Ponder This Challenge - September 2019 - Five banknote denominations

The US dollar has five common banknote denominations: 1, 5, 10, 20, and 50.
Each integer dollar value between 0 and 99 dollars can be paid in a unique way with a minimal number of notes.
If Alice and Bob each have different amounts of money, they still can have the same set of notes.
For example, if Alice has $92 and Bob has $74 (in a minimal number of notes), they both have the same set of banknotes {1,20,50}.
Let's assume that Alice and Bob have two different random amounts of money uniformly distributed in the [0,99] range with a minimal number of banknotes.
The probability that they have the same set of banknotes is approximately 3.79798%.

Your task, this month, is to find another set of five banknotes such that:

1. Each integer dollar value between 0 and 99 dollars can be paid in a unique way with a minimal number of notes; and
2. The probability above (same set of banknotes for two different random amounts of money uniformly distributed in the [0,99] range) would be exactly 4%.

Solution

• Click here to view the solution

  Many of you got the 1, 2, 4, 8, 62 solution, but there are others. The closest to the original set of notes is 1, 5, 10, 34, 50 (replacing the $20 bill with a$34 note).
  Thanks to JJ Rabeyrin who told us about the relevant paper "What This Country Needs is an 18-cent Piece".

  Thanks to Yasodhar (Pattu) Patnaik, for sending us a nice visualization you can play with: https://yamapa2.github.io/
  Thanks also to Collin Pearce for a solution to a different question (to find a range of values, such that the standard set of bills, will give a 4% chance of selecting two different values with the same bill set).

Solvers

• Alex Fleischer (05/09/2019 11:12 AM IDT)
• Alper Halbutogullari (09/09/2019 03:23 AM IDT)
• Gary M. Gerken (09/09/2019 07:43 AM IDT)
• Reiner Martin (09/09/2019 01:03 PM IDT)
• John Goh (09/09/2019 02:06 PM IDT)
• Guillaume Escamocher (09/09/2019 04:42 PM IDT)
• Almog Yair (09/09/2019 05:26 PM IDT)
• Lachezar Hristov (09/09/2019 06:24 PM IDT)
• Daniel Oliveira (09/09/2019 07:36 PM IDT)
• Uoti Urpala (09/09/2019 08:19 PM IDT)
• Bert Dobbelaere (09/09/2019 10:23 PM IDT)
• Tero Patana (10/09/2019 03:51 AM IDT)
• Hugo Pfoertner (10/09/2019 04:15 AM IDT)
• Jacoby Jaeger (10/09/2019 04:48 AM IDT)
• Doug Miller (10/09/2019 04:59 AM IDT)
• Daniel Chong Jyh Tar (10/09/2019 05:35 AM IDT)
• Ariel Landau (10/09/2019 05:37 AM IDT)
• Eden Saig (10/09/2019 07:23 AM IDT)
• Tamás Haba (10/09/2019 09:59 AM IDT)
• Thomas Huet (10/09/2019 11:17 AM IDT)
• Arthur Vause (10/09/2019 11:32 AM IDT)
• Todd Will (10/09/2019 05:35 PM IDT)
• Dieter Beckerle (10/09/2019 06:45 PM IDT)
• JJ Rabeyrin (10/09/2019 10:17 PM IDT)
• Lorenz Reichel (10/09/2019 10:19 PM IDT)
• Daniel Bitin (10/09/2019 11:27 PM IDT)
• Pål Hermunn Johansen (11/09/2019 02:17 AM IDT)
• Joseph Berman (11/09/2019 03:59 AM IDT)
• Tom Chen (11/09/2019 05:37 AM IDT)
• David Friedman (11/09/2019 06:06 AM IDT)
• Victor Chang (11/09/2019 09:35 AM IDT)
• John Tromp (11/09/2019 02:46 PM IDT)
• Graham Hemsley (11/09/2019 06:25 PM IDT)
• Ilya Tarygin (11/09/2019 07:36 PM IDT)
• Jingran Lin (12/09/2019 12:47 AM IDT)
• Siegmar Szlavik (12/09/2019 02:32 AM IDT)
• Joaquim Neves Carrapa (12/09/2019 03:48 AM IDT)
• Ralf Jonas (12/09/2019 08:39 AM IDT)
• Michael Liepelt (12/09/2019 09:28 AM IDT)
• Stanislav Grudnitskiy (12/09/2019 11:51 AM IDT)
• Vladimir Volevich (12/09/2019 05:31 PM IDT)
• Benjamin Lui (12/09/2019 07:02 PM IDT)
• James Dow Allen (13/09/2019 12:29 AM IDT)
• Kang Jin Cho (13/09/2019 02:30 PM IDT)
• David Greer (13/09/2019 03:46 PM IDT)
• Florian Fischer (14/09/2019 01:17 AM IDT)
• Xiuhan Wang (16/09/2019 06:48 AM IDT)
• Serge Thill (17/09/2019 01:00 PM IDT)
• Harald Bögeholz (17/09/2019 06:02 AM IDT)
• Omer Shechter (16/09/2019 06:40 PM IDT)
• Victorien Cornet (17/09/2019 03:49 PM IDT)
• Nico Elayda (17/09/2019 07:50 PM IDT)
• Muhammed Halbutogullari (17/09/2019 10:30 PM IDT)
• Allen Kim (17/09/2019 11:23 PM IDT)
• Hyung Sik Hwang (18/09/2019 01:20 PM IDT)
• Alexey Zyl (18/09/2019 08:25 PM IDT)
• Móra Péter (18/09/2019 10:44 PM IDT)
• Reda Kebbaj (19/09/2019 12:22 AM IDT)
• Sanandan Swaminathan (19/09/2019 03:47 AM IDT)
• Greg Janée (19/09/2019 06:23 AM IDT)
• Calvin Pozderac (19/09/2019 07:02 AM IDT)
• Andy Greig (19/09/2019 10:29 AM IDT)
• Andreas Stiller (19/09/2019 01:35 PM IDT)
• John Reid (19/09/2019 03:16 PM IDT)
• Rustam Salikhov (19/09/2019 05:23 PM IDT)
• Dan Salajan (19/09/2019 06:49 PM IDT)
• Zhongxing Xue (19/09/2019 09:32 PM IDT)
• Yasodhar Patnaik (20/09/2019 01:55 AM IDT)
• Ayush Jain (20/09/2019 09:27 AM IDT)
• Marco Bellocchi (21/09/2019 12:43 AM IDT)
• Daniel Blazewicz (21/09/2019 01:05 AM IDT)
• Ken Dsouza (21/09/2019 08:39 AM IDT)
• Mathias Schenker (21/09/2019 12:09 PM IDT)
• Mark Rickert (21/09/2019 12:53 PM IDT)
• Andrew Mullins (22/09/2019 09:53 AM IDT)
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• Rudy Cortembert (26/09/2019 02:54 PM IDT)
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• Peter Gerritson (28/09/2019 11:57 PM IDT)
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• Clive Tong (28/09/2019 04:30 PM IDT)
• Hrushikesh Tilak (29/09/2019 09:07 AM IDT)
• Fabio Negroni (29/09/2019 01:48 PM IDT)
• Shouky Dan & Tamir Ganor (29/09/2019 06:14 PM IDT)
• Motty Porat (30/09/2019 12:09 AM IDT)
• Piyush Agrawal (30/09/2019 03:36 PM IDT)
• Colas Kerkhove (30/09/2019 07:04 PM IDT)
• Michael Chirozzi (01/10/2019 12:21 AM IDT)
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• Radu-Alexandru Todor (01/10/2019 12:38 PM IDT)
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• Albert Stadler (02/10/2019 01:12 PM IDT)
• Wilder Boyden & Andrew Melendez (03/10/2019 01:56 AM IDT)
• Collin Pearce (03/10/2019 08:23 AM IDT)
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• David F.H. Dunkley (06/10/2019 10:20 AM IDT)
• Li Li (06/10/2019 11:00 AM IDT)