# Ponder This

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## February 2017 - Challenge

Ponder This Challenge:

When you run the following pseudo code on a sequence of six bits, in exactly 14 cases you get a non-zero value. How many such cases would you get for all sequences of 42 bits?

```s=2
r=0
for b in v:
if (s modulo 7) = b:
r = r+2*b-1
s = 6+s*(5+s*s*s*(2+s*(3+s))) + b*(5+s*(5+s*(6+s*s*(3+s*6))))
return r
```

Bonus question: If we would have asked a similar question for sequences of 14 bits, what would be the connection of the result to IBM?

Hint: We asked a similar bonus question in the past, and the number of solvers was then a multiplication of two prime numbers.

Update (8/2):
A. The "for b in v" part means that for every binary sequence v of length 42, perform the next three lines 42 times when the binary variable b goes over all the bits of v.
B. Note that to bet the bonus '*' you need to solve *a similar* problem...

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: 30/01/2017 @ 12:00 PM EST
Solution: 02/03/2017 @ 12:00 PM EST
List Updated: 06/03/2017 @ 12:00 PM EST

*Robert Gerbicz (30/01/2017 05:02 PM IDT)
Motty Porat (30/01/2017 06:00 PM IDT)
*Oleg Vlasii (30/01/2017 06:42 PM IDT)
*Bert Dobbelaere (30/01/2017 09:21 PM IDT)
Uoti Urpala (30/01/2017 10:56 PM IDT)
Tyler Mullen (30/01/2017 11:29 PM IDT)
*George W Barnett (31/01/2017 09:01 AM IDT)
Hanlin Ren (31/01/2017 09:47 AM IDT)
Aviv Nisgav (31/01/2017 03:53 PM IDT)
*Shwetabh Garg (31/01/2017 05:00 PM IDT)
Kang Jin Cho (31/01/2017 05:51 PM IDT)
Armin Krauss (31/01/2017 06:24 PM IDT)
Jesse Rearick (01/02/2017 04:41 AM IDT)
Ran Sharon (01/02/2017 04:14 PM IDT)
Joseph DeVincentis (01/02/2017 04:26 PM IDT)
Reiner Martin (01/02/2017 11:06 PM IDT)
Shirish Chinchalkar (02/02/2017 02:18 AM IDT)
Raymond Lo (02/02/2017 08:42 AM IDT)
Lorenz Reichel (02/02/2017 09:26 AM IDT)
*Teake Nutma (02/02/2017 11:32 AM IDT)
Dan Dima (02/02/2017 01:55 PM IDT)
Sergey Koposov (02/02/2017 05:20 PM IDT)
Yan-Wu He (02/02/2017 05:34 PM IDT)
Sebastian Bohm & Martí Bosch (02/02/2017 07:52 PM IDT)
JJ Rabeyrin (03/02/2017 02:05 AM IDT)
Kipp Johnson (03/02/2017 05:05 AM IDT)
Bryce Fore (03/02/2017 06:23 AM IDT)
Adrian Orzepowski (03/02/2017 02:51 PM IDT)
Paolo Farinelli (03/02/2017 06:10 PM IDT)
Pieter Meijer (04/02/2017 01:24 AM IDT)
Liubing Yu (04/02/2017 01:45 PM IDT)
Daniel Blazewicz (04/02/2017 08:01 PM IDT)
David F.H. Dunkley (05/02/2017 02:03 AM IDT)
Siddharth Joshi (06/02/2017 09:47 AM IDT)
Steven Langerwerf (06/02/2017 11:58 AM IDT)
Mathias Schenker (06/02/2017 05:33 PM IDT)
Stijn Vermeeren (07/02/2017 07:17 PM IDT)
Todd Will (07/02/2017 11:11 PM IDT)
Serge Batalov (08/02/2017 07:02 AM IDT)
Muralidhar Seshadri (08/02/2017 07:37 PM IDT)
Leandro Augusto de Araújo Silva (08/02/2017 08:08 PM IDT)
Peter Gerritson (09/02/2017 09:23 PM IDT)
Dieter Beckerle (09/02/2017 11:47 PM IDT)
Sean Egan (10/02/2017 09:50 AM IDT)
*Anders Bisbjerg Madsen (10/02/2017 03:22 PM IDT)
Daniel Bitin (10/02/2017 05:49 PM IDT)
Sergey Grishaev (11/02/2017 12:59 AM IDT)
Martin Thiim (12/02/2017 12:51 PM IDT)
Ricardo Koller (12/02/2017 10:02 PM IDT)
William Gunther (13/02/2017 01:34 AM IDT)
David Greer (13/02/2017 06:39 PM IDT)
Andreas Stiller (13/02/2017 07:37 PM IDT)
*Paul McKenney (13/02/2017 09:57 PM IDT)
Yoni Tate (14/02/2017 06:09 PM IDT)
Jim Clare (15/02/2017 12:52 AM IDT)
Michael J. Swart (15/02/2017 05:15 PM IDT)
William Mantzel (16/02/2017 12:05 AM IDT)
Susan Brommer (16/02/2017 07:30 PM IDT)
Thomas Satzger (17/02/2017 12:33 AM IDT)
Radu Haiduc (17/02/2017 02:33 AM IDT)
Stéphane Higueret (18/02/2017 07:40 AM IDT)
Dan Ignatoff (19/02/2017 08:38 AM IDT)
*Shouky Dan & Tamir Ganor (19/02/2017 07:32 PM IDT)
Alessandro Marzo (21/02/2017 06:01 PM IDT)
Adir HaCohen (22/02/2017 09:16 AM IDT)
Adrian Neacsu (24/02/2017 06:57 PM IDT)
Anatoly Vorobey (25/02/2017 03:01 AM IDT)
Nyles Heise (26/02/2017 07:10 AM IDT)
Vladimir M. Milovanović (26/02/2017 01:14 PM IDT)
Chris Shannon (27/02/2017 10:01 AM IDT)
Georgiy Korneev (28/02/2017 08:05 PM IDT)
Erik Wünstel (28/02/2017 11:13 PM IDT)
Radu-Alexandru Todor (28/02/2017 01:28 PM IDT)
Douglas Rofes (01/03/2017 09:41 AM IDT)
Michael Golubev (01/03/2017 09:48 AM IDT)
Martin Sergio H. Faester (01/03/2017 04:32 PM IDT)
Maxim Razin (02/03/2017 04:30 AM IDT)