Ponder This Challenge - January 2020 - 2 poisonous barrels

A gardener has 12 barrels of special fluid to water his orchids; exactly two of the barrels are poisonous. Using any amount, even a single drop, from a poisonous barrel will kill the precious orchid in 24 hours. The gardener has only three days before the orchids die unless he can figure out which ten barrels are the good ones. He is willing to sacrifice four orchids by watering them using a mix from a subset of these barrels. How can he find the poisonous barrels?

For example, for eight barrels labeled A, B, C, D, E, F, G, and H, only two days are enough:

In the first day he waters orchid #1 from barrel B, on the second day he uses a mix from barrels D and G; etc. Supply your answer in the format B.DG; DF.AB; AH.CF; C.GH (corresponding the solution to the example above).

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Solution

• Click here to view the solution

  There is a simple solution for 4 barrels and 1 day: A;B;C;D.

  Adding the prefix E,F,G,H provides a trivial solution for the example with 8 barrels and 2 days:
  E.A;F.B;G.C;H.D
  Alas, it does not work for our 12-barrel 3-day problem since I.E.A;J.F.B;K.G.C;K.H.D does not distinguish, for example, between IA and IE.

  However, the example we gave included a (very) large hint. You can add an I,J,K,L prefix to it and get the solution:
  I.B.DG;J.DF.AB;K.AH.CF;L.C.GH

  Thanks Patrik Holopainen for his blog Genetic Algorithms — Solving IBM’s January 2020 problem

Solvers

• Lorenz Reichel (01/01/2020 09:45 PM IDT)
• Guillermo Wildschut (02/01/2020 12:02 AM IDT)
• Bertram Felgenhauer (02/01/2020 12:29 AM IDT)
• Bert Dobbelaere (02/01/2020 04:39 PM IDT)
• Daniel Chong Jyh Tar (02/01/2020 05:45 AM IDT)
• Kevin Bauer (02/01/2020 06:42 PM IDT)
• Benjamin Phillabaum (03/01/2020 01:10 AM IDT)
• Hermann Jurksch (03/01/2020 05:45 AM IDT)
• Yusuf AttarBashi (03/01/2020 05:45 AM IDT)
• JJ Rabeyrin (03/01/2020 09:23 AM IDT)
• Alper Halbutogullari (03/01/2020 05:00 PM IDT)
• James Dow Allen (03/01/2020 01:32 PM IDT)
• David Greer (03/01/2020 02:33 PM IDT)
• Dominik Reichl (03/01/2020 03:07 PM IDT)
• Jingran Lin (03/01/2020 05:03 PM IDT)
• Alexander Ivrii (03/01/2020 05:12 PM IDT)
• Lorenzo Gianferrari Pini (04/01/2020 12:41 PM IDT)
• Florian Fischer (04/01/2020 06:02 PM IDT)
• Christopher Marks (04/01/2020 06:18 PM IDT)
• Kang Jin Cho (04/01/2020 08:53 PM IDT)
• David Smalling (04/01/2020 11:35 PM IDT)
• Graham Hemsley (05/01/2020 06:19 PM IDT)
• Arthur Vause (05/01/2020 06:33 PM IDT)
• Patrik Holopainen (05/01/2020 08:56 PM IDT)
• Dieter Beckerle (05/01/2020 10:57 PM IDT)
• Eden Saig (06/01/2020 12:17 AM IDT)
• Muralidhar Seshadri (06/01/2020 12:19 PM IDT)
• Paul Shaw (06/01/2020 07:08 PM IDT)
• Michael Liepelt (07/01/2020 01:52 PM IDT)
• Nyles Heise (09/01/2020 05:44 AM IDT)
• Glauber Guarinello (09/01/2020 01:52 PM IDT)
• Dimas Ramos (09/01/2020 03:54 PM IDT)
• Todd Will (09/01/2020 05:40 PM IDT)
• Jacoby Jaeger (10/01/2020 04:24 AM IDT)
• Guillaume Escamocher (10/01/2020 04:09 PM IDT)
• Yash Pote (10/01/2020 05:24 PM IDT)
• Walter Sebastian Gisler (12/01/2020 09:21 AM IDT)
• Harald Bögeholz (12/01/2020 10:04 AM IDT)
• Chuck Carroll (12/01/2020 10:10 PM IDT)
• Alex Fleischer (12/01/2020 12:18 PM IDT)
• Andreas Stiller (13/01/2020 02:25 AM IDT)
• Tamir Ganor Shoukey Dan (13/01/2020 11:23 AM IDT)
• Sanandan Swaminathan (14/01/2020 01:44 AM IDT)
• Pern Jie Quah (15/01/2020 02:16 PM IDT)
• Vladimir Volevich (15/01/2020 02:32 PM IDT)
• Joaquim Neves Carrapa (15/01/2020 07:51 PM IDT)
• Louis Slothouber (15/01/2020 08:00 PM IDT)
• Yue Kaidi (15/01/2020 08:37 PM IDT)
• Joerg Schepers (15/01/2020 09:53 PM IDT)
• Alexander Pozdneev (16/01/2020 09:55 AM IDT)
• Tyler Mullen (17/01/2020 07:19 AM IDT)
• David Keller (17/01/2020 06:39 PM IDT)
• Greg Janée (17/01/2020 11:07 PM IDT)
• Socal Surfer (18/01/2020 04:23 AM IDT)
• Salem Belhaj Letaief (20/01/2020 11:27 AM IDT)
• Kottmann Markus (20/01/2020 06:45 PM IDT)
• Dipto Thakurta (21/01/2020 11:27 PM IDT)
• Ralf Jonas (22/01/2020 02:40 PM IDT)
• Daniel Bitin (22/01/2020 04:24 PM IDT)
• Michel Hannoyer (24/01/2020 11:41 AM IDT)
• Motty Porat (26/01/2020 01:20 AM IDT)
• Fabio Michele Negroni (26/01/2020 09:52 AM IDT)
• Doug Miller (27/01/2020 01:21 AM IDT)
• Kolya Kolombet (27/01/2020 04:57 AM IDT)
• Latchezar Christov (27/01/2020 01:54 PM IDT)
• Vincent Beaud (27/01/2020 11:25 PM IDT)
• Khaled Fayed (27/01/2020 11:32 PM IDT)
• Andrew Mullins (27/01/2020 11:45 PM IDT)
• Anders Kaseorg (28/01/2020 07:08 PM IDT)
• Robert Lang (28/01/2020 07:49 PM IDT)
• Peter Gerritson (28/01/2020 08:06 PM IDT)
• Govind Jujare (28/01/2020 11:40 PM IDT)
• David Friedman (29/01/2020 01:22 AM IDT)
• Prashant Wankhede (29/01/2020 07:40 AM IDT)
• Soumitra Agarwal (31/01/2020 01:41 AM IDT)
• Erik Wünstel (01/02/2020 12:22 AM IDT)
• Franciraldo Cavalcante (01/02/2020 04:16 AM IDT)
• Li Li (01/02/2020 07:41 AM IDT)
• Oscar Volpatti (02/02/2020 07:00 AM IDT)
• Radu-Alexandru Todor (02/02/2020 08:46 PM IDT)