One of the important features of the barcode is that no bar be too wide; otherwise, the reader might get out of synchronization. Suppose we use the following barcode system, where we take a completely random sequence of bits and use it to build the bars. For example, the 7-bit-long sequence 0111001 will generate four bars of varying lengths: white(1), black(3), white(2), black(1). Such a system will generate, every once in a while, bars that are too wide. Let's call any black bar whose width is 20 bits or more a "bad bar".

What is the expected number of bits in the bars that are between two adjacent bad bars?


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Challenge: 05/01/2011 @ 10:00 AM EST
Solution: 06/01/2011 @ 10:00 AM EST
List Updated: 05/17/2011 @ 12:00 AM EST

People who answered correctly:

John T. Robinson (04/30/2011 01:32 AM EDT)
Dan Dima (04/30/2011 07:21 AM EDT)
Austin Shapiro (04/30/2011 08:07 PM EDT)
Jonathan Campbell (05/01/2011 12:41 AM EDT)
David Friedman (05/01/2011 01:39 AM EDT)
William Heller (05/01/2011 04:52 AM EDT)
Hubert Kahlert (05/01/2011 07:21 AM EDT)
Daniel Bitin (05/01/2011 06:16 PM EDT)
Jamie Niemasik (05/01/2011 06:49 PM EDT)
Jan Fricke (05/01/2011 07:23 PM EDT)
Matt Dobrin (05/02/2011 12:18 AM EDT)
Joshua Gunderson (05/02/2011 03:43 AM EDT)
Leif Jensen (05/02/2011 12:54 PM EDT)
Mark Perkins (05/02/2011 04:31 PM EDT)
Shlomi Hod & Ofir Reich (05/02/2011 08:59 PM EDT)
Rogerio Ponce da Silva (05/03/2011 10:07 AM EDT)
Joe Riel
(05/03/2011 12:14 PM EDT)
Ariel Flat (05/03/2011 01:40 PM EDT)
John Tromp (05/03/2011 02:22 PM EDT)
Shilei Zang (05/03/2011 02:51 PM EDT)
Arthur Breitman (05/03/2011 03:30 PM EDT)
Gale Greenlee (05/03/2011 04:32 PM EDT)
Harald van Dijk (05/03/2011 05:07 PM EDT)
Álvaro Begué (05/03/2011 05:19 PM EDT)
Rogerio Ponce da Silva (05/04/2011 12:13 PM EDT)
Nick McGrath (05/04/2011 12:41 PM EDT)
Joseph DeVincentis (05/04/2011 01:56 PM EDT)
Lu Wang (05/04/2011 02:27 PM EDT)
Siyu Yang (05/04/2011 02:59 PM EDT)
Matthew Paterson (05/04/2011 03:53 PM EDT)
Joshua Small (05/04/2011 10:51 PM EDT)
Donald T. Dodson (05/05/2011 04:01 PM EDT)
Nemo Publius (05/05/2011 04:19 PM EDT)
Guoxin Zhang (05/06/2011 01:14 PM EDT)
Adam and Lael Daire (05/06/2011 04:12 PM EDT)
Mark Mixer (05/08/2011 03:45 PM EDT)
Are Hjørungnes (05/08/2011 04:09 AM EDT)
Liubing Yu (05/08/2011 05:01 PM EDT)
Stephen Morris (05/08/2011 06:10 PM EDT)
J Noble Pendergrass (05/09/2011 04:35 PM EDT)
Or Zuk (05/10/2011 04:53 PM EDT)
James Dow Allen (05/10/2011 05:51 PM EDT)
John Snyder (05/12/2011 11:28 AM EDT)
Kipp Johnson & Nick Vigo (05/12/2011 11:52 AM EDT)
Thijmen Krebs (05/12/2011 01:00 PM EDT)
Geoff Kallweit (05/13/2011 04:05 PM EDT)
Motty Porat (05/13/2011 06:05 PM EDT)
John Black (05/13/2011 09:17 PM EDT)
Jeff Steele (05/15/2011 09:57 AM EDT)
Akshatha Nagesh & Sumanth Jagannath (05/15/2011 04:33 PM EDT)
Armin Krauss (05/16/2011 05:20 AM EDT)
Rino Raj (05/16/2011 09:29 AM EDT)
Ron Yu (05/16/2011 08:44 PM EDT)
John G. Fletcher (05/17/2011 01:26 AM EDT)
Ariel Landau (05/17/2011 03:49 PM EDT)
Martin Thiim (05/18/2011 10:15 AM EDT)
Christian Pape (05/18/2011 01:05 PM EDT)
Piet Orye (05/18/2011 02:33 PM EDT)
Joaquim Neves Carrapa (05/19/2011 11:50 AM EDT)
Hamidreza Bidar (05/19/2011 03:00 PM EDT)
Jon Evans (05/20/2011 03:44 PM EDT)
Joshua Katz (05/20/2011 04:43 PM EDT)
Andrea Andenna (05/22/2011 06:50 AM EDT)
Aliaksei Sanko (05/24/2011 08:40 AM EDT)
Hendrik Nigul (05/24/2011 08:45 AM EDT)
Jon Namnath (05/24/2011 07:15 PM EDT)
Pratik Poddar (05/26/2011 01:03 AM EDT)
Clive Tong (05/26/2011 07:56 AM EDT)
Raúl Mora Pastor (05/26/2011 12:00 AM EDT)
Karthik Kalyanam (05/26/2011 04:15 PM EDT)
Florian Fischer
(05/27/2011 01:12 PM EDT)
Vignesh Sethuraman (05/29/2011 02:13 PM EDT)
Ehud Schreiber (05/30/2011 05:04 AM EDT)
Vivek Nema (05/30/2011 11:21 AM EDT)
Bi Suzhi (05/30/2011 11:37 AM EDT)
Rafa Casado (05/30/2011 03:38 PM EDT)
Harald Bögeholz (05/30/2011 08:41 PM EDT)


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