IBM Research | Ponder This | August 2016 challenges

Ponder This

August 2016

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Ponder This Challenge:

A king receives 10 bags of N golden coins each. Each coin should weigh exactly 10 grams, but some bags contain (only) counterfeit coins that weigh exactly 9 grams each.
If N>=512 then one can identify the counterfeit bags using a single measurement with an accurate weighing scale. (How?)
Our challenge this month is to find a way to identify the counterfeit bags, when we know that there are at most three such bags out of the ten, and when N=174.
Bonus '*' for solving it with even smaller N.

Update (4/8): To get a '**' find a solution for the minimal N.

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: 31/07/2016 @ 12:00 PM EST
Solution: 01/02/2016 @ 12:00 PM EST
List Updated: 28/08/2016 @ 12:00 PM EST

**Lorenz Reichel (31/07/2016 05:27 PM IDT)
**Paolo Farinelli (31/07/2016 08:11 PM IDT)
**Robert Gerbicz (31/07/2016 09:36 PM IDT)
**Oleg Vlasii (31/07/2016 10:50 PM IDT)
**Uoti Urpala (31/07/2016 11:48 PM IDT)
**Florian Fischer (01/08/2016 01:59 AM IDT)
**Hanlin Ren (01/08/2016 06:21 PM IDT)
**Bert Dobbelaere (01/08/2016 06:43 PM IDT)
*James Dow Allen (01/08/2016 11:04 PM IDT)
Mathias Schenker (01/08/2016 11:12 PM IDT)
**Tom Sirgedas (02/08/2016 01:45 AM IDT)
Isaac Simmons (02/08/2016 05:03 AM IDT)
Thomas Egense (02/08/2016 10:10 AM IDT)
Clive Tong (02/08/2016 10:33 AM IDT)
*Benjamin Lui (02/08/2016 01:54 PM IDT)
**Amos Guler (03/08/2016 12:20 AM IDT)
**David F.H. Dunkley (03/08/2016 02:38 AM IDT)
Shirish Chinchalkar (03/08/2016 04:22 AM IDT)
**Sean Egan (03/08/2016 04:45 AM IDT)
Ran Sharon (03/08/2016 06:45 AM IDT)
**Toke Eskildsen (03/08/2016 08:02 AM IDT)
*Aditya Gurunathan (03/08/2016 11:45 AM IDT)
*Liubing Yu (03/08/2016 06:56 PM IDT)
**Andreas Stiller (04/08/2016 03:49 AM IDT)
*Balakrishnan Varadarajan (04/08/2016 05:29 AM IDT)
**Pål Hermunn Johansen (04/08/2016 10:25 PM IDT)
**Dieter Beckerle (05/08/2016 12:08 AM IDT)
*Sergey E. Koposov (05/08/2016 01:27 AM IDT)
Jing Xiao (05/08/2016 05:40 AM IDT)
Koon Hui Geoffrey Goh (05/08/2016 12:50 PM IDT)
Reiner Martin (06/08/2016 08:07 AM IDT)
*Raymond Lo (06/08/2016 11:36 AM IDT)
**Wilder Boyden (06/08/2016 10:31 PM IDT)
**Serge Batalov (07/08/2016 10:00 PM IDT)
Michael D Schuresko (08/08/2016 12:04 AM IDT)
*Harald Bögeholz (08/08/2016 12:17 PM IDT)
**Daniel Chong Jyh Tar (08/08/2016 12:44 PM IDT)
Dejan Stakić (08/08/2016 07:18 PM IDT)
**José Eduardo Gaboardi de Carvalho (09/08/2016 08:10 PM IDT)
Todd Will (10/08/2016 12:12 AM IDT)
**Kang Jin Cho (10/08/2016 09:41 AM IDT)
Ayaskant Pani (10/08/2016 11:15 PM IDT)
Tamir Ganor & Shouky Dan (12/08/2016 11:01 AM IDT)
*Joseph DeVincentis (12/08/2016 10:44 PM IDT)
**Francis Golding (13/08/2016 11:27 AM IDT)
Jimmy Waters (13/08/2016 01:45 PM IDT)
Peter Gerritson (14/08/2016 06:33 PM IDT)
**David Greer (15/08/2016 12:53 AM IDT)
*Yuan Li (15/08/2016 11:09 AM IDT)
*Yuan Li & Ye Fan (15/08/2016 11:09 AM IDT)
**Aviv Nisgav (15/08/2016 03:00 PM IDT)
**Gary M. Gerken (16/08/2016 05:09 AM IDT)
**Yan-Wu He (16/08/2016 07:59 AM IDT)
Jason Lee (16/08/2016 07:37 PM IDT)
**Siddharth Joshi (18/08/2016 02:14 PM IDT)
Itay Hazan (19/08/2016 10:44 AM IDT)
Fabio Michele Negroni (20/08/2016 09:20 PM IDT)
Nagendra Gulur (21/08/2016 06:19 AM IDT)
**Arthur Vause (21/08/2016 05:33 PM IDT)
**Bryce Fore (22/08/2016 12:12 AM IDT)
**Emir Haleva (22/08/2016 08:47 AM IDT)
Alex Fleischer (22/08/2016 10:47 AM IDT)
*Jim Clare (22/08/2016 01:21 PM IDT)
**Teake Nutma (22/08/2016 01:44 PM IDT)
*Claudio Baiocchi (23/08/2016 12:20 PM IDT)
Nigel Brumpton (24/08/2016 11:39 AM IDT)
*David Vainapel (26/08/2016 09:57 AM IDT)
Fabio Filatrella (26/08/2016 12:27 PM IDT)
*Gale Greenlee (26/08/2016 05:48 PM IDT)
J. Eric Ivancich (26/08/2016 07:43 PM IDT)
**Zoltan Haindrich (26/08/2016 10:22 PM IDT)
**Jess Thrysoee (27/08/2016 03:27 PM IDT)
Maple Guan July (27/08/2016 09:59 PM IDT)
**Daniel Bitin (27/08/2016 11:22 PM IDT)
*Nyles Heise (28/08/2016 07:11 AM IDT)
Ante Turudic (28/08/2016 08:56 PM IDT)
**Motty Porat (29/08/2016 12:07 AM IDT)
Julian Ma & Louise Lam (29/08/2016 02:39 AM IDT)
**Tommi Libdgren (29/08/2016 10:34 AM IDT)
Jesse Rearick (30/08/2016 04:19 PM IDT)
*Steve Dalton (30/08/2016 05:14 PM IDT)
**LaurV (30/08/2016 08:31 PM IDT)
**Armin Krauss (31/08/2016 11:44 AM IDT)
*Jens Voss (31/08/2016 03:24 PM IDT)
*Erik Wünstel (31/08/2016 05:07 PM IDT)
*Radu-Alexandru Todor (31/08/2016 10:19 PM IDT)
**Hugo Pfoertner (01/09/2016 12:26 AM IDT)
**Rogerio Ponce da Silva (01/09/2016 05:55 PM IDT)