Ponder This Challenge - July 2018 - Aging obscure triplets

This month's challenge is based on a riddle I heard from Odelia Moshe Ostrovsky (thanks!).

Let's call a triplet of natural numbers "obscure" if one cannot uniquely deduce them from their sum and product. For example, {2,8,9} is an obscure triplet, because {3,4,12} shares the same sum (19) and the same product (144).

Find a triplet of ages {a,b,c} that is obscure and stays obscure for three more years: {a+1,b+1,c+1}, {a+2,b+2,c+2} and {a+3,b+3,c+3}.

Solution

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  Most of you found the following solution:

  obscure triplet	sum	product	shared triplet
  {7,30,54} {8,31,55} {9,32,56} {10,33,57}	91 94 97 100	11340 13640 16128 18810	{10,18,63} {10,22,62} {12,21,64} {15,19,66}

Solvers

• Steven Langerwerf (27/06/18 04:01 PM IDT)
• Daniëlle van den Berg (27/06/18 04:31 PM IDT)
• Guillaume Escamocher (27/06/18 04:57 PM IDT)
• Davin Choo (27/06/18 05:25 PM IDT)
• Paolo Farinelli (27/06/18 05:41 PM IDT)
• Francisco Couzo (27/06/18 06:11 PM IDT)
• Daniel Chong Jyh Tar (27/06/18 06:46 PM IDT)
• Rickard Björklund (27/06/18 07:23 PM IDT)
• Bert Dobbelaere (27/06/18 19:26 IDT)
• Nguyen Khac Tung (27/06/18 07:49 PM IDT)
• *David F.H. Dunkley (27/06/18 07:52 PM IDT)
• Mark Mammel (27/06/18 09:46 PM IDT)
• *Uoti Urpala (27/06/18 09:47 PM IDT)
• Muralidhar Seshadri (27/06/18 09:53 PM IDT)
• *Alper Halbutogullari (27/06/18 10:04 PM IDT)
• Alex Fleischer (27/06/18 10:42 PM IDT)
• Nir Lavee & Omer Shechter (27/06/18 11:17 PM IDT)
• Joaquim Neves Carrapa (27/06/18 11:24 PM IDT)
• Susan Brommer (28/06/18 12:09 AM IDT)
• *Dieter Beckerle (28/06/18 12:15 AM IDT)
• *Noam Lasry (28/06/18 02:23 AM IDT)
• *Phil Muhm (28/06/18 06:26 AM IDT)
• Eric Loh (28/06/18 07:56 AM IDT)
• *Li Li (28/06/18 08:54 AM IDT)
• Alistair Ong (28/06/18 09:17 AM IDT)
• Loukas Sidiropoulos (28/06/18 10:28 AM IDT)
• Jiao Zi-Nan (28/06/18 10:35 AM IDT)
• Félix Breton (28/06/18 11:35 AM IDT)
• Graham Hemsley (28/06/18 01:44 PM IDT)
• Robson Moon (28/06/18 07:05 PM IDT)
• Todd Will (28/06/18 07:47 PM IDT)
• Kang Jin Cho (28/06/18 07:51 PM IDT)
• Franciraldo Cavalcante (28/06/18 08:37 PM IDT)
• Vladimir M. Milovanović (28/06/18 09:19 PM IDT)
• JJ Rabeyrin (28/06/18 10:57 PM IDT)
• Almog Yair (28/06/18 11:19 PM IDT)
• *David Greer (29/06/18 00:50 AM IDT)
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• *Igor Karp (29/06/18 04:15 AM IDT)
• Erik Hostens (29/06/18 12:43 PM IDT)
• Andreas Eisele (29/06/18 12:44 PM IDT)
• *Oleg Vlasii (29/06/18 01:37 PM IDT)
• Mykola Zubach (29/06/18 03:03 PM IDT)
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• Eden Saig (29/06/18 04:50 PM IDT)
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• *Andreas Stiller (29/06/18 09:42 PM IDT)
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• Dominik Reichl (30/06/18 06:50 PM IDT)
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• *Victor Chang (01/07/18 09:31 AM IDT)
• Rashid Naimi (01/07/18 10:37 AM IDT)
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• Vivek Nema (01/07/18 12:43 PM IDT)
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• Greg Janée (01/07/18 04:28 PM IDT)
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• *Keith Schneider (02/07/18 06:03 PM IDT)
• *Franciraldo Cavalcante (03/07/18 12:42 AM IDT)
• Darren Tan (03/07/18 07:26 AM IDT)
• Sanandan Swaminathan (03/07/18 07:33 AM IDT)
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• Michael Liepelt (06/07/18 05:03 PM IDT)
• Hao Zheng (06/07/18 06:38 PM IDT)
• Feyzullah Egriboyun (06/07/18 07:35 PM IDT)
• *Kang Jin Cho (07/07/18 07:57 AM IDT)
• *Allen Zhu (07/07/18 09:00 AM IDT)
• *Anonymous (07/07/18 11:24 AM IDT)
• Noam Zaks (07/07/18 02:39 PM IDT)
• *Ethan (EJ) Watkins (08/07/18 04:21 AM IDT)
• Raine Virta (08/07/18 11:09 AM IDT)
• Christian Pfaffenzeller (09/07/18 01:52 AM IDT)
• Yue Ru Sun (09/07/18 08:18 AM IDT)
• Boris Rakús (09/07/18 05:35 PM IDT)
• Ed Hall (09/07/18 06:31 PM IDT)
• David Friedman (10/07/18 05:39 AM IDT)
• Jordan Venderley (10/07/18 05:41 AM IDT)
• *Vladimir Volevich (10/07/18 11:24 AM IDT)
• Yasodhar (Pattu) Patnaik (10/07/18 02:22 PM IDT)
• Adam Kozdroń (10/07/18 02:44 PM IDT)
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• Bryce Fore (11/07/18 12:38 AM IDT)
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• Peter Gerritson (11/07/18 11:39 PM IDT)
• *Pi-Ching Liu (12/07/18 05:50 AM IDT)
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• *Motty Porat (13/07/18 03:26 PM IDT)
• *Tim Lewis (13/07/18 04:01 PM IDT)
• *Florian Fischer (14/07/18 10:10 AM IDT)
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• Yongxing Jim Wang (15/07/18 12:52 AM IDT)
• Fabio Michele Negroni (15/07/18 08:30 PM IDT)
• Stijn Theunis (16/07/18 03:51 PM IDT)
• Rajesh Sathiyanarayanan (16/07/18 07:58 PM IDT)
• Charles Joscelyne (17/07/18 01:12 PM IDT)
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• *Thomas Huet (17/07/18 10:05 PM IDT)
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• *Tom Sirgedas (20/07/18 01:00 AM IDT)
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• Sri Mallikarjun J (31/07/18 06:23 PM IDT)
• *Hugo Pfoertner (31/07/18 08:42 PM IDT)
• Itsik Horovitz (01/08/18 12:17 AM IDT)
• Radu-Alexandru Todor (01/08/18 02:26 AM IDT)