Puzzle
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Ponder This Challenge - October 2019 - Five banknotes II

Let's assume that Alice and Bob have two (possibly the same) integer amounts of money, uniformly distributed in the [0,99] range with a minimal number of banknotes.
Using the standard US dollar banknotes denominations of 1, 5, 10, 20, and 50, if the set of notes of Alice and Bob is the same - the probability of the amount being the same is about 21%.
Your task, this month, is to find the set of five banknote denominations that uniquely determines the set with the minimal number of notes while maximizing the above probability.

Solution

  • The best set of five possible banknote denominations that maximizes the probability of two amounts in the [0,99] range being the same is 1, 2, 12, 16, and 48, which gives a probability of ~29.07%.

Solvers

  • Alper Halbutogullari (02/10/2019 04:25 PM IDT)
  • Uoti Urpala (02/10/2019 05:12 PM IDT)
  • Lorenz Reichel (02/10/2019 08:02 PM IDT)
  • Dieter Beckerle (02/10/2019 11:36 PM IDT)
  • Bert Dobbelaere (02/10/2019 11:53 PM IDT)
  • Eden Saig (03/10/2019 12:07 AM IDT)
  • John Reid (03/10/2019 02:24 AM IDT)
  • Andreas Stiller (03/10/2019 02:46 AM IDT)
  • David Greer (03/10/2019 04:03 AM IDT)
  • Sanandan Swaminathan (03/10/2019 04:25 AM IDT)
  • Amos Guler (03/10/2019 09:55 AM IDT)
  • Ayush Jain (03/10/2019 12:27 PM IDT)
  • Colas Kerkhove (03/10/2019 12:37 PM IDT)
  • James Dow Allen (03/10/2019 04:06 PM IDT)
  • Alex Fleischer (03/10/2019 04:36 PM IDT)
  • Daniel Chong Jyh Tar (03/10/2019 04:53 PM IDT)
  • Erik Hostens (03/10/2019 06:37 PM IDT)
  • Graham Hemsley (03/10/2019 07:32 PM IDT)
  • Calvin Pozderac (04/10/2019 12:59 AM IDT)
  • Collin Pearce (04/10/2019 04:00 AM IDT)
  • Motty Porat (04/10/2019 02:10 PM IDT)
  • Benjamin Lui (04/10/2019 05:58 PM IDT)
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  • Todd Will (04/10/2019 08:59 PM IDT)
  • Greg Janée (04/10/2019 09:20 PM IDT)
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  • Jacoby Jaeger (05/10/2019 04:01 AM IDT)
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  • Paul McKenney (05/10/2019 09:36 PM IDT)
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  • Keith Schneider (06/10/2019 07:45 AM IDT)
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  • Thomas Huet (08/10/2019 08:55 AM IDT)
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  • Guillaume Escamocher (09/10/2019 03:08 PM IDT)
  • Sebastian Bohm & Martí Bosch (09/10/2019 03:27 PM IDT)
  • Raymond Lo (09/10/2019 04:28 PM IDT)
  • Kang Jin Cho (09/10/2019 05:19 PM IDT)
  • Latchezar Christov (09/10/2019 07:39 PM IDT)
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  • Almog Yair (10/10/2019 06:28 PM IDT)
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  • Richard Gosiorovsky (11/10/2019 08:47 AM IDT)
  • Wilder Boyden & Michael Leslie (11/10/2019 09:35 PM IDT)
  • Victor Chang (12/10/2019 07:52 PM IDT)
  • Dominik Reichl (13/10/2019 12:46 PM IDT)
  • Stanislav Grudnitskiy (13/10/2019 06:44 PM IDT)
  • Muhammed Halbutogullari (14/10/2019 12:23 AM IDT)
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  • Kevin Bauer (14/10/2019 05:45 PM IDT)
  • Victorien Cornet (14/10/2019 05:53 PM IDT)
  • Michael Liepelt (14/10/2019 07:42 PM IDT)
  • Dan Salajan (15/10/2019 01:37 AM IDT)
  • Arthur Vause (16/10/2019 0:47 AM IDT)
  • Peter Gerritson (16/10/2019 8:50 PM IDT)
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  • Chen Yingxiang (18/10/2019 06:03 PM IDT)
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  • John Goh Choo Ern (25/10/2019 04:40 AM IDT)
  • Albert Stadler (25/10/2019 08:47 AM IDT)
  • Paolo Farinelli (25/10/2019 12:58 AM IDT)
  • Nyles Heis (26/10/2019 01:28 AM IDT)
  • Alistair Letcher (28/10/2019 01:26 PM IDT)
  • David F.H. Dunkley (30/10/2019 10:44 AM IDT)
  • Ken Dsouza (30/10/2019 11:34 PM IDT)
  • Damien Devlies (31/10/2019 12:27 PM IDT)
  • Oscar Volpatti (31/10/2019 04:37 PM IDT)
  • Reiner Martin (31/10/2019 08:23 PM IDT)
  • Radu-Alexandru Todor (01/11/2019 02:37 AM IDT)
  • Glauber de Lima Guarinello (06/11/2019 09:14 PM IDT)

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