# Ponder This

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## March 2017 - Challenge

Ponder This Challenge:

An octopus has eight arms. Let's name them as A, B, C,...,H. We have eight octopuses. Let's call them 1, 2,...,8. Each octopus is wearing an analog wrist watch on each of its arms (for a total of 64 watches).
To adjust the hour on the watches, we can move all the watches of a single octopus (#3 for example) one hour ahead, or move all the watches on a specific arm of all the octopuses (arm C for example) one hour ahead.
All the watches have marks at the hours of 12, 3, 6, and 9. We would like to make as many watches as possible point to one of the four marks.

If the initial times of all the watches are as follows:

```
A  B  C  D  E  F  G  H
1  1  2  3  4  5  6  7  8
2  2  4  6  8 10 12  2  4
3  3  6  9 12  3  6  9 12
4  4  8 12  4  8 12  4  8
5  5 10  3  8  1  6 11  4
6  6 12  6 12  6 12  6 12
7  7  2  9  4 11  6  1  8
8  8  4 12  8  4 12  8  4

```

By applying a sequence of adjustments as described above, we can get 43 watches to point to a mark (how?).
Your challenge is to find an initial configuration for the 64 watches which, after any legal sequence of adjustments, will result in no more than 37 watches pointing to a mark.
Bonus '*' for each watch below 37.

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: 27/02/2017 @ 12:00 PM EST
Solution: 02/04/2017 @ 12:00 PM EST
List Updated: 02/04/2017 @ 12:00 PM EST

*Robert Gerbicz (27/02/2017 04:18 PM IDT)
Joseph DeVincentis (27/02/2017 07:16 PM IDT)
Jesse Rearick (28/02/2017 03:52 AM IDT)
Johan de Ruiter (28/02/2017 08:04 AM IDT)
Bert Dobbelaere (28/02/2017 10:15 AM IDT)
Hanlin Ren (28/02/2017 10:22 AM IDT)
*Oleg Vlasii (28/02/2017 11:45 AM IDT)
Lorenz Reichel (28/02/2017 12:01 PM IDT)
*Yan-Wu He (28/02/2017 04:46 PM IDT)
Reiner Martin (28/02/2017 04:05 PM IDT)
Georgiy Korneev (28/02/2017 09:41 PM IDT)
Steven Langerwerf (28/02/2017 11:08 PM IDT)
*Uoti Urpala (01/03/2017 05:57 AM IDT)
Harald Bögeholz (01/03/2017 01:23 PM IDT)
*Sergey Koposov (01/03/2017 04:23 PM IDT)
Tyler Mullen (02/03/2017 11:46 AM IDT)
Paolo Farinelli (02/03/2017 02:44 PM IDT)
*Daniëlle van den Berg (02/03/2017 06:07 PM IDT)
Ben Bogardus (02/03/2017 09:17 PM IDT)
Sergey Shashkov (03/03/2017 12:52 AM IDT)
Maxim Yurchuk (03/03/2017 02:02 PM IDT)
Denis Yermolov (03/03/2017 05:21 PM IDT)
*Siddharth Joshi (03/03/2017 07:19 PM IDT)
Adrian Orzepowski (03/03/2017 10:40 PM IDT)
Armin Krauss (04/03/2017 12:40 AM IDT)
*Motty Porat (04/03/2017 07:00 PM IDT)
*Andreas Stiller (04/03/2017 07:09 PM IDT)
JJ Rabeyrin (04/03/2017 07:29 PM IDT)
Aleksey Nekrasov (04/03/2017 08:46 PM IDT)
Liubing Yu (05/03/2017 10:52 PM IDT)
*Anatoly Vorobey (06/03/2017 01:25 PM IDT)
Shirish Chinchalkar (07/03/2017 04:43 AM IDT)
*Aviv Nisgav (07/03/2017 07:31 AM IDT)
*Dmitry Kim (08/03/2017 03:42 AM IDT)
Susan Brommer (09/03/2017 03:47 PM IDT)
Al Zimmermann (09/03/2017 08:34 PM IDT)
Alex Fleischer (11/03/2017 10:11 AM IDT)
Thomas Satzger (11/03/2017 01:32 PM IDT)
Peter Gerritson (11/03/2017 10:14 PM IDT)
*Leonid Kalmankin (12/03/2017 08:48 AM IDT)
*Hanlin Ren (14/03/2017 12:43 PM IDT)
Stéphane Higueret (15/03/2017 07:48 PM IDT)
*Alexander Korshkov (16/03/2017 07:32 PM IDT)
Matan Nov (19/03/2017 09:03 AM IDT)
*David Greer (19/03/2017 10:51 PM IDT)
Abdelrahman Hammad (21/03/2017 10:57 PM IDT)
*Stephen Lesko (23/03/2017 09:30 PM IDT)
Daniel Bitin (24/03/2017 06:00 PM IDT)
David F.H. Dunkley (25/03/2017 10:49 PM IDT)
Chris Shannon (29/03/2017 10:12 AM IDT)
*Pieter Vandercammen (29/03/2017 10:58 PM IDT)
Pål Hermunn Johansen (31/03/2017 12:05 PM IDT)
Joaquim Neves Carrapa (31/03/2017 05:31 PM IDT)
*Oscar Volpatti (01/04/2017 02:58 PM IDT)
*Alexander Chetverin (01/04/2017 07:34 AM IDT)